9725:(Now Mr. Pfaundler has joined these two phenomena in a single concept by considering the observed limit as the result of two opposing reactions, driving the one in the example cited to the formation of sea salt and nitric acid, the other to hydrochloric acid and sodium nitrate. This consideration, which experiment validates, justifies the expression "chemical equilibrium", which is used to characterize the final state of limited reactions. I would propose to translate this expression by the following symbol:
2335:
7741:
10249:
4156:
3163:
2063:
9417:
2531:
296:
6324:
5649:
3909:
2330:{\displaystyle \Delta _{\mathrm {r} }G_{T,p}=(\sigma \mu _{\mathrm {S} }^{\ominus }+\tau \mu _{\mathrm {T} }^{\ominus })-(\alpha \mu _{\mathrm {A} }^{\ominus }+\beta \mu _{\mathrm {B} }^{\ominus })+(\sigma RT\ln\{\mathrm {S} \}+\tau RT\ln\{\mathrm {T} \})-(\alpha RT\ln\{\mathrm {A} \}+\beta RT\ln\{\mathrm {B} \})}
4358:
444:
6921:
In these applications, terms such as stability constant, formation constant, binding constant, affinity constant, association constant and dissociation constant are used. In biochemistry, it is common to give units for binding constants, which serve to define the concentration units used when the
9124:
4498:
types of charged species in solution. When the concentration of dissolved salt is much higher than the analytical concentrations of the reagents, the ions originating from the dissolved salt determine the ionic strength, and the ionic strength is effectively constant. Since activity coefficients
2051:
8759:
atomic element conservation equations for the mass constraint is straightforward, and replaces the use of the stoichiometric coefficient equations. The results are consistent with those specified by chemical equations. For example, if equilibrium is specified by a single chemical equation:,
2747:
591:
736:. For example, adding more S (to the chemical reaction above) from the outside will cause an excess of products, and the system will try to counteract this by increasing the reverse reaction and pushing the equilibrium point backward (though the equilibrium constant will stay the same).
2894:
743:
is added to the acetic acid mixture, increasing the concentration of hydronium ion, the amount of dissociation must decrease as the reaction is driven to the left in accordance with this principle. This can also be deduced from the equilibrium constant expression for the reaction:
9113:
2347:
1285:) to states containing equal mixture of products and reactants and gives rise to a distinctive minimum in the Gibbs energy as a function of the extent of reaction. The standard Gibbs energy change, together with the Gibbs energy of mixing, determine the equilibrium state.
180:
6764:
Equilibrium can be broadly classified as heterogeneous and homogeneous equilibrium. Homogeneous equilibrium consists of reactants and products belonging in the same phase whereas heterogeneous equilibrium comes into play for reactants and products in different phases.
5951:
159:
The equilibrium concentration position of a reaction is said to lie "far to the right" if, at equilibrium, nearly all the reactants are consumed. Conversely the equilibrium position is said to be "far to the left" if hardly any product is formed from the reactants.
1510:
3515:
4560:
will vary with ionic strength. If it is measured at a series of different ionic strengths, the value can be extrapolated to zero ionic strength. The concentration quotient obtained in this manner is known, paradoxically, as a thermodynamic equilibrium constant.
9739:
I thus replace, in this case, the = sign in the chemical equation by the sign ⇌, which in reality doesn't express just equality but shows also the direction of the reaction. This clearly expresses that a chemical action occurs simultaneously in two opposing
5298:
1924:
9687:" … la décomposition du muriate de soude continue donc jusqu'à ce qu'il se soit formé assez de muriate de chaux, parce que l'acide muriatique devant se partager entre les deux bases en raison de leur action, il arrive un terme où leurs forces se balancent."
3327:
4151:{\displaystyle K={\frac {^{\sigma }^{\tau }...}{^{\alpha }^{\beta }...}}\times {\frac {{\gamma _{\mathrm {S} }}^{\sigma }{\gamma _{\mathrm {T} }}^{\tau }...}{{\gamma _{\mathrm {A} }}^{\alpha }{\gamma _{\mathrm {B} }}^{\beta }...}}=K_{\mathrm {c} }\Gamma }
8698:
8433:
9668:
On pp. 404–407, Berthellot mentions that when he accompanied
Napoleon on his expedition to Egypt, he (Berthellot) visited Lake Natron and found sodium carbonate along its shores. He realized that this was a product of the reverse of the usual reaction
8578:
7468:
1421:
times the stoichiometric coefficients of the products is equal to the sum of those corresponding to the reactants. Therefore, the sum of the Gibbs energies of the reactants must be the equal to the sum of the Gibbs energies of the products.
660:
will affect both the forward reaction and the reverse reaction in the same way and will not have an effect on the equilibrium constant. The catalyst will speed up both reactions thereby increasing the speed at which equilibrium is reached.
8141:
For a closed system, no particles may enter or leave, although they may combine in various ways. The total number of atoms of each element will remain constant. This means that the minimization above must be subjected to the constraints:
3633:
7313:
2620:
6666:
7845:
in action: Increasing the concentration of the hydroxide ion causes more aluminium hydroxide to precipitate, which removes hydroxide from the solution. When the hydroxide concentration becomes sufficiently high the soluble aluminate,
6546:
4217:
2995:
1281:(completely pure), then there would be no reversibility and no equilibrium. Indeed, they would necessarily occupy disjoint volumes of space. The mixing of the products and reactants contributes a large entropy increase (known as
329:
9412:{\displaystyle \Delta G=\sum _{j=1}^{m}\nu _{j}\mu _{j}=\sum _{j=1}^{m}\nu _{j}(\mu _{j}^{\ominus }+RT\ln(\{R_{j}\}))=\Delta G^{\ominus }+RT\ln \left(\prod _{j=1}^{m}\{R_{j}\}^{\nu _{j}}\right)=\Delta G^{\ominus }+RT\ln(K_{c})}
880:
651:
Despite the limitations of this derivation, the equilibrium constant for a reaction is indeed a constant, independent of the activities of the various species involved, though it does depend on temperature as observed by the
719:
a proton may hop from one molecule of acetic acid onto a water molecule and then onto an acetate anion to form another molecule of acetic acid and leaving the number of acetic acid molecules unchanged. This is an example of
6941:
The most basic approach is to manipulate the various equilibrium constants until the desired concentrations are expressed in terms of measured equilibrium constants (equivalent to measuring chemical potentials) and initial
9693:
of the sodium chloride thus continues until enough calcium chloride is formed, because the hydrochloric acid must be shared between the two bases in the ratio of their action ; it reaches an end at which their forces are
1938:
1604:
1195:
5936:
3076:
3154:
7727:
7600:
2640:
459:
5274:
5047:
2758:
4889:
8932:
3400:
2526:{\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}+RT\ln {\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}
1037:
3405:
4471:
291:{\displaystyle {\begin{aligned}{\text{forward reaction rate}}&=k_{+}{\ce {A}}^{\alpha }{\ce {B}}^{\beta }\\{\text{backward reaction rate}}&=k_{-}{\ce {S}}^{\sigma }{\ce {T}}^{\tau }\end{aligned}}}
6319:{\displaystyle {\begin{array}{ll}{\ce {A^2- + H+ <=> HA-}}:&\beta _{1}={\frac {{\ce {}}}{{\ce {}}}}\\{\ce {A^2- + 2H+ <=> H2A}}:&\beta _{2}={\frac {{\ce {}}}{{\ce {^2}}}}\end{array}}}
3874:
3750:
8083:
958:
of reactants and products at the composition of the reaction mixture. This criterion is both necessary and sufficient. If a mixture is not at equilibrium, the liberation of the excess Gibbs energy (or
1399:
3219:
1731:
7473:
so the concentrations of the "complexes" are calculated from the free concentrations and the equilibrium constants. General expressions applicable to all systems with two reagents, A and B would be
7175:
When the equilibrium constants are known and the total concentrations are specified there are two equations in two unknown "free concentrations" and . This follows from the fact that =
3807:
3683:
4548:
8222:
7978:
5797:
4894:
For all but very concentrated solutions, the water can be considered a "pure" liquid, and therefore it has an activity of one. The equilibrium constant expression is therefore usually written as
185:
7163:
1428:
938:
of the system is at its minimum value (assuming the reaction is carried out at a constant temperature and pressure). What this means is that the derivative of the Gibbs energy with respect to
7063:
68:
of the forward and backward reactions are generally not zero, but they are equal. Thus, there are no net changes in the concentrations of the reactants and products. Such a state is known as
8917:
6930:
When the only equilibrium is that of the formation of a 1:1 adduct as the composition of a mixture, there are many ways that the composition of a mixture can be calculated. For example, see
5644:{\displaystyle {\begin{array}{rl}{\ce {H2A <=> HA^- + H+}}:&K_{1}={\frac {{\ce {}}}{{\ce {}}}}\\{\ce {HA- <=> A^2- + H+}}:&K_{2}={\frac {{\ce {}}}{{\ce {}}}}\end{array}}}
8825:
5142:
1796:
962:
at constant volume reactions) is the "driving force" for the composition of the mixture to change until equilibrium is reached. The equilibrium constant can be related to the standard
8584:
8296:
3526:
8469:
8118:
4689:
When pure substances (liquids or solids) are involved in equilibria their activities do not appear in the equilibrium constant because their numerical values are considered one.
4564:
Before using a published value of an equilibrium constant in conditions of ionic strength different from the conditions used in its determination, the value should be adjusted.
7319:
1784:
6675:
with temperature. In practice, however, the method is unreliable because error propagation almost always gives very large errors on the values calculated in this way.
7861:
Another common instance where precipitation occurs is when a metal cation interacts with an anionic ligand to form an electrically neutral complex. If the complex is
6913:
When molecules on each side of the equilibrium are able to further react irreversibly in secondary reactions, the final product ratio is determined according to the
5945:
because the products on the right hand side of the equilibrium expression are dissociation products. In many systems, it is preferable to use association constants.
7201:
2537:
6577:
5179:
Solids also do not appear in the equilibrium constant expression, if they are considered to be pure and thus their activities taken to be one. An example is the
4353:{\displaystyle \mu =\mu ^{\ominus }+RT\ln \left({\frac {f}{\mathrm {bar} }}\right)=\mu ^{\ominus }+RT\ln \left({\frac {p}{\mathrm {bar} }}\right)+RT\ln \gamma }
439:{\displaystyle k_{+}\left\{{\ce {A}}\right\}^{\alpha }\left\{{\ce {B}}\right\}^{\beta }=k_{-}\left\{{\ce {S}}\right\}^{\sigma }\left\{{\ce {T}}\right\}^{\tau }}
7790:
that is not one of the main species in the solution equilibrium may be formed. At pH just below 5.5 the main species present in a 5 μM solution of Al are
6464:
2905:
4161:
is the concentration of reagent A, etc. It is possible in principle to obtain values of the activity coefficients, γ. For solutions, equations such as the
750:
2046:{\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }-\alpha \mu _{\mathrm {A} }-\beta \mu _{\mathrm {B} }\,}
3332:
9626:
4180:
is a constant, and to use the concentration quotient in place of the thermodynamic equilibrium constant. It is also general practice to use the term
1535:
6952:. The equations of mass balance are simply statements that demonstrate that the total concentration of each reactant must be constant by the law of
7775:
3812:
3688:
3006:
2742:{\displaystyle Q_{\mathrm {r} }={\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}
1090:
586:{\displaystyle K_{c}={\frac {k_{+}}{k_{-}}}={\frac {\{{\ce {S}}\}^{\sigma }\{{\ce {T}}\}^{\tau }}{\{{\ce {A}}\}^{\alpha }\{{\ce {B}}\}^{\beta }}}}
5805:
3087:
7606:
7479:
3203:
If the activities of constituents are modified, the value of the reaction quotient changes and becomes different from the equilibrium constant:
2889:{\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln Q_{\mathrm {r} }}
10281:
5201:
8755:
This method of calculating equilibrium chemical concentrations is useful for systems with a large number of different molecules. The use of
3762:
3638:
8744:
as long as the chemical activities are known as functions of the concentrations at the given temperature and pressure. (In the ideal case,
4900:
4499:
depend on ionic strength, the activity coefficients of the species are effectively independent of concentration. Thus, the assumption that
9108:{\displaystyle 0=\sum _{j=1}^{m}\nu _{j}\mu _{j}+\sum _{j=1}^{m}\sum _{i=1}^{k}\nu _{j}\lambda _{i}a_{ij}=\sum _{j=1}^{m}\nu _{j}\mu _{j}}
10023:
9529:
8749:
4727:
4692:
Applying the general formula for an equilibrium constant to the specific case of a dilute solution of acetic acid in water one obtains
972:
6671:
At first sight this appears to offer a means of obtaining the standard molar enthalpy of the reaction by studying the variation of
4397:
734:
If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to partially reverse the change
7172:
the total concentration of species A. Note that it is customary to omit the ionic charges when writing and using these equations.
1409:
In order to meet the thermodynamic condition for equilibrium, the Gibbs energy must be stationary, meaning that the derivative of
8016:
10384:
9470:
1337:
1213:
9890:
1642:
9611:
10070:
9685:↓ and therefore that the final state of a reaction was a state of equilibrium between two opposing processes. From p. 405:
10253:
9823:
Clugston, Michael J. (1990). "A mathematical verification of the second law of thermodynamics from the entropy of mixing".
4511:
17:
8148:
7906:
1505:{\displaystyle \alpha \mu _{\mathrm {A} }+\beta \mu _{\mathrm {B} }=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }\,}
5688:
645:
641:
621:
7069:
3510:{\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=RT\ln \left({\frac {Q_{\mathrm {r} }}{K_{\mathrm {eq} }}}\right)~}
1292:
case is considered. The relation between the Gibbs free energy and the equilibrium constant can be found by considering
668:
equilibrium concentrations are constant in time, reactions do occur at the molecular level. For example, in the case of
9480:
1633:
954:. This derivative is called the reaction Gibbs energy (or energy change) and corresponds to the difference between the
6987:
10274:
10170:
9956:
9759:
9583:
8855:
8766:
4371:
In aqueous solution, equilibrium constants are usually determined in the presence of an "inert" electrolyte such as
1919:{\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\sum _{i=1}^{k}\mu _{i}\nu _{i}=\Delta _{\mathrm {r} }G_{T,p}}
10475:
56:
which have no further tendency to change with time, so that there is no observable change in the properties of the
5078:
10188:
10135:
9704:
4169:
3322:{\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln Q_{\mathrm {r} }~}
7877:): in this case the lattice energy of the solid is not particularly large, but it greatly exceeds the energy of
10561:
8693:{\displaystyle 0={\frac {\partial {\mathcal {G}}}{\partial \lambda _{i}}}=\sum _{j=1}^{m}a_{ij}N_{j}-b_{i}^{0}}
8428:{\displaystyle {\mathcal {G}}=G+\sum _{i=1}^{k}\lambda _{i}\left(\sum _{j=1}^{m}a_{ij}N_{j}-b_{i}^{0}\right)=0}
4572:
A mixture may appear to have no tendency to change, though it is not at equilibrium. For example, a mixture of
8573:{\displaystyle 0={\frac {\partial {\mathcal {G}}}{\partial N_{j}}}=\mu _{j}+\sum _{i=1}^{k}\lambda _{i}a_{ij}}
7842:
6965:
In general, the calculations are rather complicated or complex. For instance, in the case of a dibasic acid, H
5072:
Because water is the solvent, and has an activity of one, the self-ionization constant of water is defined as
728:
10566:
9490:
3159:
Obtaining the value of the standard Gibbs energy change, allows the calculation of the equilibrium constant.
724:. Equilibria, like the rest of thermodynamics, are statistical phenomena, averages of microscopic behavior.
10533:
10437:
10267:
9519:
9465:
6914:
6814:
1320:
7463:{\displaystyle T_{\mathrm {H} }=\mathrm {} +\beta _{1}\mathrm {} +2\beta _{2}\mathrm {} ^{2}-K_{w}^{-1}\,}
4207:, is the product of partial pressure and fugacity coefficient. The chemical potential of a species in the
4162:
10571:
10346:
9534:
8091:
3888:
The expression for the equilibrium constant can be rewritten as the product of a concentration quotient,
10453:
8276:
6872:
6842:
5942:
5155:
of the proton is constant (in dilute solutions) and so does not affect the equilibrium concentrations.
4505:
is constant is justified. The concentration quotient is a simple multiple of the equilibrium constant.
3752:
The reaction will shift to the right (i.e. in the forward direction, and thus more products will form).
1753:
133:
6937:
There are three approaches to the general calculation of the composition of a mixture at equilibrium.
6910:
in electrochemistry gives the difference in electrode potential as a function of redox concentrations.
4363:
so the general expression defining an equilibrium constant is valid for both solution and gas phases.
3876:
The reaction will shift to the left (i.e. in the reverse direction, and thus less products will form).
10361:
10329:
7787:
6858:
732:(1884) predicts the behavior of an equilibrium system when changes to its reaction conditions occur.
9721:
Van 't Hoff called reactions that didn't proceed to completion "limited reactions". From pp. 4–5:
9710:
5292:
A, HA and A. This equilibrium can be split into two steps in each of which one proton is liberated.
10502:
10497:
10458:
9524:
9437:
8280:
6886:
6882:
5054:
1205:
163:
9723:"Or M. Pfaundler a relié ces deux phénomênes … s'accomplit en même temps dans deux sens opposés."
6780:
6696:
6456:
653:
85:
10071:"Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications"
9987:
7756:
The composition of solutions containing reactants A and H is easy to calculate as a function of
10521:
10411:
10012:
9690:
8745:
8007:
6827:
3628:{\displaystyle Q_{\mathrm {r} }={\frac {\prod (a_{j})^{\nu _{j}}}{\prod (a_{i})^{\nu _{i}}}}~,}
1759:
1331:
must be negative if the reaction happens; at the equilibrium this derivative is equal to zero.
1262:, for the reaction; and at constant internal energy and volume, one must consider the entropy,
1047:
9575:
7308:{\displaystyle T_{\mathrm {A} }=\mathrm {} +\beta _{1}\mathrm {} +\beta _{2}\mathrm {} ^{2}\,}
10514:
10509:
10487:
10432:
10339:
10319:
8460:
7760:. When is known, the free concentration is calculated from the mass-balance equation in A.
6903:, the approach to equilibrium is not asymptotically but in the form of a damped oscillation .
6890:
6804:
6796:
6790:
5165:
The concentrations of H and OH are not independent quantities. Most commonly is replaced by
4380:
2615:{\displaystyle \sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}=\Delta _{\mathrm {r} }G^{\ominus }}
1274:
1255:
31:
6661:{\displaystyle {\frac {d\ln K}{d(T^{-1})}}=-{\frac {\Delta H_{\mathrm {m} }^{\ominus }}{R}}}
917:
O is left out, as it is the solvent and its concentration remains high and nearly constant.
10396:
10379:
10202:
9832:
9797:
9475:
9430:
8704:
8284:
6953:
6900:
6894:
4196:
3896:
1526:
1209:
1070:
1062:
927:
613:
450:
302:
57:
10048:
7893:
At equilibrium, at a specified temperature and pressure, and with no external forces, the
1238:. These constants are easier to measure and encountered in high-school chemistry courses.
8:
10492:
10470:
10356:
10314:
7823:
7791:
7778:
as a function of pH. Each concentration is shown as a percentage of the total aluminium.
6876:
6541:{\displaystyle {\frac {d\ln K}{dT}}={\frac {\Delta H_{\mathrm {m} }^{\ominus }}{RT^{2}}}}
939:
721:
93:
69:
61:
49:
9836:
9801:
6977:, H. The following equations of mass-balance could apply equally well to a base such as
1277:
where pressure variations are significant. Note that, if reactants and products were in
950:
for all reactants to a maximum for all products) vanishes (because dG = 0), signaling a
10480:
10371:
10304:
9460:
7988:
6811:: important for pharmaceuticals where lipophilicity is a significant property of a drug
6444:
5180:
4678:
4176:
may be used. However this is not always possible. It is common practice to assume that
1522:
1418:
1308:
1293:
955:
943:
935:
601:
171:
2990:{\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=0}
10526:
10406:
10334:
10324:
10166:
9952:
9943:
9755:
9657:
9607:
9579:
9568:
9485:
7894:
6868:
4591:
2631:
1786:) and a differential that denotes the reaction occurring to an infinitesimal extent (
1300:
1282:
1247:
931:
921:
101:
89:
37:
9636:
875:{\displaystyle K={\frac {\{{\ce {CH3CO2-}}\}\{{\ce {H3O+}}\}}{{\ce {\{CH3CO2H\}}}}}}
27:
When the ratio of reactants to products of a chemical reaction is constant with time
10465:
10351:
9897:
9840:
9805:
9640:
9631:
8752:.) Note that the second equation is just the initial constraints for minimization.
7870:
4192:
4173:
1235:
959:
951:
637:
605:
81:
10077:
9719:] (in French). Amsterdam, Netherlands: Frederik Muller & Co. pp. 4–5.
10427:
8272:
matrix specifying the respective charge on each molecule which will sum to zero.
6978:
6907:
6850:
6783:(depicted right) takes place through a succession of equilibrium steps including
4625:
4595:
4166:
100:
of the forward and backward (reverse) reactions must be equal. In the following
60:. This state results when the forward reaction proceeds at the same rate as the
10538:
9788:
Schultz, Mary Jane (1999). "Why
Equilibrium? Understanding Entropy of Mixing".
7834:
6970:
6822:
5303:
4636:
4573:
4388:
4372:
1599:{\displaystyle \mu _{\mathrm {A} }=\mu _{A}^{\ominus }+RT\ln\{\mathrm {A} \}\,}
1299:
At constant temperature and pressure in the absence of an applied voltage, the
1278:
1224:
1066:
109:
7774:
shows the species concentrations for a 5 × 10 M solution of an
6455:
The effect of changing temperature on an equilibrium constant is given by the
5956:
4199:
in place of activity coefficient. In the real world, for example, when making
1790:). At constant pressure and temperature the above equations can be written as
10555:
10391:
9635:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
6934:
for a traditional method of calculating the pH of a solution of a weak acid.
6770:
6684:
5173:
5148:
4587:
4200:
1201:
1190:{\displaystyle K_{\ce {c}}={\frac {^{\sigma }^{\tau }}{^{\alpha }^{\beta }}}}
617:
604:
is valid only for concerted one-step reactions that proceed through a single
320:
115:
97:
65:
53:
9644:
8445:
are the
Lagrange multipliers, one for each element. This allows each of the
5931:{\displaystyle \beta _{{\ce {D}}}={\frac {{\ce {^2}}}{{\ce {}}}}=K_{1}K_{2}}
3071:{\displaystyle 0=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln K_{\mathrm {eq} }}
8260:, which is a constant, since the system is closed. If there are a total of
8125:
6949:
6854:
6818:
3149:{\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\ln K_{\mathrm {eq} }}
1629:
1270:
963:
740:
7722:{\displaystyle T_{\mathrm {B} }=+\sum _{i}q_{i}\beta _{i}^{p_{i}}^{q_{i}}}
7595:{\displaystyle T_{\mathrm {A} }=+\sum _{i}p_{i}\beta _{i}^{p_{i}}^{q_{i}}}
3880:
Note that activities and equilibrium constants are dimensionless numbers.
8268:
such equations. If ions are involved, an additional row is added to the a
7862:
6564:
4632:
4203:
in industry, fugacity coefficients must be taken into account. Fugacity,
1516:
1316:
1055:
669:
665:
167:
449:
and the ratio of the rate constants is also a constant, now known as an
10401:
10139:
9809:
7767:
7745:
6846:
6833:
6784:
6712:
6552:
5269:{\displaystyle K_{\mathrm {c} }={\frac {\mathrm {} }{\mathrm {^{2}} }}}
10259:
10123:
9844:
7732:
It is easy to see how this can be extended to three or more reagents.
6571:
increases with an increase temperature. An alternative formulation is
620:
of the reaction as
Guldberg and Waage had proposed (see, for example,
10309:
9455:
7878:
7764:
7749:
6974:
6931:
6864:
5152:
5042:{\displaystyle K={\frac {\mathrm {} }{\mathrm {} }}=K_{\mathrm {c} }}
4621:
677:
597:
8459:
to be treated independently, and it can be shown using the tools of
9450:
8737:) and may, therefore, be solved for the equilibrium concentrations
4884:{\displaystyle K_{\mathrm {c} }={\frac {\mathrm {} }{\mathrm {} }}}
4628:, but the catalyst does not affect the equilibrium concentrations.
4208:
657:
629:
105:
10225:
Computational
Methods for the Determination of Formation Constants
5172:
in equilibrium constant expressions which would otherwise include
1254:, while at constant temperature and volume, one must consider the
640:). Equality of forward and backward reaction rates, however, is a
9540:
7763:
The diagram alongside, shows an example of the hydrolysis of the
6981:, in which case the base itself is designated as the reactant A:
6776:
3395:{\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\ln K_{eq}~}
673:
633:
45:
8838:
th molecule (negative for reactants, positive for products) and
7740:
6683:
The effect of electric field on equilibrium has been studied by
1032:{\displaystyle \Delta _{r}G^{\ominus }=-RT\ln K_{\mathrm {eq} }}
10248:
7866:
6969:
A dissolved in water the two reactants can be specified as the
4675:
4580:
8283:. The most common method of solving it is using the method of
1417:, must be zero. It can be shown that in this case, the sum of
104:, arrows point both ways to indicate equilibrium. A and B are
10096:
Chemical
Reaction Equilibrium Analysis: Theory and Algorithms
5195:
for which the equation (without solid carbon) is written as:
4640:
4500:
4466:{\displaystyle I={\frac {1}{2}}\sum _{i=1}^{N}c_{i}z_{i}^{2}}
1525:. The chemical potential of a reagent A is a function of the
1208:
of the reactants. For this reason, equilibrium constants for
323:. Since at equilibrium forward and backward rates are equal:
121:
5162:
varies with variation in ionic strength and/or temperature.
3869:{\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}>0~}
3745:{\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}<0~}
1246:
At constant temperature and pressure, one must consider the
9495:
947:
10109:
8078:{\displaystyle \mu _{j}=\mu _{j}^{\ominus }+RT\ln {A_{j}}}
7829:
precipitates from the solution. This occurs because Al(OH)
4674:
but almost instantaneous in the presence of the catalytic
3162:
9891:"Guidelines for the extrapolation to zero ionic strength"
9703:
The notation ⇌ was proposed in 1884 by the Dutch chemist
9508:
9436:
Analogous procedures exist for the minimization of other
7865:, it will precipitate out of water. This occurs with the
6678:
6248:
6206:
5892:
5704:
5458:
5317:
4490:
stand for the concentration and ionic charge of ion type
2630:
that can be calculated using thermodynamical tables. The
1394:{\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=0~}
859:
846:
813:
777:
127:
1726:{\displaystyle dG=Vdp-SdT+\sum _{i=1}^{k}\mu _{i}dN_{i}}
930:
suggested in 1873 that equilibrium is attained when the
96:. For any reaction mixture to exist at equilibrium, the
10076:. NASA Reference publication 1311. NASA. Archived from
9503:
7757:
1929:
which is the "Gibbs free energy change for the reaction
10098:(Reprinted ed.). Malabar, FL: Krieger Publishing.
6443:
For multiple equilibrium systems, also see: theory of
6177:
6007:
5732:
5507:
5344:
5288:
A. When dissolved in water, the mixture will contain H
3802:{\displaystyle Q_{\mathrm {r} }>K_{\mathrm {eq} }~}
3678:{\displaystyle Q_{\mathrm {r} }<K_{\mathrm {eq} }~}
10160:
9127:
8935:
8922:
Multiplying the first equilibrium condition by ν
8858:
8849:
th molecule, a properly balanced equation will obey:
8769:
8587:
8472:
8299:
8151:
8094:
8019:
7909:
7609:
7482:
7322:
7204:
7072:
6990:
6580:
6467:
5954:
5808:
5691:
5301:
5204:
5081:
4903:
4730:
4543:{\displaystyle K_{\mathrm {c} }={\frac {K}{\Gamma }}}
4514:
4400:
4220:
3912:
3815:
3765:
3691:
3641:
3529:
3408:
3335:
3222:
3090:
3009:
2908:
2761:
2643:
2540:
2350:
2066:
1941:
1799:
1762:
1645:
1538:
1431:
1340:
1093:
975:
753:
462:
332:
183:
170:(1865), building on Berthollet's ideas, proposed the
84:
of chemical equilibrium was developed in 1803, after
8217:{\displaystyle \sum _{j=1}^{m}a_{ij}N_{j}=b_{i}^{0}}
7973:{\displaystyle dG=\sum _{j=1}^{m}\mu _{j}\,dN_{j}=0}
6563:
decreases with an increase in temperature, but, for
5792:{\displaystyle {\ce {{H2A}<=>{A^{2-}}+{2H+}}}}
3169:
108:chemical species, S and T are product species, and
10212:
9942:
9567:
9411:
9107:
8911:
8819:
8692:
8572:
8427:
8216:
8112:
8077:
7972:
7721:
7594:
7462:
7307:
7158:{\displaystyle T_{\mathrm {H} }=\mathrm {++2-} \,}
7157:
7057:
6660:
6540:
6318:
5930:
5791:
5643:
5268:
5136:
5041:
4883:
4542:
4465:
4352:
4150:
3868:
3801:
3744:
3677:
3627:
3509:
3394:
3321:
3148:
3070:
2989:
2888:
2741:
2614:
2525:
2329:
2045:
1918:
1778:
1725:
1598:
1504:
1393:
1189:
1031:
874:
585:
438:
290:
10231:
8264:types of atoms in the system, then there will be
8120:is the chemical potential in the standard state,
6185:
6184:
6167:
6166:
6015:
6014:
5997:
5996:
5740:
5739:
5722:
5721:
5515:
5514:
5497:
5496:
5352:
5351:
5334:
5333:
1227:, temperature and pressure (or volume). Likewise
10553:
10234:The Determination and Use of Stability Constants
9920:
7058:{\displaystyle T_{\mathrm {A} }=\mathrm {++} \,}
1521:is in this case a partial molar Gibbs energy, a
9774:Atkins, P.; de Paula, J.; Friedman, R. (2014).
9708:
9666:] (in French). Paris, France: Firmin Didot.
8912:{\displaystyle \sum _{j=1}^{m}a_{ij}\nu _{j}=0}
7888:
7786:The diagram above illustrates the point that a
6342:are examples of association constants. Clearly
9776:Physical Chemistry – Quanta, Matter and Change
9565:
8820:{\displaystyle \sum _{j=0}^{m}\nu _{j}R_{j}=0}
1073:may be taken to be constant. In that case the
10275:
10068:
9537:(NRTL model) – Phase equilibrium calculations
7841:comes out of solution. This is an example of
7781:
5147:It is perfectly legitimate to write for the
2628:standard Gibbs energy change for the reaction
10069:Gordon, Sanford; McBride, Bonnie J. (1994).
9851:
9341:
9327:
9261:
9248:
5137:{\displaystyle K_{\mathrm {w} }=\mathrm {} }
2727:
2718:
2709:
2700:
2689:
2680:
2671:
2662:
2511:
2502:
2493:
2484:
2473:
2464:
2455:
2446:
2321:
2313:
2292:
2284:
2257:
2249:
2228:
2220:
1592:
1584:
865:
833:
827:
799:
796:
763:
571:
562:
553:
544:
533:
524:
515:
506:
10219:Mainly concerned with gas-phase equilibria.
10093:
9971:
9601:
9530:Thermodynamic databases for pure substances
9433:, and ΔG will be zero at equilibrium.
8750:Thermodynamic databases for pure substances
8463:that the equilibrium condition is given by
6925:
644:for chemical equilibrium, though it is not
10282:
10268:
10232:Martell, A. E.; Motekaitis, R. J. (1992).
9976:(2nd ed.). Budapest: Akadémiai Kaidó.
9768:
9655:
9604:Chemical Principles: The Quest for Insight
8834:is the stoichiometric coefficient for the
8748:are proportional to concentrations.) (See
4366:
1319:), and can only decrease according to the
136:of the respective reactants and products:
75:
10122:The diagram was created with the program
9921:Rossotti, F. J. C.; Rossotti, H. (1961).
9888:
9884:
9882:
9861:, 3rd ed., p. 305, Academic Press, 2008.
9602:Atkins, Peter W.; Jones, Loretta (2008).
7950:
7459:
7304:
7154:
7054:
6960:
6272:
6145:
6088:
5839:
5776:
5760:
5586:
4624:is also present in the mixture as in the
2057:By substituting the chemical potentials:
2042:
1595:
1501:
1269:The constant volume case is important in
10213:Van Zeggeren, F.; Storey, S. H. (1970).
10136:"Chemical Equilibrium with Applications"
10128:
9940:
9923:The Determination of Stability Constants
9822:
9574:(8th ed.). W. H. Freeman. pp.
9561:
9559:
9557:
8256:is the total number of atoms of element
7739:
6945:Minimize the Gibbs energy of the system.
6450:
5682:, is product of the stepwise constants.
3883:
3174:For a reactional system at equilibrium:
3161:
1413:with respect to the extent of reaction,
966:change for the reaction by the equation
10289:
10222:
10154:
10064:
10062:
10060:
10058:
9787:
9566:Atkins, Peter; De Paula, Julio (2006).
6690:
6160:
5990:
5715:
5490:
5327:
4188:. This practice will be followed here.
1307:, for the reaction depends only on the
920:A quantitative version is given by the
14:
10554:
10215:The Computation of Chemical Equilibria
9936:
9934:
9932:
9879:
9870:
9543:model – Phase equilibrium calculations
9471:Determination of equilibrium constants
8287:(although other methods may be used).
7837:. As the pH rises more and more Al(OH)
6742:N (adsorbed) + 3 H(adsorbed) ⇌ NH
6679:Effect of electric and magnetic fields
5279:
4567:
4195:is used in place of concentration and
3635:the reaction quotient decreases. Then
10263:
10165:(2 ed.). W. H. Freeman Company.
10010:
9749:
9554:
8926:and using the above equation yields:
5284:Consider the case of a dibasic acid H
4643:is very slow under normal conditions
596:By convention, the products form the
10094:Smith, W. R.; Missen, R. W. (1991).
10055:
10011:Eigen, Manfred (December 11, 1967).
9597:
9595:
4494:, and the sum is taken over all the
10161:C. Kittel, H. Kroemer (1980). "9".
9988:"The Nobel Prize in Chemistry 1967"
9929:
8113:{\displaystyle \mu _{j}^{\ominus }}
8002:is the amount of molecular species
6795:Seawater and other natural waters:
4620:The barrier can be overcome when a
648:to explain why equilibrium occurs.
622:nucleophilic aliphatic substitution
24:
10182:
9632:Compendium of Chemical Terminology
9365:
9273:
9128:
8609:
8602:
8597:
8494:
8487:
8482:
8302:
8234:is the number of atoms of element
8006:. It may be expressed in terms of
7735:
7698:
7673:
7629:
7616:
7571:
7546:
7502:
7489:
7442:
7412:
7403:
7375:
7366:
7342:
7329:
7291:
7282:
7257:
7248:
7224:
7211:
7147:
7144:
7132:
7123:
7107:
7104:
7092:
7079:
7047:
7038:
7025:
7022:
7010:
6997:
6641:
6632:
6509:
6500:
5250:
5247:
5230:
5226:
5211:
5151:concentration, since the state of
5121:
5117:
5102:
5088:
5033:
5014:
5005:
5001:
4992:
4988:
4969:
4960:
4935:
4931:
4922:
4918:
4871:
4862:
4850:
4841:
4837:
4828:
4824:
4805:
4796:
4771:
4767:
4758:
4754:
4737:
4684:
4535:
4521:
4322:
4319:
4316:
4268:
4265:
4262:
4145:
4139:
4105:
4084:
4052:
4031:
3991:
3973:
3944:
3926:
3790:
3787:
3772:
3666:
3663:
3648:
3536:
3492:
3489:
3477:
3342:
3337:
3310:
3273:
3268:
3140:
3137:
3097:
3092:
3062:
3059:
3022:
3017:
2959:
2954:
2880:
2843:
2838:
2812:
2807:
2722:
2704:
2684:
2666:
2650:
2596:
2591:
2506:
2488:
2468:
2450:
2357:
2352:
2317:
2288:
2253:
2224:
2185:
2162:
2133:
2110:
2073:
2068:
2036:
2018:
2000:
1982:
1948:
1943:
1894:
1889:
1634:fundamental thermodynamic relation
1588:
1545:
1495:
1477:
1459:
1441:
1323:. It means that the derivative of
1204:of A, etc., is independent of the
1023:
1020:
977:
25:
10583:
10241:
9972:Beck, M. T.; Nagypál, I. (1990).
9752:Chemistry: Matter and Its Changes
9592:
8131:is the absolute temperature, and
6922:constant's value was determined.
6775:The industrial synthesis such as
3170:Addition of reactants or products
1241:
1216:in media of high ionic strength.
10247:
6832:Uptake and release of oxygen by
6801:Distribution between two phases
6739:(adsorbed) ⇌ 2 H (adsorbed)
6721:(adsorbed) ⇌ 2 N (adsorbed)
1752:into the above equation gives a
946:that has occurred, ranging from
10116:
10102:
10087:
10041:
10029:from the original on 2022-10-09
10004:
9980:
9974:Chemistry of Complex Equilibria
9965:
9914:
9864:
4191:For reactions in the gas phase
4170:Specific ion interaction theory
672:dissolved in water and forming
616:do not, in general, follow the
44:is the state in which both the
9949:Concise Encyclopedia Chemistry
9816:
9781:
9778:, 2nd ed., Fig. 73.2. Freeman.
9750:Brady, James E. (2004-02-04).
9743:
9697:
9649:
9620:
9481:Henderson–Hasselbalch equation
9406:
9393:
9267:
9264:
9245:
9212:
8275:This is a standard problem in
7744:Species concentrations during
7703:
7694:
7678:
7669:
7633:
7625:
7576:
7567:
7551:
7542:
7506:
7498:
7447:
7438:
7415:
7409:
7406:
7400:
7378:
7372:
7369:
7363:
7345:
7339:
7294:
7288:
7285:
7279:
7260:
7254:
7251:
7245:
7227:
7221:
7150:
7141:
7135:
7119:
7110:
7101:
7095:
7089:
7050:
7034:
7028:
7019:
7013:
7007:
6617:
6601:
6299:
6286:
6280:
6261:
6254:
6235:
6187:
6162:
6114:
6101:
6096:
6077:
6070:
6059:
6017:
5992:
5941:Note that these constants are
5898:
5879:
5866:
5853:
5847:
5828:
5801:
5742:
5717:
5630:
5619:
5612:
5599:
5594:
5575:
5517:
5492:
5464:
5445:
5438:
5425:
5420:
5409:
5354:
5329:
5254:
5244:
5239:
5223:
5130:
5114:
5111:
5098:
5018:
4984:
4979:
4954:
4951:
4913:
4875:
4857:
4854:
4820:
4815:
4790:
4787:
4749:
3996:
3987:
3978:
3969:
3949:
3940:
3931:
3922:
3600:
3586:
3565:
3551:
2324:
2266:
2260:
2202:
2196:
2150:
2144:
2098:
1403:
1175:
1166:
1157:
1148:
1137:
1128:
1119:
1110:
13:
1:
10217:. Cambridge University Press.
10013:"Immeasurably fast reactions"
9825:Journal of Chemical Education
9790:Journal of Chemical Education
9754:(4th ed.). Fred Senese.
9548:
4594:to formation of the product,
4184:instead of the more accurate
10223:Leggett, D. J., ed. (1985).
10049:"Equilibrium constants – Kc"
9717:Studies of chemical dynamics
9712:Études de Dynamique Chemique
9705:Jacobus Henricus van 't Hoff
7889:Minimization of Gibbs energy
6567:reactions, (ΔH is positive)
1632:equation interacts with the
1321:second law of thermodynamics
7:
9535:Non-random two-liquid model
9443:
9118:As above, defining ΔG
6863:Metal–ligand complexation:
5671:equilibrium constants. The
4631:Likewise, the formation of
1623:standard chemical potential
134:stoichiometric coefficients
10:
10588:
9709:van 't Hoff, J.H. (1884).
9659:Essai de statique chimique
9570:Atkins' Physical Chemistry
7782:Solution and precipitation
6843:acid dissociation constant
4391:of a solution is given by
2341:the relationship becomes:
1754:stoichiometric coefficient
29:
10446:
10420:
10370:
10362:Thermodynamic equilibrium
10297:
10203:Resources in your library
9664:Essay on chemical statics
9656:Berthollet, C.L. (1803).
9491:Michaelis–Menten kinetics
5053:A particular case is the
3755:If activity of a product
3519:If activity of a reagent
1779:{\displaystyle \nu _{i}~}
1288:In this article only the
10515:Distribution coefficient
10459:Hammett acidity function
10438:Liquid–liquid extraction
10347:Le Chatelier's principle
9944:"Biochemistry (2nd Ed.)"
9889:Grenthe, I.; Wanner, H.
9525:Steady state (chemistry)
9466:Benesi–Hildebrand method
9438:thermodynamic potentials
8281:constrained minimisation
7881:of the molecule Ni(dmgH)
7843:Le Châtelier's principle
7822:, but on raising the pH
6948:Satisfy the equation of
6926:Composition of a mixture
6915:Curtin–Hammett principle
6887:supramolecular chemistry
6815:Liquid–liquid extraction
6809:distribution coefficient
5055:self-ionization of water
1206:analytical concentration
729:Le Châtelier's principle
301:where A, B, S and T are
9941:Eagleson, Mary (1994).
9645:10.1351/goldbook.C01023
4367:Concentration quotients
1529:, {A} of that reagent.
1061:When the reactants are
76:Historical introduction
10476:Coordination complexes
10412:Thermodynamic activity
10138:. NASA. Archived from
9871:Davies, C. W. (1962).
9413:
9326:
9201:
9157:
9109:
9084:
9027:
9006:
8962:
8913:
8879:
8845:is the symbol for the
8821:
8790:
8694:
8648:
8574:
8546:
8429:
8372:
8336:
8218:
8172:
8114:
8079:
8008:thermodynamic activity
7974:
7939:
7753:
7723:
7596:
7464:
7309:
7159:
7059:
6961:Mass-balance equations
6841:Acid–base equilibria:
6761:
6662:
6542:
6320:
5943:dissociation constants
5932:
5793:
5675:equilibrium constant,
5645:
5270:
5138:
5043:
4885:
4544:
4467:
4437:
4354:
4186:concentration quotient
4165:or extensions such as
4152:
3870:
3803:
3746:
3679:
3629:
3511:
3396:
3323:
3166:
3150:
3072:
2991:
2890:
2743:
2616:
2561:
2527:
2402:
2331:
2047:
1920:
1864:
1780:
1727:
1699:
1628:The definition of the
1600:
1506:
1395:
1191:
1075:concentration quotient
1048:universal gas constant
1033:
876:
587:
440:
292:
240:backward reaction rate
10562:Equilibrium chemistry
10488:Dissociation constant
10433:Equilibrium unfolding
10320:Equilibrium chemistry
9414:
9306:
9181:
9137:
9110:
9064:
9007:
8986:
8942:
8914:
8859:
8822:
8770:
8707:.) This is a set of (
8695:
8628:
8575:
8526:
8461:multivariate calculus
8430:
8352:
8316:
8219:
8152:
8115:
8080:
7991:of molecular species
7975:
7919:
7743:
7724:
7597:
7465:
7310:
7160:
7060:
6901:oscillating reactions
6891:molecular recognition
6873:MRI contrast reagents
6859:acid–base homeostasis
6797:chemical oceanography
6791:Atmospheric chemistry
6700:
6663:
6543:
6451:Effect of temperature
6321:
5933:
5794:
5646:
5271:
5139:
5044:
4886:
4545:
4468:
4417:
4381:potassium perchlorate
4355:
4163:Debye–Hückel equation
4153:
3884:Treatment of activity
3871:
3804:
3747:
3680:
3630:
3512:
3397:
3324:
3165:
3151:
3073:
2992:
2891:
2744:
2617:
2541:
2528:
2382:
2332:
2048:
1921:
1844:
1781:
1728:
1679:
1601:
1507:
1396:
1275:atmospheric chemistry
1256:Helmholtz free energy
1234:for gases depends on
1192:
1071:activity coefficients
1034:
897:H} must increase and
877:
588:
441:
293:
190:forward reaction rate
32:Equilibrium chemistry
10567:Analytical chemistry
10397:Predominance diagram
10380:Equilibrium constant
10256:at Wikimedia Commons
10194:Chemical equilibrium
10142:on September 1, 2000
9637:chemical equilibrium
9476:Equilibrium constant
9431:equilibrium constant
9125:
8933:
8856:
8767:
8705:Lagrange multipliers
8585:
8470:
8297:
8285:Lagrange multipliers
8149:
8092:
8017:
7907:
7792:aluminium hydroxides
7607:
7480:
7320:
7202:
7070:
6988:
6954:conservation of mass
6895:dinitrogen tetroxide
6883:host–guest chemistry
6691:Types of equilibrium
6578:
6465:
6457:van 't Hoff equation
5952:
5806:
5689:
5299:
5202:
5079:
4901:
4728:
4512:
4398:
4218:
4197:fugacity coefficient
4182:equilibrium constant
3910:
3897:activity coefficient
3813:
3763:
3689:
3639:
3527:
3406:
3333:
3220:
3088:
3007:
2906:
2759:
2641:
2538:
2348:
2064:
1939:
1797:
1760:
1643:
1536:
1429:
1338:
1266:, for the reaction.
1091:
1065:in a medium of high
973:
913:must decrease. The H
751:
654:van 't Hoff equation
610:not valid in general
460:
451:equilibrium constant
330:
181:
42:chemical equilibrium
18:Equilibrium reaction
10471:Binding selectivity
10447:Specific equilibria
10357:Reversible reaction
10315:Dynamic equilibrium
10291:Chemical equilibria
10254:Chemical equilibria
9837:1990JChEd..67Q.203C
9802:1999JChEd..76.1391S
9229:
8689:
8413:
8213:
8109:
8047:
6877:Schlenk equilibrium
6865:sequestering agents
6781:Haber–Bosch process
6697:Haber–Bosch process
6651:
6519:
6250:
6208:
6173:
6003:
5894:
5728:
5706:
5503:
5460:
5340:
5319:
5280:Multiple equilibria
4568:Metastable mixtures
4462:
2576:
2417:
2195:
2172:
2143:
2120:
1568:
1419:chemical potentials
1294:chemical potentials
956:chemical potentials
940:reaction coordinate
861:
848:
815:
794:
779:
722:dynamic equilibrium
642:necessary condition
70:dynamic equilibrium
10572:Physical chemistry
10481:Macrocyclic effect
10305:Chemical stability
10110:"Mathtrek Systems"
9859:Physical Chemistry
9810:10.1021/ed076p1391
9461:Arterial blood gas
9409:
9215:
9105:
8909:
8817:
8690:
8675:
8570:
8425:
8399:
8214:
8199:
8110:
8095:
8075:
8033:
7989:chemical potential
7970:
7754:
7719:
7648:
7592:
7521:
7460:
7305:
7155:
7055:
6881:Adduct formation:
6828:Solubility product
6769:In the gas phase:
6658:
6635:
6538:
6503:
6445:Response reactions
6316:
6314:
6238:
6196:
6192:
6022:
5928:
5882:
5789:
5747:
5694:
5641:
5639:
5522:
5448:
5359:
5307:
5266:
5181:Boudouard reaction
5134:
5039:
4881:
4679:carbonic anhydrase
4540:
4463:
4448:
4350:
4211:phase is given by
4148:
3866:
3799:
3742:
3675:
3625:
3507:
3392:
3319:
3167:
3146:
3068:
2987:
2886:
2739:
2612:
2562:
2523:
2403:
2327:
2179:
2156:
2127:
2104:
2043:
1931:. This results in:
1916:
1776:
1723:
1596:
1554:
1523:chemical potential
1502:
1391:
1309:extent of reaction
1187:
1029:
944:extent of reaction
942:(a measure of the
936:chemical potential
872:
849:
836:
803:
780:
767:
602:law of mass action
583:
436:
288:
286:
172:law of mass action
90:chemical reactions
10549:
10548:
10527:Common-ion effect
10454:Acid dissociation
10407:Reaction quotient
10325:Equilibrium stage
10252:Media related to
10189:Library resources
9845:10.1021/ed067p203
9613:978-0-7167-9903-0
9486:Mass-action ratio
8623:
8508:
8138:is the activity.
7900:is at a minimum:
7895:Gibbs free energy
7833:has a very large
7639:
7512:
7189:and =
6979:1,2-diaminoethane
6869:chelation therapy
6656:
6621:
6536:
6492:
6310:
6292:
6267:
6253:
6241:
6211:
6199:
6194:
6149:
6129:
6119:
6107:
6083:
6064:
6029:
6024:
5979:
5963:
5903:
5897:
5885:
5859:
5834:
5817:
5780:
5755:
5749:
5709:
5697:
5635:
5624:
5605:
5581:
5545:
5529:
5524:
5479:
5469:
5463:
5451:
5431:
5414:
5379:
5366:
5361:
5322:
5310:
5264:
5022:
4879:
4538:
4415:
4326:
4272:
4128:
4015:
3865:
3839:
3798:
3741:
3715:
3674:
3621:
3617:
3506:
3498:
3432:
3391:
3318:
3246:
2932:
2785:
2737:
2632:reaction quotient
2521:
1823:
1775:
1390:
1364:
1301:Gibbs free energy
1290:constant pressure
1283:entropy of mixing
1248:Gibbs free energy
1185:
1172:
1154:
1134:
1116:
1101:
964:Gibbs free energy
932:Gibbs free energy
922:reaction quotient
870:
864:
852:
839:
819:
806:
783:
770:
628:1 or reaction of
581:
568:
550:
530:
512:
498:
424:
404:
371:
351:
276:
264:
241:
226:
214:
191:
102:chemical equation
38:chemical reaction
16:(Redirected from
10579:
10466:Binding constant
10352:Phase separation
10284:
10277:
10270:
10261:
10260:
10251:
10237:
10228:
10218:
10177:
10176:
10158:
10152:
10151:
10149:
10147:
10132:
10126:
10120:
10114:
10113:
10106:
10100:
10099:
10091:
10085:
10084:
10082:
10075:
10066:
10053:
10052:
10045:
10039:
10038:
10036:
10034:
10028:
10017:
10008:
10002:
10001:
9999:
9998:
9984:
9978:
9977:
9969:
9963:
9962:
9946:
9938:
9927:
9926:
9918:
9912:
9911:
9909:
9908:
9902:
9896:. Archived from
9895:
9886:
9877:
9876:
9868:
9862:
9857:Mortimer, R. G.
9855:
9849:
9848:
9820:
9814:
9813:
9785:
9779:
9772:
9766:
9765:
9747:
9741:
9720:
9701:
9695:
9667:
9653:
9647:
9624:
9618:
9617:
9606:(2nd ed.).
9599:
9590:
9589:
9573:
9563:
9520:Redox equilibria
9418:
9416:
9415:
9410:
9405:
9404:
9377:
9376:
9361:
9357:
9356:
9355:
9354:
9353:
9339:
9338:
9325:
9320:
9285:
9284:
9260:
9259:
9228:
9223:
9211:
9210:
9200:
9195:
9177:
9176:
9167:
9166:
9156:
9151:
9114:
9112:
9111:
9106:
9104:
9103:
9094:
9093:
9083:
9078:
9060:
9059:
9047:
9046:
9037:
9036:
9026:
9021:
9005:
9000:
8982:
8981:
8972:
8971:
8961:
8956:
8918:
8916:
8915:
8910:
8902:
8901:
8892:
8891:
8878:
8873:
8826:
8824:
8823:
8818:
8810:
8809:
8800:
8799:
8789:
8784:
8723:) unknowns (the
8715:) equations in (
8699:
8697:
8696:
8691:
8688:
8683:
8671:
8670:
8661:
8660:
8647:
8642:
8624:
8622:
8621:
8620:
8607:
8606:
8605:
8595:
8579:
8577:
8576:
8571:
8569:
8568:
8556:
8555:
8545:
8540:
8522:
8521:
8509:
8507:
8506:
8505:
8492:
8491:
8490:
8480:
8434:
8432:
8431:
8426:
8418:
8414:
8412:
8407:
8395:
8394:
8385:
8384:
8371:
8366:
8346:
8345:
8335:
8330:
8306:
8305:
8255:
8254:
8223:
8221:
8220:
8215:
8212:
8207:
8195:
8194:
8185:
8184:
8171:
8166:
8119:
8117:
8116:
8111:
8108:
8103:
8084:
8082:
8081:
8076:
8074:
8073:
8072:
8046:
8041:
8029:
8028:
7979:
7977:
7976:
7971:
7963:
7962:
7949:
7948:
7938:
7933:
7871:dimethylglyoxime
7857:
7856:
7855:
7852:
7821:
7820:
7819:
7816:
7805:
7804:
7803:
7800:
7728:
7726:
7725:
7720:
7718:
7717:
7716:
7715:
7701:
7693:
7692:
7691:
7690:
7676:
7668:
7667:
7658:
7657:
7647:
7632:
7621:
7620:
7619:
7601:
7599:
7598:
7593:
7591:
7590:
7589:
7588:
7574:
7566:
7565:
7564:
7563:
7549:
7541:
7540:
7531:
7530:
7520:
7505:
7494:
7493:
7492:
7469:
7467:
7466:
7461:
7458:
7457:
7445:
7437:
7436:
7424:
7423:
7418:
7397:
7396:
7381:
7361:
7360:
7348:
7334:
7333:
7332:
7314:
7312:
7311:
7306:
7303:
7302:
7297:
7276:
7275:
7263:
7243:
7242:
7230:
7216:
7215:
7214:
7164:
7162:
7161:
7156:
7153:
7131:
7130:
7084:
7083:
7082:
7064:
7062:
7061:
7056:
7053:
7046:
7045:
7002:
7001:
7000:
6851:buffer solutions
6667:
6665:
6664:
6659:
6657:
6652:
6650:
6645:
6644:
6630:
6622:
6620:
6616:
6615:
6596:
6582:
6547:
6545:
6544:
6539:
6537:
6535:
6534:
6533:
6520:
6518:
6513:
6512:
6498:
6493:
6491:
6483:
6469:
6442:
6418:
6401:
6400:
6398:
6397:
6389:
6386:
6371:
6370:
6368:
6367:
6359:
6356:
6325:
6323:
6322:
6317:
6315:
6311:
6309:
6308:
6307:
6302:
6298:
6297:
6290:
6283:
6279:
6278:
6277:
6265:
6258:
6257:
6251:
6249:
6246:
6239:
6232:
6227:
6226:
6212:
6209:
6207:
6204:
6197:
6195:
6193:
6191:
6190:
6183:
6175:
6174:
6172:
6165:
6157:
6155:
6154:
6147:
6138:
6137:
6127:
6120:
6118:
6117:
6113:
6112:
6105:
6099:
6095:
6094:
6093:
6081:
6074:
6073:
6069:
6062:
6056:
6051:
6050:
6036:
6035:
6034:
6027:
6025:
6023:
6021:
6020:
6013:
6005:
6004:
6002:
5995:
5987:
5985:
5984:
5977:
5972:
5971:
5961:
5937:
5935:
5934:
5929:
5927:
5926:
5917:
5916:
5904:
5902:
5901:
5895:
5893:
5890:
5883:
5876:
5875:
5874:
5869:
5865:
5864:
5857:
5850:
5846:
5845:
5844:
5832:
5825:
5820:
5819:
5818:
5815:
5802:
5798:
5796:
5795:
5790:
5788:
5787:
5786:
5785:
5778:
5768:
5767:
5766:
5765:
5753:
5750:
5748:
5746:
5745:
5738:
5730:
5729:
5727:
5720:
5712:
5710:
5707:
5705:
5702:
5695:
5667:are examples of
5650:
5648:
5647:
5642:
5640:
5636:
5634:
5633:
5629:
5622:
5616:
5615:
5611:
5610:
5603:
5597:
5593:
5592:
5591:
5579:
5572:
5567:
5566:
5552:
5551:
5550:
5543:
5538:
5537:
5527:
5525:
5523:
5521:
5520:
5513:
5505:
5504:
5502:
5495:
5487:
5485:
5484:
5477:
5470:
5468:
5467:
5461:
5459:
5456:
5449:
5442:
5441:
5437:
5436:
5429:
5423:
5419:
5412:
5406:
5401:
5400:
5386:
5385:
5384:
5377:
5372:
5371:
5364:
5362:
5360:
5358:
5357:
5350:
5342:
5341:
5339:
5332:
5324:
5320:
5318:
5315:
5308:
5275:
5273:
5272:
5267:
5265:
5263:
5262:
5261:
5242:
5238:
5237:
5221:
5216:
5215:
5214:
5143:
5141:
5140:
5135:
5133:
5129:
5128:
5110:
5109:
5093:
5092:
5091:
5048:
5046:
5045:
5040:
5038:
5037:
5036:
5023:
5021:
5017:
5013:
5012:
5000:
4999:
4982:
4978:
4977:
4972:
4968:
4967:
4950:
4949:
4944:
4943:
4942:
4930:
4929:
4911:
4890:
4888:
4887:
4882:
4880:
4878:
4874:
4870:
4869:
4853:
4849:
4848:
4836:
4835:
4818:
4814:
4813:
4808:
4804:
4803:
4786:
4785:
4780:
4779:
4778:
4766:
4765:
4747:
4742:
4741:
4740:
4670:
4664:
4663:
4660:
4549:
4547:
4546:
4541:
4539:
4531:
4526:
4525:
4524:
4472:
4470:
4469:
4464:
4461:
4456:
4447:
4446:
4436:
4431:
4416:
4408:
4359:
4357:
4356:
4351:
4331:
4327:
4325:
4311:
4290:
4289:
4277:
4273:
4271:
4257:
4236:
4235:
4193:partial pressure
4174:Pitzer equations
4157:
4155:
4154:
4149:
4144:
4143:
4142:
4129:
4127:
4117:
4116:
4111:
4110:
4109:
4108:
4096:
4095:
4090:
4089:
4088:
4087:
4074:
4064:
4063:
4058:
4057:
4056:
4055:
4043:
4042:
4037:
4036:
4035:
4034:
4021:
4016:
4014:
4004:
4003:
3994:
3986:
3985:
3976:
3967:
3957:
3956:
3947:
3939:
3938:
3929:
3920:
3875:
3873:
3872:
3867:
3863:
3856:
3855:
3844:
3840:
3838:
3830:
3822:
3808:
3806:
3805:
3800:
3796:
3795:
3794:
3793:
3777:
3776:
3775:
3759:increases, then
3751:
3749:
3748:
3743:
3739:
3732:
3731:
3720:
3716:
3714:
3706:
3698:
3684:
3682:
3681:
3676:
3672:
3671:
3670:
3669:
3653:
3652:
3651:
3634:
3632:
3631:
3626:
3619:
3618:
3616:
3615:
3614:
3613:
3612:
3598:
3597:
3581:
3580:
3579:
3578:
3577:
3563:
3562:
3546:
3541:
3540:
3539:
3516:
3514:
3513:
3508:
3504:
3503:
3499:
3497:
3496:
3495:
3482:
3481:
3480:
3470:
3449:
3448:
3437:
3433:
3431:
3423:
3415:
3401:
3399:
3398:
3393:
3389:
3388:
3387:
3357:
3356:
3347:
3346:
3345:
3328:
3326:
3325:
3320:
3316:
3315:
3314:
3313:
3288:
3287:
3278:
3277:
3276:
3263:
3262:
3251:
3247:
3245:
3237:
3229:
3155:
3153:
3152:
3147:
3145:
3144:
3143:
3112:
3111:
3102:
3101:
3100:
3077:
3075:
3074:
3069:
3067:
3066:
3065:
3037:
3036:
3027:
3026:
3025:
2996:
2994:
2993:
2988:
2980:
2979:
2964:
2963:
2962:
2949:
2948:
2937:
2933:
2931:
2923:
2915:
2899:At equilibrium:
2895:
2893:
2892:
2887:
2885:
2884:
2883:
2858:
2857:
2848:
2847:
2846:
2833:
2832:
2817:
2816:
2815:
2802:
2801:
2790:
2786:
2784:
2776:
2768:
2748:
2746:
2745:
2740:
2738:
2736:
2735:
2734:
2725:
2717:
2716:
2707:
2698:
2697:
2696:
2687:
2679:
2678:
2669:
2660:
2655:
2654:
2653:
2621:
2619:
2618:
2613:
2611:
2610:
2601:
2600:
2599:
2586:
2585:
2575:
2570:
2560:
2555:
2532:
2530:
2529:
2524:
2522:
2520:
2519:
2518:
2509:
2501:
2500:
2491:
2482:
2481:
2480:
2471:
2463:
2462:
2453:
2444:
2427:
2426:
2416:
2411:
2401:
2396:
2378:
2377:
2362:
2361:
2360:
2336:
2334:
2333:
2328:
2320:
2291:
2256:
2227:
2194:
2189:
2188:
2171:
2166:
2165:
2142:
2137:
2136:
2119:
2114:
2113:
2094:
2093:
2078:
2077:
2076:
2052:
2050:
2049:
2044:
2041:
2040:
2039:
2023:
2022:
2021:
2005:
2004:
2003:
1987:
1986:
1985:
1969:
1968:
1953:
1952:
1951:
1925:
1923:
1922:
1917:
1915:
1914:
1899:
1898:
1897:
1884:
1883:
1874:
1873:
1863:
1858:
1840:
1839:
1828:
1824:
1822:
1814:
1806:
1785:
1783:
1782:
1777:
1773:
1772:
1771:
1732:
1730:
1729:
1724:
1722:
1721:
1709:
1708:
1698:
1693:
1620:
1619:
1605:
1603:
1602:
1597:
1591:
1567:
1562:
1550:
1549:
1548:
1511:
1509:
1508:
1503:
1500:
1499:
1498:
1482:
1481:
1480:
1464:
1463:
1462:
1446:
1445:
1444:
1404:
1400:
1398:
1397:
1392:
1388:
1381:
1380:
1369:
1365:
1363:
1355:
1347:
1327:with respect to
1236:partial pressure
1196:
1194:
1193:
1188:
1186:
1184:
1183:
1182:
1173:
1170:
1165:
1164:
1155:
1152:
1146:
1145:
1144:
1135:
1132:
1127:
1126:
1117:
1114:
1108:
1103:
1102:
1099:
1069:the quotient of
1038:
1036:
1035:
1030:
1028:
1027:
1026:
995:
994:
985:
984:
960:Helmholtz energy
952:stationary point
912:
911:
910:
907:
889:O} increases {CH
881:
879:
878:
873:
871:
869:
868:
862:
860:
857:
850:
847:
844:
837:
830:
826:
825:
824:
817:
814:
811:
804:
795:
793:
788:
781:
778:
775:
768:
761:
715:
709:
708:
705:
638:hydrogen bromide
606:transition state
592:
590:
589:
584:
582:
580:
579:
578:
569:
566:
561:
560:
551:
548:
542:
541:
540:
531:
528:
523:
522:
513:
510:
504:
499:
497:
496:
487:
486:
477:
472:
471:
445:
443:
442:
437:
435:
434:
429:
425:
422:
415:
414:
409:
405:
402:
395:
394:
382:
381:
376:
372:
369:
362:
361:
356:
352:
349:
342:
341:
297:
295:
294:
289:
287:
283:
282:
277:
274:
271:
270:
265:
262:
259:
258:
242:
239:
233:
232:
227:
224:
221:
220:
215:
212:
209:
208:
192:
189:
88:found that some
62:reverse reaction
21:
10587:
10586:
10582:
10581:
10580:
10578:
10577:
10576:
10552:
10551:
10550:
10545:
10498:Self-ionization
10442:
10428:Buffer solution
10416:
10366:
10293:
10288:
10244:
10227:. Plenum Press.
10209:
10208:
10207:
10197:
10196:
10192:
10185:
10183:Further reading
10180:
10173:
10163:Thermal Physics
10159:
10155:
10145:
10143:
10134:
10133:
10129:
10121:
10117:
10108:
10107:
10103:
10092:
10088:
10080:
10073:
10067:
10056:
10047:
10046:
10042:
10032:
10030:
10026:
10015:
10009:
10005:
9996:
9994:
9986:
9985:
9981:
9970:
9966:
9959:
9939:
9930:
9919:
9915:
9906:
9904:
9900:
9893:
9887:
9880:
9875:. Butterworths.
9873:Ion Association
9869:
9865:
9856:
9852:
9821:
9817:
9786:
9782:
9773:
9769:
9762:
9748:
9744:
9735:
9731:
9702:
9698:
9684:
9680:
9676:
9672:
9654:
9650:
9625:
9621:
9614:
9600:
9593:
9586:
9564:
9555:
9551:
9546:
9515:
9499:
9446:
9427:
9400:
9396:
9372:
9368:
9349:
9345:
9344:
9340:
9334:
9330:
9321:
9310:
9305:
9301:
9280:
9276:
9255:
9251:
9224:
9219:
9206:
9202:
9196:
9185:
9172:
9168:
9162:
9158:
9152:
9141:
9126:
9123:
9122:
9099:
9095:
9089:
9085:
9079:
9068:
9052:
9048:
9042:
9038:
9032:
9028:
9022:
9011:
9001:
8990:
8977:
8973:
8967:
8963:
8957:
8946:
8934:
8931:
8930:
8925:
8897:
8893:
8884:
8880:
8874:
8863:
8857:
8854:
8853:
8843:
8833:
8805:
8801:
8795:
8791:
8785:
8774:
8768:
8765:
8764:
8742:
8735:
8728:
8703:(For proof see
8684:
8679:
8666:
8662:
8653:
8649:
8643:
8632:
8616:
8612:
8608:
8601:
8600:
8596:
8594:
8586:
8583:
8582:
8561:
8557:
8551:
8547:
8541:
8530:
8517:
8513:
8501:
8497:
8493:
8486:
8485:
8481:
8479:
8471:
8468:
8467:
8457:
8450:
8443:
8408:
8403:
8390:
8386:
8377:
8373:
8367:
8356:
8351:
8347:
8341:
8337:
8331:
8320:
8301:
8300:
8298:
8295:
8294:
8271:
8253:
8248:
8247:
8246:
8232:
8208:
8203:
8190:
8186:
8177:
8173:
8167:
8156:
8150:
8147:
8146:
8136:
8104:
8099:
8093:
8090:
8089:
8068:
8064:
8063:
8042:
8037:
8024:
8020:
8018:
8015:
8014:
8000:
7986:
7958:
7954:
7944:
7940:
7934:
7923:
7908:
7905:
7904:
7891:
7884:
7876:
7853:
7850:
7849:
7847:
7840:
7832:
7827:
7817:
7814:
7813:
7811:
7807:
7801:
7798:
7797:
7795:
7784:
7773:
7738:
7736:Polybasic acids
7711:
7707:
7706:
7702:
7697:
7686:
7682:
7681:
7677:
7672:
7663:
7659:
7653:
7649:
7643:
7628:
7615:
7614:
7610:
7608:
7605:
7604:
7584:
7580:
7579:
7575:
7570:
7559:
7555:
7554:
7550:
7545:
7536:
7532:
7526:
7522:
7516:
7501:
7488:
7487:
7483:
7481:
7478:
7477:
7450:
7446:
7441:
7432:
7428:
7419:
7399:
7398:
7392:
7388:
7362:
7356:
7352:
7338:
7328:
7327:
7323:
7321:
7318:
7317:
7298:
7278:
7277:
7271:
7267:
7244:
7238:
7234:
7220:
7210:
7209:
7205:
7203:
7200:
7199:
7195:
7188:
7182:, =
7181:
7171:
7126:
7122:
7088:
7078:
7077:
7073:
7071:
7068:
7067:
7041:
7037:
7006:
6996:
6995:
6991:
6989:
6986:
6985:
6968:
6963:
6928:
6908:Nernst equation
6762:
6760:
6756:
6753:(adsorbed) ⇌ NH
6752:
6745:
6738:
6731:
6727:
6720:
6711:
6707:
6699:
6693:
6681:
6646:
6640:
6639:
6631:
6629:
6608:
6604:
6597:
6583:
6581:
6579:
6576:
6575:
6529:
6525:
6521:
6514:
6508:
6507:
6499:
6497:
6484:
6470:
6468:
6466:
6463:
6462:
6453:
6441:
6434:
6427:
6420:
6417:
6410:
6403:
6396:
6390:
6387:
6384:
6383:
6381:
6379:
6373:
6366:
6360:
6357:
6354:
6353:
6351:
6349:
6343:
6341:
6334:
6313:
6312:
6303:
6293:
6289:
6285:
6284:
6273:
6268:
6264:
6260:
6259:
6247:
6242:
6234:
6233:
6231:
6222:
6218:
6216:
6205:
6200:
6186:
6179:
6178:
6176:
6168:
6161:
6159:
6158:
6156:
6150:
6146:
6130:
6126:
6125:
6122:
6121:
6108:
6104:
6100:
6089:
6084:
6080:
6076:
6075:
6065:
6058:
6057:
6055:
6046:
6042:
6040:
6030:
6026:
6016:
6009:
6008:
6006:
5998:
5991:
5989:
5988:
5986:
5980:
5976:
5964:
5960:
5959:
5955:
5953:
5950:
5949:
5922:
5918:
5912:
5908:
5891:
5886:
5878:
5877:
5870:
5860:
5856:
5852:
5851:
5840:
5835:
5831:
5827:
5826:
5824:
5814:
5813:
5809:
5807:
5804:
5803:
5800:
5781:
5777:
5772:
5761:
5756:
5752:
5751:
5741:
5734:
5733:
5731:
5723:
5716:
5714:
5713:
5711:
5703:
5698:
5693:
5692:
5690:
5687:
5686:
5681:
5666:
5659:
5638:
5637:
5625:
5618:
5617:
5606:
5602:
5598:
5587:
5582:
5578:
5574:
5573:
5571:
5562:
5558:
5556:
5546:
5542:
5530:
5526:
5516:
5509:
5508:
5506:
5498:
5491:
5489:
5488:
5486:
5480:
5476:
5475:
5472:
5471:
5457:
5452:
5444:
5443:
5432:
5428:
5424:
5415:
5408:
5407:
5405:
5396:
5392:
5390:
5380:
5376:
5367:
5363:
5353:
5346:
5345:
5343:
5335:
5328:
5326:
5325:
5323:
5316:
5311:
5306:
5302:
5300:
5297:
5296:
5291:
5287:
5282:
5257:
5253:
5243:
5233:
5229:
5222:
5220:
5210:
5209:
5205:
5203:
5200:
5199:
5190:
5171:
5161:
5124:
5120:
5105:
5101:
5097:
5087:
5086:
5082:
5080:
5077:
5076:
5067:
5063:
5032:
5031:
5027:
5008:
5004:
4995:
4991:
4987:
4983:
4973:
4963:
4959:
4958:
4957:
4945:
4938:
4934:
4925:
4921:
4917:
4916:
4912:
4910:
4902:
4899:
4898:
4865:
4861:
4860:
4844:
4840:
4831:
4827:
4823:
4819:
4809:
4799:
4795:
4794:
4793:
4781:
4774:
4770:
4761:
4757:
4753:
4752:
4748:
4746:
4736:
4735:
4731:
4729:
4726:
4725:
4719:
4715:
4711:
4707:
4703:
4699:
4687:
4685:Pure substances
4668:
4661:
4658:
4657:
4655:
4651:
4647:
4626:contact process
4616:
4612:
4608:
4599:
4592:kinetic barrier
4584:
4577:
4570:
4559:
4530:
4520:
4519:
4515:
4513:
4510:
4509:
4488:
4481:
4457:
4452:
4442:
4438:
4432:
4421:
4407:
4399:
4396:
4395:
4386:
4378:
4369:
4315:
4310:
4306:
4285:
4281:
4261:
4256:
4252:
4231:
4227:
4219:
4216:
4215:
4167:Davies equation
4138:
4137:
4133:
4112:
4104:
4103:
4099:
4098:
4097:
4091:
4083:
4082:
4078:
4077:
4076:
4075:
4059:
4051:
4050:
4046:
4045:
4044:
4038:
4030:
4029:
4025:
4024:
4023:
4022:
4020:
3999:
3995:
3990:
3981:
3977:
3972:
3968:
3952:
3948:
3943:
3934:
3930:
3925:
3921:
3919:
3911:
3908:
3907:
3894:
3886:
3845:
3831:
3823:
3821:
3817:
3816:
3814:
3811:
3810:
3786:
3785:
3781:
3771:
3770:
3766:
3764:
3761:
3760:
3721:
3707:
3699:
3697:
3693:
3692:
3690:
3687:
3686:
3662:
3661:
3657:
3647:
3646:
3642:
3640:
3637:
3636:
3608:
3604:
3603:
3599:
3593:
3589:
3582:
3573:
3569:
3568:
3564:
3558:
3554:
3547:
3545:
3535:
3534:
3530:
3528:
3525:
3524:
3488:
3487:
3483:
3476:
3475:
3471:
3469:
3465:
3438:
3424:
3416:
3414:
3410:
3409:
3407:
3404:
3403:
3380:
3376:
3352:
3348:
3341:
3340:
3336:
3334:
3331:
3330:
3309:
3308:
3304:
3283:
3279:
3272:
3271:
3267:
3252:
3238:
3230:
3228:
3224:
3223:
3221:
3218:
3217:
3216:
3209:
3198:
3187:
3180:
3172:
3136:
3135:
3131:
3107:
3103:
3096:
3095:
3091:
3089:
3086:
3085:
3058:
3057:
3053:
3032:
3028:
3021:
3020:
3016:
3008:
3005:
3004:
2969:
2965:
2958:
2957:
2953:
2938:
2924:
2916:
2914:
2910:
2909:
2907:
2904:
2903:
2879:
2878:
2874:
2853:
2849:
2842:
2841:
2837:
2822:
2818:
2811:
2810:
2806:
2791:
2777:
2769:
2767:
2763:
2762:
2760:
2757:
2756:
2730:
2726:
2721:
2712:
2708:
2703:
2699:
2692:
2688:
2683:
2674:
2670:
2665:
2661:
2659:
2649:
2648:
2644:
2642:
2639:
2638:
2634:is defined as:
2606:
2602:
2595:
2594:
2590:
2581:
2577:
2571:
2566:
2556:
2545:
2539:
2536:
2535:
2514:
2510:
2505:
2496:
2492:
2487:
2483:
2476:
2472:
2467:
2458:
2454:
2449:
2445:
2443:
2422:
2418:
2412:
2407:
2397:
2386:
2367:
2363:
2356:
2355:
2351:
2349:
2346:
2345:
2316:
2287:
2252:
2223:
2190:
2184:
2183:
2167:
2161:
2160:
2138:
2132:
2131:
2115:
2109:
2108:
2083:
2079:
2072:
2071:
2067:
2065:
2062:
2061:
2035:
2034:
2030:
2017:
2016:
2012:
1999:
1998:
1994:
1981:
1980:
1976:
1958:
1954:
1947:
1946:
1942:
1940:
1937:
1936:
1904:
1900:
1893:
1892:
1888:
1879:
1875:
1869:
1865:
1859:
1848:
1829:
1815:
1807:
1805:
1801:
1800:
1798:
1795:
1794:
1767:
1763:
1761:
1758:
1757:
1749:
1742:
1717:
1713:
1704:
1700:
1694:
1683:
1644:
1641:
1640:
1618:
1615:
1614:
1613:
1587:
1563:
1558:
1544:
1543:
1539:
1537:
1534:
1533:
1494:
1493:
1489:
1476:
1475:
1471:
1458:
1457:
1453:
1440:
1439:
1435:
1430:
1427:
1426:
1402:
1370:
1356:
1348:
1346:
1342:
1341:
1339:
1336:
1335:
1244:
1232:
1221:
1178:
1174:
1169:
1160:
1156:
1151:
1147:
1140:
1136:
1131:
1122:
1118:
1113:
1109:
1107:
1098:
1094:
1092:
1089:
1088:
1083:
1019:
1018:
1014:
990:
986:
980:
976:
974:
971:
970:
916:
908:
905:
904:
902:
898:
896:
892:
888:
858:
853:
845:
840:
832:
831:
820:
816:
812:
807:
802:
789:
784:
776:
771:
766:
762:
760:
752:
749:
748:
713:
706:
703:
702:
700:
696:
692:
688:
684:
627:
600:. However, the
574:
570:
565:
556:
552:
547:
543:
536:
532:
527:
518:
514:
509:
505:
503:
492:
488:
482:
478:
476:
467:
463:
461:
458:
457:
430:
421:
417:
416:
410:
401:
397:
396:
390:
386:
377:
368:
364:
363:
357:
348:
344:
343:
337:
333:
331:
328:
327:
318:
311:
285:
284:
278:
273:
272:
266:
261:
260:
254:
250:
243:
238:
235:
234:
228:
223:
222:
216:
211:
210:
204:
200:
193:
188:
184:
182:
179:
178:
78:
52:are present in
34:
28:
23:
22:
15:
12:
11:
5:
10585:
10575:
10574:
10569:
10564:
10547:
10546:
10544:
10543:
10542:
10541:
10531:
10530:
10529:
10519:
10518:
10517:
10507:
10506:
10505:
10495:
10490:
10485:
10484:
10483:
10473:
10468:
10463:
10462:
10461:
10450:
10448:
10444:
10443:
10441:
10440:
10435:
10430:
10424:
10422:
10418:
10417:
10415:
10414:
10409:
10404:
10399:
10394:
10389:
10388:
10387:
10376:
10374:
10368:
10367:
10365:
10364:
10359:
10354:
10349:
10344:
10343:
10342:
10337:
10327:
10322:
10317:
10312:
10307:
10301:
10299:
10295:
10294:
10287:
10286:
10279:
10272:
10264:
10258:
10257:
10243:
10242:External links
10240:
10239:
10238:
10229:
10220:
10206:
10205:
10199:
10198:
10187:
10186:
10184:
10181:
10179:
10178:
10171:
10153:
10127:
10115:
10101:
10086:
10083:on 2006-04-21.
10054:
10040:
10003:
9992:NobelPrize.org
9979:
9964:
9957:
9928:
9925:. McGraw-Hill.
9913:
9878:
9863:
9850:
9815:
9780:
9767:
9760:
9742:
9738:
9737:
9733:
9729:
9696:
9682:
9681:→ 2NaCl + CaCO
9678:
9674:
9670:
9648:
9619:
9612:
9591:
9584:
9552:
9550:
9547:
9545:
9544:
9538:
9532:
9527:
9522:
9517:
9513:
9506:
9501:
9497:
9493:
9488:
9483:
9478:
9473:
9468:
9463:
9458:
9453:
9447:
9445:
9442:
9425:
9420:
9419:
9408:
9403:
9399:
9395:
9392:
9389:
9386:
9383:
9380:
9375:
9371:
9367:
9364:
9360:
9352:
9348:
9343:
9337:
9333:
9329:
9324:
9319:
9316:
9313:
9309:
9304:
9300:
9297:
9294:
9291:
9288:
9283:
9279:
9275:
9272:
9269:
9266:
9263:
9258:
9254:
9250:
9247:
9244:
9241:
9238:
9235:
9232:
9227:
9222:
9218:
9214:
9209:
9205:
9199:
9194:
9191:
9188:
9184:
9180:
9175:
9171:
9165:
9161:
9155:
9150:
9147:
9144:
9140:
9136:
9133:
9130:
9116:
9115:
9102:
9098:
9092:
9088:
9082:
9077:
9074:
9071:
9067:
9063:
9058:
9055:
9051:
9045:
9041:
9035:
9031:
9025:
9020:
9017:
9014:
9010:
9004:
8999:
8996:
8993:
8989:
8985:
8980:
8976:
8970:
8966:
8960:
8955:
8952:
8949:
8945:
8941:
8938:
8923:
8920:
8919:
8908:
8905:
8900:
8896:
8890:
8887:
8883:
8877:
8872:
8869:
8866:
8862:
8841:
8831:
8828:
8827:
8816:
8813:
8808:
8804:
8798:
8794:
8788:
8783:
8780:
8777:
8773:
8740:
8733:
8726:
8701:
8700:
8687:
8682:
8678:
8674:
8669:
8665:
8659:
8656:
8652:
8646:
8641:
8638:
8635:
8631:
8627:
8619:
8615:
8611:
8604:
8599:
8593:
8590:
8580:
8567:
8564:
8560:
8554:
8550:
8544:
8539:
8536:
8533:
8529:
8525:
8520:
8516:
8512:
8504:
8500:
8496:
8489:
8484:
8478:
8475:
8455:
8448:
8441:
8436:
8435:
8424:
8421:
8417:
8411:
8406:
8402:
8398:
8393:
8389:
8383:
8380:
8376:
8370:
8365:
8362:
8359:
8355:
8350:
8344:
8340:
8334:
8329:
8326:
8323:
8319:
8315:
8312:
8309:
8304:
8269:
8249:
8230:
8225:
8224:
8211:
8206:
8202:
8198:
8193:
8189:
8183:
8180:
8176:
8170:
8165:
8162:
8159:
8155:
8134:
8107:
8102:
8098:
8086:
8085:
8071:
8067:
8062:
8059:
8056:
8053:
8050:
8045:
8040:
8036:
8032:
8027:
8023:
7998:
7984:
7981:
7980:
7969:
7966:
7961:
7957:
7953:
7947:
7943:
7937:
7932:
7929:
7926:
7922:
7918:
7915:
7912:
7890:
7887:
7882:
7874:
7838:
7835:lattice energy
7830:
7825:
7809:
7783:
7780:
7776:aluminium salt
7771:
7737:
7734:
7730:
7729:
7714:
7710:
7705:
7700:
7696:
7689:
7685:
7680:
7675:
7671:
7666:
7662:
7656:
7652:
7646:
7642:
7638:
7635:
7631:
7627:
7624:
7618:
7613:
7602:
7587:
7583:
7578:
7573:
7569:
7562:
7558:
7553:
7548:
7544:
7539:
7535:
7529:
7525:
7519:
7515:
7511:
7508:
7504:
7500:
7497:
7491:
7486:
7471:
7470:
7456:
7453:
7449:
7444:
7440:
7435:
7431:
7427:
7422:
7417:
7414:
7411:
7408:
7405:
7402:
7395:
7391:
7387:
7384:
7380:
7377:
7374:
7371:
7368:
7365:
7359:
7355:
7351:
7347:
7344:
7341:
7337:
7331:
7326:
7315:
7301:
7296:
7293:
7290:
7287:
7284:
7281:
7274:
7270:
7266:
7262:
7259:
7256:
7253:
7250:
7247:
7241:
7237:
7233:
7229:
7226:
7223:
7219:
7213:
7208:
7193:
7186:
7179:
7169:
7166:
7165:
7152:
7149:
7146:
7143:
7140:
7137:
7134:
7129:
7125:
7121:
7118:
7115:
7112:
7109:
7106:
7103:
7100:
7097:
7094:
7091:
7087:
7081:
7076:
7065:
7052:
7049:
7044:
7040:
7036:
7033:
7030:
7027:
7024:
7021:
7018:
7015:
7012:
7009:
7005:
6999:
6994:
6971:conjugate base
6966:
6962:
6959:
6958:
6957:
6946:
6943:
6927:
6924:
6919:
6918:
6911:
6904:
6897:
6879:
6861:
6839:
6838:
6837:
6830:
6825:
6823:Chromatography
6812:
6799:
6793:
6788:
6773:
6771:rocket engines
6759:
6758:
6754:
6750:
6747:
6743:
6740:
6736:
6733:
6729:
6725:
6722:
6718:
6715:
6709:
6705:
6701:
6695:
6694:
6692:
6689:
6687:among others.
6680:
6677:
6669:
6668:
6655:
6649:
6643:
6638:
6634:
6628:
6625:
6619:
6614:
6611:
6607:
6603:
6600:
6595:
6592:
6589:
6586:
6559:is negative),
6549:
6548:
6532:
6528:
6524:
6517:
6511:
6506:
6502:
6496:
6490:
6487:
6482:
6479:
6476:
6473:
6452:
6449:
6439:
6435: + p
6432:
6428: = p
6425:
6415:
6411: = p
6408:
6394:
6377:
6364:
6347:
6339:
6332:
6327:
6326:
6306:
6301:
6296:
6288:
6282:
6276:
6271:
6263:
6256:
6245:
6237:
6230:
6225:
6221:
6217:
6215:
6203:
6189:
6182:
6171:
6164:
6153:
6144:
6141:
6136:
6133:
6124:
6123:
6116:
6111:
6103:
6098:
6092:
6087:
6079:
6072:
6068:
6061:
6054:
6049:
6045:
6041:
6039:
6033:
6019:
6012:
6001:
5994:
5983:
5975:
5970:
5967:
5958:
5957:
5939:
5938:
5925:
5921:
5915:
5911:
5907:
5900:
5889:
5881:
5873:
5868:
5863:
5855:
5849:
5843:
5838:
5830:
5823:
5812:
5784:
5775:
5771:
5764:
5759:
5744:
5737:
5726:
5719:
5701:
5679:
5664:
5657:
5652:
5651:
5632:
5628:
5621:
5614:
5609:
5601:
5596:
5590:
5585:
5577:
5570:
5565:
5561:
5557:
5555:
5549:
5541:
5536:
5533:
5519:
5512:
5501:
5494:
5483:
5474:
5473:
5466:
5455:
5447:
5440:
5435:
5427:
5422:
5418:
5411:
5404:
5399:
5395:
5391:
5389:
5383:
5375:
5370:
5356:
5349:
5338:
5331:
5314:
5305:
5304:
5289:
5285:
5281:
5278:
5277:
5276:
5260:
5256:
5252:
5249:
5246:
5241:
5236:
5232:
5228:
5225:
5219:
5213:
5208:
5193:
5192:
5188:
5187:2 CO ⇌ CO
5169:
5159:
5145:
5144:
5132:
5127:
5123:
5119:
5116:
5113:
5108:
5104:
5100:
5096:
5090:
5085:
5070:
5069:
5065:
5061:
5051:
5050:
5035:
5030:
5026:
5020:
5016:
5011:
5007:
5003:
4998:
4994:
4990:
4986:
4981:
4976:
4971:
4966:
4962:
4956:
4953:
4948:
4941:
4937:
4933:
4928:
4924:
4920:
4915:
4909:
4906:
4892:
4891:
4877:
4873:
4868:
4864:
4859:
4856:
4852:
4847:
4843:
4839:
4834:
4830:
4826:
4822:
4817:
4812:
4807:
4802:
4798:
4792:
4789:
4784:
4777:
4773:
4769:
4764:
4760:
4756:
4751:
4745:
4739:
4734:
4722:
4721:
4717:
4713:
4709:
4705:
4701:
4697:
4686:
4683:
4672:
4671:
4666:
4653:
4649:
4637:carbon dioxide
4618:
4617:
4614:
4610:
4606:
4597:
4590:as there is a
4582:
4575:
4569:
4566:
4557:
4551:
4550:
4537:
4534:
4529:
4523:
4518:
4486:
4479:
4474:
4473:
4460:
4455:
4451:
4445:
4441:
4435:
4430:
4427:
4424:
4420:
4414:
4411:
4406:
4403:
4389:ionic strength
4384:
4376:
4373:sodium nitrate
4368:
4365:
4361:
4360:
4349:
4346:
4343:
4340:
4337:
4334:
4330:
4324:
4321:
4318:
4314:
4309:
4305:
4302:
4299:
4296:
4293:
4288:
4284:
4280:
4276:
4270:
4267:
4264:
4260:
4255:
4251:
4248:
4245:
4242:
4239:
4234:
4230:
4226:
4223:
4159:
4158:
4147:
4141:
4136:
4132:
4126:
4123:
4120:
4115:
4107:
4102:
4094:
4086:
4081:
4073:
4070:
4067:
4062:
4054:
4049:
4041:
4033:
4028:
4019:
4013:
4010:
4007:
4002:
3998:
3993:
3989:
3984:
3980:
3975:
3971:
3966:
3963:
3960:
3955:
3951:
3946:
3942:
3937:
3933:
3928:
3924:
3918:
3915:
3892:
3885:
3882:
3878:
3877:
3862:
3859:
3854:
3851:
3848:
3843:
3837:
3834:
3829:
3826:
3820:
3792:
3789:
3784:
3780:
3774:
3769:
3753:
3738:
3735:
3730:
3727:
3724:
3719:
3713:
3710:
3705:
3702:
3696:
3668:
3665:
3660:
3656:
3650:
3645:
3624:
3611:
3607:
3602:
3596:
3592:
3588:
3585:
3576:
3572:
3567:
3561:
3557:
3553:
3550:
3544:
3538:
3533:
3517:
3502:
3494:
3491:
3486:
3479:
3474:
3468:
3464:
3461:
3458:
3455:
3452:
3447:
3444:
3441:
3436:
3430:
3427:
3422:
3419:
3413:
3386:
3383:
3379:
3375:
3372:
3369:
3366:
3363:
3360:
3355:
3351:
3344:
3339:
3312:
3307:
3303:
3300:
3297:
3294:
3291:
3286:
3282:
3275:
3270:
3266:
3261:
3258:
3255:
3250:
3244:
3241:
3236:
3233:
3227:
3214:
3207:
3196:
3185:
3178:
3171:
3168:
3157:
3156:
3142:
3139:
3134:
3130:
3127:
3124:
3121:
3118:
3115:
3110:
3106:
3099:
3094:
3079:
3078:
3064:
3061:
3056:
3052:
3049:
3046:
3043:
3040:
3035:
3031:
3024:
3019:
3015:
3012:
2998:
2997:
2986:
2983:
2978:
2975:
2972:
2968:
2961:
2956:
2952:
2947:
2944:
2941:
2936:
2930:
2927:
2922:
2919:
2913:
2897:
2896:
2882:
2877:
2873:
2870:
2867:
2864:
2861:
2856:
2852:
2845:
2840:
2836:
2831:
2828:
2825:
2821:
2814:
2809:
2805:
2800:
2797:
2794:
2789:
2783:
2780:
2775:
2772:
2766:
2750:
2749:
2733:
2729:
2724:
2720:
2715:
2711:
2706:
2702:
2695:
2691:
2686:
2682:
2677:
2673:
2668:
2664:
2658:
2652:
2647:
2624:
2623:
2609:
2605:
2598:
2593:
2589:
2584:
2580:
2574:
2569:
2565:
2559:
2554:
2551:
2548:
2544:
2533:
2517:
2513:
2508:
2504:
2499:
2495:
2490:
2486:
2479:
2475:
2470:
2466:
2461:
2457:
2452:
2448:
2442:
2439:
2436:
2433:
2430:
2425:
2421:
2415:
2410:
2406:
2400:
2395:
2392:
2389:
2385:
2381:
2376:
2373:
2370:
2366:
2359:
2354:
2339:
2338:
2326:
2323:
2319:
2315:
2312:
2309:
2306:
2303:
2300:
2297:
2294:
2290:
2286:
2283:
2280:
2277:
2274:
2271:
2268:
2265:
2262:
2259:
2255:
2251:
2248:
2245:
2242:
2239:
2236:
2233:
2230:
2226:
2222:
2219:
2216:
2213:
2210:
2207:
2204:
2201:
2198:
2193:
2187:
2182:
2178:
2175:
2170:
2164:
2159:
2155:
2152:
2149:
2146:
2141:
2135:
2130:
2126:
2123:
2118:
2112:
2107:
2103:
2100:
2097:
2092:
2089:
2086:
2082:
2075:
2070:
2055:
2054:
2038:
2033:
2029:
2026:
2020:
2015:
2011:
2008:
2002:
1997:
1993:
1990:
1984:
1979:
1975:
1972:
1967:
1964:
1961:
1957:
1950:
1945:
1927:
1926:
1913:
1910:
1907:
1903:
1896:
1891:
1887:
1882:
1878:
1872:
1868:
1862:
1857:
1854:
1851:
1847:
1843:
1838:
1835:
1832:
1827:
1821:
1818:
1813:
1810:
1804:
1770:
1766:
1747:
1740:
1735:
1734:
1720:
1716:
1712:
1707:
1703:
1697:
1692:
1689:
1686:
1682:
1678:
1675:
1672:
1669:
1666:
1663:
1660:
1657:
1654:
1651:
1648:
1616:
1607:
1606:
1594:
1590:
1586:
1583:
1580:
1577:
1574:
1571:
1566:
1561:
1557:
1553:
1547:
1542:
1513:
1512:
1497:
1492:
1488:
1485:
1479:
1474:
1470:
1467:
1461:
1456:
1452:
1449:
1443:
1438:
1434:
1407:
1406:
1387:
1384:
1379:
1376:
1373:
1368:
1362:
1359:
1354:
1351:
1345:
1315:(Greek letter
1279:standard state
1243:
1242:Thermodynamics
1240:
1230:
1225:ionic strength
1219:
1200:where is the
1198:
1197:
1181:
1177:
1168:
1163:
1159:
1150:
1143:
1139:
1130:
1125:
1121:
1112:
1106:
1097:
1081:
1067:ionic strength
1040:
1039:
1025:
1022:
1017:
1013:
1010:
1007:
1004:
1001:
998:
993:
989:
983:
979:
914:
900:
894:
890:
886:
883:
882:
867:
856:
843:
835:
829:
823:
810:
801:
798:
792:
787:
774:
765:
759:
756:
717:
716:
711:
698:
694:
690:
686:
625:
614:rate equations
594:
593:
577:
573:
564:
559:
555:
546:
539:
535:
526:
521:
517:
508:
502:
495:
491:
485:
481:
475:
470:
466:
447:
446:
433:
428:
420:
413:
408:
400:
393:
389:
385:
380:
375:
367:
360:
355:
347:
340:
336:
321:rate constants
316:
309:
299:
298:
281:
269:
257:
253:
249:
246:
244:
237:
236:
231:
219:
207:
203:
199:
196:
194:
187:
186:
157:
156:
77:
74:
66:reaction rates
54:concentrations
26:
9:
6:
4:
3:
2:
10584:
10573:
10570:
10568:
10565:
10563:
10560:
10559:
10557:
10540:
10537:
10536:
10535:
10532:
10528:
10525:
10524:
10523:
10520:
10516:
10513:
10512:
10511:
10508:
10504:
10501:
10500:
10499:
10496:
10494:
10491:
10489:
10486:
10482:
10479:
10478:
10477:
10474:
10472:
10469:
10467:
10464:
10460:
10457:
10456:
10455:
10452:
10451:
10449:
10445:
10439:
10436:
10434:
10431:
10429:
10426:
10425:
10423:
10419:
10413:
10410:
10408:
10405:
10403:
10400:
10398:
10395:
10393:
10392:Phase diagram
10390:
10386:
10385:determination
10383:
10382:
10381:
10378:
10377:
10375:
10373:
10369:
10363:
10360:
10358:
10355:
10353:
10350:
10348:
10345:
10341:
10338:
10336:
10333:
10332:
10331:
10328:
10326:
10323:
10321:
10318:
10316:
10313:
10311:
10308:
10306:
10303:
10302:
10300:
10296:
10292:
10285:
10280:
10278:
10273:
10271:
10266:
10265:
10262:
10255:
10250:
10246:
10245:
10235:
10230:
10226:
10221:
10216:
10211:
10210:
10204:
10201:
10200:
10195:
10190:
10174:
10172:0-7167-1088-9
10168:
10164:
10157:
10141:
10137:
10131:
10125:
10119:
10111:
10105:
10097:
10090:
10079:
10072:
10065:
10063:
10061:
10059:
10050:
10044:
10025:
10021:
10014:
10007:
9993:
9989:
9983:
9975:
9968:
9960:
9958:0-89925-457-8
9954:
9950:
9945:
9937:
9935:
9933:
9924:
9917:
9903:on 2008-12-17
9899:
9892:
9885:
9883:
9874:
9867:
9860:
9854:
9846:
9842:
9838:
9834:
9830:
9826:
9819:
9811:
9807:
9803:
9799:
9795:
9791:
9784:
9777:
9771:
9763:
9761:0-471-21517-1
9757:
9753:
9746:
9727:
9726:
9724:
9718:
9714:
9713:
9706:
9700:
9692:
9691:decomposition
9688:
9665:
9661:
9660:
9652:
9646:
9642:
9638:
9634:
9633:
9628:
9623:
9615:
9609:
9605:
9598:
9596:
9587:
9585:0-7167-8759-8
9581:
9577:
9572:
9571:
9562:
9560:
9558:
9553:
9542:
9539:
9536:
9533:
9531:
9528:
9526:
9523:
9521:
9518:
9516:
9512:
9507:
9505:
9502:
9500:
9494:
9492:
9489:
9487:
9484:
9482:
9479:
9477:
9474:
9472:
9469:
9467:
9464:
9462:
9459:
9457:
9454:
9452:
9449:
9448:
9441:
9439:
9434:
9432:
9428:
9401:
9397:
9390:
9387:
9384:
9381:
9378:
9373:
9369:
9362:
9358:
9350:
9346:
9335:
9331:
9322:
9317:
9314:
9311:
9307:
9302:
9298:
9295:
9292:
9289:
9286:
9281:
9277:
9270:
9256:
9252:
9242:
9239:
9236:
9233:
9230:
9225:
9220:
9216:
9207:
9203:
9197:
9192:
9189:
9186:
9182:
9178:
9173:
9169:
9163:
9159:
9153:
9148:
9145:
9142:
9138:
9134:
9131:
9121:
9120:
9119:
9100:
9096:
9090:
9086:
9080:
9075:
9072:
9069:
9065:
9061:
9056:
9053:
9049:
9043:
9039:
9033:
9029:
9023:
9018:
9015:
9012:
9008:
9002:
8997:
8994:
8991:
8987:
8983:
8978:
8974:
8968:
8964:
8958:
8953:
8950:
8947:
8943:
8939:
8936:
8929:
8928:
8927:
8906:
8903:
8898:
8894:
8888:
8885:
8881:
8875:
8870:
8867:
8864:
8860:
8852:
8851:
8850:
8848:
8844:
8837:
8814:
8811:
8806:
8802:
8796:
8792:
8786:
8781:
8778:
8775:
8771:
8763:
8762:
8761:
8758:
8753:
8751:
8747:
8743:
8736:
8729:
8722:
8719: +
8718:
8714:
8711: +
8710:
8706:
8685:
8680:
8676:
8672:
8667:
8663:
8657:
8654:
8650:
8644:
8639:
8636:
8633:
8629:
8625:
8617:
8613:
8591:
8588:
8581:
8565:
8562:
8558:
8552:
8548:
8542:
8537:
8534:
8531:
8527:
8523:
8518:
8514:
8510:
8502:
8498:
8476:
8473:
8466:
8465:
8464:
8462:
8458:
8451:
8444:
8422:
8419:
8415:
8409:
8404:
8400:
8396:
8391:
8387:
8381:
8378:
8374:
8368:
8363:
8360:
8357:
8353:
8348:
8342:
8338:
8332:
8327:
8324:
8321:
8317:
8313:
8310:
8307:
8293:
8292:
8291:
8288:
8286:
8282:
8278:
8273:
8267:
8263:
8259:
8252:
8245:
8241:
8237:
8233:
8209:
8204:
8200:
8196:
8191:
8187:
8181:
8178:
8174:
8168:
8163:
8160:
8157:
8153:
8145:
8144:
8143:
8139:
8137:
8130:
8127:
8123:
8105:
8100:
8096:
8069:
8065:
8060:
8057:
8054:
8051:
8048:
8043:
8038:
8034:
8030:
8025:
8021:
8013:
8012:
8011:
8009:
8005:
8001:
7994:
7990:
7967:
7964:
7959:
7955:
7951:
7945:
7941:
7935:
7930:
7927:
7924:
7920:
7916:
7913:
7910:
7903:
7902:
7901:
7899:
7896:
7886:
7880:
7872:
7868:
7864:
7859:
7858:, is formed.
7844:
7836:
7828:
7793:
7789:
7779:
7777:
7769:
7766:
7761:
7759:
7751:
7747:
7742:
7733:
7712:
7708:
7687:
7683:
7664:
7660:
7654:
7650:
7644:
7640:
7636:
7622:
7611:
7603:
7585:
7581:
7560:
7556:
7537:
7533:
7527:
7523:
7517:
7513:
7509:
7495:
7484:
7476:
7475:
7474:
7454:
7451:
7433:
7429:
7425:
7420:
7393:
7389:
7385:
7382:
7357:
7353:
7349:
7335:
7324:
7316:
7299:
7272:
7268:
7264:
7239:
7235:
7231:
7217:
7206:
7198:
7197:
7196:
7192:
7185:
7178:
7173:
7138:
7127:
7116:
7113:
7098:
7085:
7074:
7066:
7042:
7031:
7016:
7003:
6992:
6984:
6983:
6982:
6980:
6976:
6973:, A, and the
6972:
6955:
6951:
6947:
6944:
6940:
6939:
6938:
6935:
6933:
6923:
6916:
6912:
6909:
6905:
6902:
6898:
6896:
6892:
6888:
6884:
6880:
6878:
6874:
6870:
6866:
6862:
6860:
6856:
6852:
6848:
6844:
6840:
6835:
6831:
6829:
6826:
6824:
6820:
6816:
6813:
6810:
6808:
6803:
6802:
6800:
6798:
6794:
6792:
6789:
6786:
6782:
6778:
6774:
6772:
6768:
6767:
6766:
6748:
6741:
6734:
6723:
6716:
6714:
6703:
6702:
6698:
6688:
6686:
6685:Manfred Eigen
6676:
6674:
6653:
6647:
6636:
6626:
6623:
6612:
6609:
6605:
6598:
6593:
6590:
6587:
6584:
6574:
6573:
6572:
6570:
6566:
6562:
6558:
6554:
6530:
6526:
6522:
6515:
6504:
6494:
6488:
6485:
6480:
6477:
6474:
6471:
6461:
6460:
6459:
6458:
6448:
6446:
6438:
6431:
6424:
6414:
6407:
6393:
6380: =
6376:
6363:
6350: =
6346:
6338:
6331:
6304:
6294:
6274:
6269:
6243:
6228:
6223:
6219:
6213:
6201:
6180:
6169:
6151:
6142:
6139:
6134:
6131:
6109:
6090:
6085:
6066:
6052:
6047:
6043:
6037:
6031:
6010:
5999:
5981:
5973:
5968:
5965:
5948:
5947:
5946:
5944:
5923:
5919:
5913:
5909:
5905:
5887:
5871:
5861:
5841:
5836:
5821:
5810:
5782:
5773:
5769:
5762:
5757:
5735:
5724:
5699:
5685:
5684:
5683:
5678:
5674:
5670:
5663:
5656:
5626:
5607:
5588:
5583:
5568:
5563:
5559:
5553:
5547:
5539:
5534:
5531:
5510:
5499:
5481:
5453:
5433:
5416:
5402:
5397:
5393:
5387:
5381:
5373:
5368:
5347:
5336:
5312:
5295:
5294:
5293:
5258:
5234:
5217:
5206:
5198:
5197:
5196:
5186:
5185:
5184:
5182:
5177:
5175:
5174:hydroxide ion
5168:
5163:
5158:
5154:
5150:
5149:hydronium ion
5125:
5106:
5094:
5083:
5075:
5074:
5073:
5059:
5058:
5057:
5056:
5028:
5024:
5009:
4996:
4974:
4964:
4946:
4939:
4926:
4907:
4904:
4897:
4896:
4895:
4866:
4845:
4832:
4810:
4800:
4782:
4775:
4762:
4743:
4732:
4724:
4723:
4695:
4694:
4693:
4690:
4682:
4680:
4677:
4646:
4645:
4644:
4642:
4638:
4634:
4629:
4627:
4623:
4604:
4603:
4602:
4600:
4593:
4589:
4585:
4578:
4565:
4562:
4556:
4532:
4527:
4516:
4508:
4507:
4506:
4504:
4503:
4497:
4493:
4489:
4482:
4458:
4453:
4449:
4443:
4439:
4433:
4428:
4425:
4422:
4418:
4412:
4409:
4404:
4401:
4394:
4393:
4392:
4390:
4382:
4374:
4364:
4347:
4344:
4341:
4338:
4335:
4332:
4328:
4312:
4307:
4303:
4300:
4297:
4294:
4291:
4286:
4282:
4278:
4274:
4258:
4253:
4249:
4246:
4243:
4240:
4237:
4232:
4228:
4224:
4221:
4214:
4213:
4212:
4210:
4206:
4202:
4198:
4194:
4189:
4187:
4183:
4179:
4175:
4171:
4168:
4164:
4134:
4130:
4124:
4121:
4118:
4113:
4100:
4092:
4079:
4071:
4068:
4065:
4060:
4047:
4039:
4026:
4017:
4011:
4008:
4005:
4000:
3982:
3964:
3961:
3958:
3953:
3935:
3916:
3913:
3906:
3905:
3904:
3902:
3898:
3891:
3881:
3860:
3857:
3852:
3849:
3846:
3841:
3835:
3832:
3827:
3824:
3818:
3782:
3778:
3767:
3758:
3754:
3736:
3733:
3728:
3725:
3722:
3717:
3711:
3708:
3703:
3700:
3694:
3658:
3654:
3643:
3622:
3609:
3605:
3594:
3590:
3583:
3574:
3570:
3559:
3555:
3548:
3542:
3531:
3522:
3518:
3500:
3484:
3472:
3466:
3462:
3459:
3456:
3453:
3450:
3445:
3442:
3439:
3434:
3428:
3425:
3420:
3417:
3411:
3384:
3381:
3377:
3373:
3370:
3367:
3364:
3361:
3358:
3353:
3349:
3305:
3301:
3298:
3295:
3292:
3289:
3284:
3280:
3264:
3259:
3256:
3253:
3248:
3242:
3239:
3234:
3231:
3225:
3213:
3210: ≠
3206:
3202:
3201:
3200:
3195:
3192: =
3191:
3184:
3181: =
3177:
3164:
3160:
3132:
3128:
3125:
3122:
3119:
3116:
3113:
3108:
3104:
3084:
3083:
3082:
3054:
3050:
3047:
3044:
3041:
3038:
3033:
3029:
3013:
3010:
3003:
3002:
3001:
2984:
2981:
2976:
2973:
2970:
2966:
2950:
2945:
2942:
2939:
2934:
2928:
2925:
2920:
2917:
2911:
2902:
2901:
2900:
2875:
2871:
2868:
2865:
2862:
2859:
2854:
2850:
2834:
2829:
2826:
2823:
2819:
2803:
2798:
2795:
2792:
2787:
2781:
2778:
2773:
2770:
2764:
2755:
2754:
2753:
2731:
2713:
2693:
2675:
2656:
2645:
2637:
2636:
2635:
2633:
2629:
2626:which is the
2607:
2603:
2587:
2582:
2578:
2572:
2567:
2563:
2557:
2552:
2549:
2546:
2542:
2534:
2515:
2497:
2477:
2459:
2440:
2437:
2434:
2431:
2428:
2423:
2419:
2413:
2408:
2404:
2398:
2393:
2390:
2387:
2383:
2379:
2374:
2371:
2368:
2364:
2344:
2343:
2342:
2310:
2307:
2304:
2301:
2298:
2295:
2281:
2278:
2275:
2272:
2269:
2263:
2246:
2243:
2240:
2237:
2234:
2231:
2217:
2214:
2211:
2208:
2205:
2199:
2191:
2180:
2176:
2173:
2168:
2157:
2153:
2147:
2139:
2128:
2124:
2121:
2116:
2105:
2101:
2095:
2090:
2087:
2084:
2080:
2060:
2059:
2058:
2031:
2027:
2024:
2013:
2009:
2006:
1995:
1991:
1988:
1977:
1973:
1970:
1965:
1962:
1959:
1955:
1935:
1934:
1933:
1932:
1911:
1908:
1905:
1901:
1885:
1880:
1876:
1870:
1866:
1860:
1855:
1852:
1849:
1845:
1841:
1836:
1833:
1830:
1825:
1819:
1816:
1811:
1808:
1802:
1793:
1792:
1791:
1789:
1768:
1764:
1755:
1751:
1743:
1718:
1714:
1710:
1705:
1701:
1695:
1690:
1687:
1684:
1680:
1676:
1673:
1670:
1667:
1664:
1661:
1658:
1655:
1652:
1649:
1646:
1639:
1638:
1637:
1635:
1631:
1626:
1624:
1612:
1581:
1578:
1575:
1572:
1569:
1564:
1559:
1555:
1551:
1540:
1532:
1531:
1530:
1528:
1524:
1520:
1519:
1490:
1486:
1483:
1472:
1468:
1465:
1454:
1450:
1447:
1436:
1432:
1425:
1424:
1423:
1420:
1416:
1412:
1385:
1382:
1377:
1374:
1371:
1366:
1360:
1357:
1352:
1349:
1343:
1334:
1333:
1332:
1330:
1326:
1322:
1318:
1314:
1310:
1306:
1302:
1297:
1295:
1291:
1286:
1284:
1280:
1276:
1272:
1267:
1265:
1261:
1257:
1253:
1249:
1239:
1237:
1233:
1226:
1222:
1215:
1211:
1207:
1203:
1202:concentration
1179:
1161:
1141:
1123:
1104:
1095:
1087:
1086:
1085:
1080:
1076:
1072:
1068:
1064:
1059:
1057:
1053:
1049:
1045:
1015:
1011:
1008:
1005:
1002:
999:
996:
991:
987:
981:
969:
968:
967:
965:
961:
957:
953:
949:
945:
941:
937:
933:
929:
925:
923:
918:
854:
841:
821:
808:
790:
785:
772:
757:
754:
747:
746:
745:
742:
737:
735:
731:
730:
725:
723:
683:
682:
681:
679:
675:
671:
667:
664:Although the
662:
659:
655:
649:
647:
643:
639:
635:
631:
623:
619:
618:stoichiometry
615:
611:
607:
603:
599:
575:
557:
537:
519:
500:
493:
489:
483:
479:
473:
468:
464:
456:
455:
454:
452:
431:
426:
418:
411:
406:
398:
391:
387:
383:
378:
373:
365:
358:
353:
345:
338:
334:
326:
325:
324:
322:
315:
308:
304:
303:active masses
279:
267:
255:
251:
247:
245:
229:
217:
205:
201:
197:
195:
177:
176:
175:
173:
169:
165:
161:
154:
150:
146:
142:
139:
138:
137:
135:
131:
130:
125:
124:
119:
118:
113:
112:
107:
103:
99:
95:
91:
87:
83:
73:
71:
67:
63:
59:
55:
51:
47:
43:
39:
33:
19:
10534:Vapor–liquid
10421:Applications
10290:
10236:. Wiley-VCH.
10233:
10224:
10214:
10193:
10162:
10156:
10144:. Retrieved
10140:the original
10130:
10118:
10104:
10095:
10089:
10078:the original
10043:
10031:. Retrieved
10019:
10006:
9995:. Retrieved
9991:
9982:
9973:
9967:
9948:
9922:
9916:
9905:. Retrieved
9898:the original
9872:
9866:
9858:
9853:
9828:
9824:
9818:
9796:(10): 1391.
9793:
9789:
9783:
9775:
9770:
9751:
9745:
9740:directions.)
9722:
9716:
9711:
9699:
9686:
9663:
9658:
9651:
9630:
9622:
9603:
9569:
9510:
9435:
9423:
9421:
9117:
8921:
8846:
8839:
8835:
8830:where ν
8829:
8756:
8754:
8738:
8731:
8724:
8720:
8716:
8712:
8708:
8702:
8453:
8446:
8439:
8437:
8289:
8277:optimisation
8274:
8265:
8261:
8257:
8250:
8243:
8239:
8238:in molecule
8235:
8228:
8226:
8140:
8132:
8128:
8126:gas constant
8121:
8087:
8003:
7996:
7992:
7983:where μ
7982:
7897:
7892:
7860:
7785:
7762:
7755:
7731:
7472:
7190:
7183:
7176:
7174:
7167:
6964:
6950:mass balance
6936:
6929:
6920:
6906:The related
6819:Ion exchange
6806:
6763:
6682:
6672:
6670:
6568:
6560:
6556:
6555:reactions (Δ
6550:
6454:
6436:
6429:
6422:
6412:
6405:
6391:
6374:
6361:
6344:
6336:
6329:
6328:
5940:
5676:
5672:
5668:
5661:
5654:
5653:
5283:
5194:
5178:
5166:
5164:
5156:
5146:
5071:
5052:
4893:
4691:
4688:
4673:
4630:
4619:
4571:
4563:
4554:
4552:
4501:
4495:
4491:
4484:
4477:
4475:
4370:
4362:
4204:
4190:
4185:
4181:
4177:
4160:
3900:
3889:
3887:
3879:
3756:
3520:
3211:
3204:
3193:
3189:
3182:
3175:
3173:
3158:
3080:
3000:leading to:
2999:
2898:
2751:
2627:
2625:
2340:
2056:
1930:
1928:
1787:
1745:
1738:
1736:
1630:Gibbs energy
1627:
1622:
1610:
1608:
1517:
1514:
1414:
1410:
1408:
1328:
1324:
1312:
1304:
1298:
1289:
1287:
1271:geochemistry
1268:
1263:
1259:
1251:
1245:
1228:
1223:varies with
1217:
1212:are usually
1199:
1078:
1074:
1060:
1051:
1043:
1041:
926:
919:
884:
741:mineral acid
738:
733:
727:
726:
718:
663:
650:
609:
595:
448:
313:
306:
300:
162:
158:
152:
148:
144:
140:
128:
122:
116:
110:
79:
41:
35:
10539:Henry's law
10330:Free energy
10033:November 2,
10020:Nobel Prize
9736:H + Cl Na .
8279:, known as
7869:ion Ni and
7863:hydrophobic
7788:precipitate
6942:conditions.
6899:In certain
6565:endothermic
4633:bicarbonate
4613:⇌ 2 SO
2752:Therefore,
1636:to produce
1405:equilibrium
1056:temperature
928:J. W. Gibbs
670:acetic acid
666:macroscopic
656:. Adding a
10556:Categories
10522:Solubility
10493:Hydrolysis
10402:Phase rule
10146:October 5,
9997:2019-11-02
9907:2007-05-16
9831:(3): 203.
9694:balanced.)
9549:References
8746:activities
8438:where the
7768:Lewis acid
7746:hydrolysis
6855:indicators
6847:hydrolysis
6834:hemoglobin
6785:adsorption
6746:(adsorbed)
6732:(adsorbed)
6713:(adsorbed)
6553:exothermic
6551:Thus, for
4588:metastable
3899:quotient,
3523:increases
1737:Inserting
1214:determined
646:sufficient
151: S +
147: B ⇌
143: A +
94:reversible
86:Berthollet
30:See also:
10510:Partition
10340:Helmholtz
10310:Chelation
9456:Alkalosis
9391:
9374:⊖
9366:Δ
9347:ν
9308:∏
9299:
9282:⊖
9274:Δ
9243:
9226:⊖
9217:μ
9204:ν
9183:∑
9170:μ
9160:ν
9139:∑
9129:Δ
9097:μ
9087:ν
9066:∑
9040:λ
9030:ν
9009:∑
8988:∑
8975:μ
8965:ν
8944:∑
8895:ν
8861:∑
8793:ν
8772:∑
8673:−
8630:∑
8614:λ
8610:∂
8598:∂
8549:λ
8528:∑
8515:μ
8495:∂
8483:∂
8397:−
8354:∑
8339:λ
8318:∑
8154:∑
8106:⊖
8097:μ
8061:
8044:⊖
8035:μ
8022:μ
7942:μ
7921:∑
7879:solvation
7765:aluminium
7750:aluminium
7661:β
7641:∑
7534:β
7514:∑
7452:−
7426:−
7390:β
7354:β
7269:β
7236:β
7139:−
6932:ICE table
6787:processes
6648:⊖
6633:Δ
6627:−
6610:−
6591:
6516:⊖
6501:Δ
6478:
6421:log
6404:log
6275:−
6220:β
6188:⇀
6181:−
6170:−
6163:↽
6135:−
6091:−
6067:−
6044:β
6032:−
6018:⇀
6011:−
6000:−
5993:↽
5969:−
5842:−
5811:β
5763:−
5743:⇀
5736:−
5725:−
5718:↽
5627:−
5589:−
5535:−
5518:⇀
5511:−
5500:−
5493:↽
5482:−
5417:−
5369:−
5355:⇀
5348:−
5337:−
5330:↽
5153:solvation
5126:−
4947:−
4783:−
4656:O ⇌ HCO
4605:2 SO
4553:However,
4536:Γ
4419:∑
4348:γ
4345:
4304:
4287:⊖
4283:μ
4250:
4233:⊖
4229:μ
4222:μ
4146:Γ
4114:β
4101:γ
4093:α
4080:γ
4061:τ
4048:γ
4040:σ
4027:γ
4018:×
4001:β
3983:α
3954:τ
3936:σ
3836:ξ
3712:ξ
3606:ν
3584:∏
3571:ν
3549:∏
3463:
3429:ξ
3374:
3362:−
3354:⊖
3338:Δ
3302:
3285:⊖
3269:Δ
3243:ξ
3129:
3117:−
3109:⊖
3093:Δ
3051:
3034:⊖
3018:Δ
2955:Δ
2929:ξ
2872:
2855:⊖
2839:Δ
2808:Δ
2782:ξ
2732:β
2714:α
2694:τ
2676:σ
2608:⊖
2592:Δ
2579:ν
2573:⊖
2564:μ
2543:∑
2516:β
2498:α
2478:τ
2460:σ
2441:
2420:ν
2414:⊖
2405:μ
2384:∑
2353:Δ
2311:
2299:β
2282:
2270:α
2264:−
2247:
2235:τ
2218:
2206:σ
2192:⊖
2181:μ
2177:β
2169:⊖
2158:μ
2154:α
2148:−
2140:⊖
2129:μ
2125:τ
2117:⊖
2106:μ
2102:σ
2069:Δ
2032:μ
2028:β
2025:−
2014:μ
2010:α
2007:−
1996:μ
1992:τ
1978:μ
1974:σ
1944:Δ
1890:Δ
1877:ν
1867:μ
1846:∑
1820:ξ
1765:ν
1702:μ
1681:∑
1665:−
1582:
1565:⊖
1556:μ
1541:μ
1491:μ
1487:τ
1473:μ
1469:σ
1455:μ
1451:β
1437:μ
1433:α
1361:ξ
1210:solutions
1180:β
1162:α
1142:τ
1124:σ
1063:dissolved
1012:
1000:−
992:⊖
978:Δ
791:−
678:hydronium
598:numerator
576:β
558:α
538:τ
520:σ
494:−
432:τ
412:σ
392:−
379:β
359:α
280:τ
268:σ
256:−
230:β
218:α
46:reactants
10503:of water
10298:Concepts
10024:Archived
9728:HCl + NO
9689:( … the
9451:Acidosis
9444:See also
8730:and the
8290:Define:
7794:Al(OH),
6836:in blood
5669:stepwise
5060:2 H
4622:catalyst
4209:real gas
1750: dξ
1744: =
1527:activity
697:O ⇌ CH
658:catalyst
636:to form
630:hydrogen
612:because
164:Guldberg
132:are the
106:reactant
50:products
9833:Bibcode
9798:Bibcode
9732:Na ⇌ NO
9707:. See:
9576:200–202
9541:UNIQUAC
9429:is the
8124:is the
7987:is the
7873:, (dmgH
7748:of the
6779:in the
6777:ammonia
6728:(g) ⇌ H
6708:(g) ⇌ N
6399:
6382:
6369:
6352:
5673:overall
4201:ammonia
3895:and an
1621:is the
1609:(where
1046:is the
934:of the
674:acetate
634:bromine
608:and is
155: T
82:concept
10372:Models
10191:about
10169:
9955:
9758:
9677:+ CaCl
9610:
9582:
9422:where
8454:λ
8227:where
8088:where
7995:, and
7867:nickel
7848:Al(OH)
7824:Al(OH)
7168:with T
6975:proton
5068:O + OH
4708:O ⇌ CH
4676:enzyme
4476:where
4387:. The
4383:, KClO
4375:, NaNO
3864:
3797:
3740:
3673:
3620:
3505:
3390:
3317:
1774:
1515:where
1389:
1042:where
680:ions,
126:, and
64:. The
58:system
10335:Gibbs
10081:(PDF)
10074:(PDF)
10027:(PDF)
10016:(PDF)
9901:(PDF)
9894:(PDF)
9715:[
9662:[
9627:IUPAC
5064:O ⇌ H
4704:H + H
4652:+ 2 H
4641:water
4635:from
4379:, or
3402:then
885:If {H
693:H + H
168:Waage
98:rates
36:In a
10167:ISBN
10148:2019
10124:HySS
10035:2019
9953:ISBN
9756:ISBN
9608:ISBN
9580:ISBN
8452:and
8242:and
8010:as:
7812:(OH)
7806:and
7796:AlOH
7772:(aq)
6805:log
6419:and
6372:and
6335:and
4639:and
4579:and
4483:and
3858:>
3809:and
3779:>
3734:<
3685:and
3655:<
3329:and
3081:and
1273:and
1054:the
1050:and
948:zero
676:and
632:and
624:by S
319:are
312:and
305:and
166:and
92:are
80:The
48:and
9841:doi
9806:doi
9641:doi
9639:".
9496:pCO
6757:(g)
5660:and
5191:+ C
4716:+ H
4665:+ H
4609:+ O
4586:is
4172:or
1625:).
739:If
710:+ H
10558::
10057:^
10022:.
10018:.
9990:.
9951:.
9947:.
9931:^
9881:^
9839:.
9829:67
9827:.
9804:.
9794:76
9792:.
9673:CO
9669:Na
9629:,
9594:^
9578:.
9556:^
9504:pH
9440:.
9388:ln
9296:ln
9240:ln
8270:ij
8231:ij
8058:ln
7885:.
7818:32
7815:7+
7810:13
7808:Al
7770:Al
6893:,
6889:,
6885:,
6875:,
6871:,
6867:,
6857:,
6853:,
6849:,
6845:,
6821:,
6817:,
6749:NH
6588:ln
6475:ln
6447:.
6402:;
6063:HA
6028:HA
5623:HA
5478:HA
5413:HA
5365:HA
5183::
5176:.
4712:CO
4700:CO
4696:CH
4681:.
4648:CO
4601:.
4596:SO
4574:SO
4342:ln
4301:ln
4247:ln
3903:.
3460:ln
3371:ln
3299:ln
3215:eq
3199:.
3197:eq
3188:;
3186:eq
3126:ln
3048:ln
2869:ln
2438:ln
2308:ln
2279:ln
2244:ln
2215:ln
1788:dξ
1739:dN
1579:ln
1317:xi
1311::
1303:,
1296:.
1258:,
1250:,
1084:,
1077:,
1058:.
1009:ln
924:.
903:CO
899:CH
893:CO
851:CO
838:CH
782:CO
769:CH
701:CO
689:CO
685:CH
453:.
174::
120:,
114:,
72:.
40:,
10283:e
10276:t
10269:v
10175:.
10150:.
10112:.
10051:.
10037:.
10000:.
9961:.
9910:.
9847:.
9843::
9835::
9812:.
9808::
9800::
9764:.
9734:3
9730:3
9683:3
9679:2
9675:3
9671:2
9643::
9616:.
9588:.
9514:a
9511:K
9509:p
9498:2
9426:c
9424:K
9407:)
9402:c
9398:K
9394:(
9385:T
9382:R
9379:+
9370:G
9363:=
9359:)
9351:j
9342:}
9336:j
9332:R
9328:{
9323:m
9318:1
9315:=
9312:j
9303:(
9293:T
9290:R
9287:+
9278:G
9271:=
9268:)
9265:)
9262:}
9257:j
9253:R
9249:{
9246:(
9237:T
9234:R
9231:+
9221:j
9213:(
9208:j
9198:m
9193:1
9190:=
9187:j
9179:=
9174:j
9164:j
9154:m
9149:1
9146:=
9143:j
9135:=
9132:G
9101:j
9091:j
9081:m
9076:1
9073:=
9070:j
9062:=
9057:j
9054:i
9050:a
9044:i
9034:j
9024:k
9019:1
9016:=
9013:i
9003:m
8998:1
8995:=
8992:j
8984:+
8979:j
8969:j
8959:m
8954:1
8951:=
8948:j
8940:=
8937:0
8924:j
8907:0
8904:=
8899:j
8889:j
8886:i
8882:a
8876:m
8871:1
8868:=
8865:j
8847:j
8842:j
8840:R
8836:j
8832:j
8815:0
8812:=
8807:j
8803:R
8797:j
8787:m
8782:0
8779:=
8776:j
8757:k
8741:j
8739:N
8734:i
8732:λ
8727:j
8725:N
8721:k
8717:m
8713:k
8709:m
8686:0
8681:i
8677:b
8668:j
8664:N
8658:j
8655:i
8651:a
8645:m
8640:1
8637:=
8634:j
8626:=
8618:i
8603:G
8592:=
8589:0
8566:j
8563:i
8559:a
8553:i
8543:k
8538:1
8535:=
8532:i
8524:+
8519:j
8511:=
8503:j
8499:N
8488:G
8477:=
8474:0
8456:j
8449:j
8447:N
8442:i
8440:λ
8423:0
8420:=
8416:)
8410:0
8405:i
8401:b
8392:j
8388:N
8382:j
8379:i
8375:a
8369:m
8364:1
8361:=
8358:j
8349:(
8343:i
8333:k
8328:1
8325:=
8322:i
8314:+
8311:G
8308:=
8303:G
8266:k
8262:k
8258:i
8251:i
8244:b
8240:j
8236:i
8229:a
8210:0
8205:i
8201:b
8197:=
8192:j
8188:N
8182:j
8179:i
8175:a
8169:m
8164:1
8161:=
8158:j
8135:j
8133:A
8129:T
8122:R
8101:j
8070:j
8066:A
8055:T
8052:R
8049:+
8039:j
8031:=
8026:j
8004:j
7999:j
7997:N
7993:j
7985:j
7968:0
7965:=
7960:j
7956:N
7952:d
7946:j
7936:m
7931:1
7928:=
7925:j
7917:=
7914:G
7911:d
7898:G
7883:2
7875:2
7854:4
7851:−
7839:3
7831:3
7826:3
7802:2
7799:+
7758:p
7752:.
7713:i
7709:q
7704:]
7699:B
7695:[
7688:i
7684:p
7679:]
7674:A
7670:[
7665:i
7655:i
7651:q
7645:i
7637:+
7634:]
7630:B
7626:[
7623:=
7617:B
7612:T
7586:i
7582:q
7577:]
7572:B
7568:[
7561:i
7557:p
7552:]
7547:A
7543:[
7538:i
7528:i
7524:p
7518:i
7510:+
7507:]
7503:A
7499:[
7496:=
7490:A
7485:T
7455:1
7448:]
7443:H
7439:[
7434:w
7430:K
7421:2
7416:]
7413:H
7410:[
7407:]
7404:A
7401:[
7394:2
7386:2
7383:+
7379:]
7376:H
7373:[
7370:]
7367:A
7364:[
7358:1
7350:+
7346:]
7343:H
7340:[
7336:=
7330:H
7325:T
7300:2
7295:]
7292:H
7289:[
7286:]
7283:A
7280:[
7273:2
7265:+
7261:]
7258:H
7255:[
7252:]
7249:A
7246:[
7240:1
7232:+
7228:]
7225:A
7222:[
7218:=
7212:A
7207:T
7194:w
7191:K
7187:2
7184:β
7180:1
7177:β
7170:A
7151:]
7148:H
7145:O
7142:[
7136:]
7133:A
7128:2
7124:H
7120:[
7117:2
7114:+
7111:]
7108:A
7105:H
7102:[
7099:+
7096:]
7093:H
7090:[
7086:=
7080:H
7075:T
7051:]
7048:A
7043:2
7039:H
7035:[
7032:+
7029:]
7026:A
7023:H
7020:[
7017:+
7014:]
7011:A
7008:[
7004:=
6998:A
6993:T
6967:2
6956:.
6917:.
6807:D
6755:3
6751:3
6744:3
6737:2
6735:H
6730:2
6726:2
6724:H
6719:2
6717:N
6710:2
6706:2
6704:N
6673:K
6654:R
6642:m
6637:H
6624:=
6618:)
6613:1
6606:T
6602:(
6599:d
6594:K
6585:d
6569:K
6561:K
6557:H
6531:2
6527:T
6523:R
6510:m
6505:H
6495:=
6489:T
6486:d
6481:K
6472:d
6440:1
6437:K
6433:2
6430:K
6426:2
6423:β
6416:2
6413:K
6409:1
6406:β
6395:D
6392:β
6388:/
6385:1
6378:2
6375:β
6365:2
6362:K
6358:/
6355:1
6348:1
6345:β
6340:2
6337:β
6333:1
6330:β
6305:2
6300:]
6295:+
6291:H
6287:[
6281:]
6270:2
6266:A
6262:[
6255:]
6252:A
6244:2
6240:H
6236:[
6229:=
6224:2
6214::
6210:A
6202:2
6198:H
6152:+
6148:H
6143:2
6140:+
6132:2
6128:A
6115:]
6110:+
6106:H
6102:[
6097:]
6086:2
6082:A
6078:[
6071:]
6060:[
6053:=
6048:1
6038::
5982:+
5978:H
5974:+
5966:2
5962:A
5924:2
5920:K
5914:1
5910:K
5906:=
5899:]
5896:A
5888:2
5884:H
5880:[
5872:2
5867:]
5862:+
5858:H
5854:[
5848:]
5837:2
5833:A
5829:[
5822:=
5816:D
5799::
5783:+
5779:H
5774:2
5770:+
5758:2
5754:A
5708:A
5700:2
5696:H
5680:D
5677:β
5665:2
5662:K
5658:1
5655:K
5631:]
5620:[
5613:]
5608:+
5604:H
5600:[
5595:]
5584:2
5580:A
5576:[
5569:=
5564:2
5560:K
5554::
5548:+
5544:H
5540:+
5532:2
5528:A
5465:]
5462:A
5454:2
5450:H
5446:[
5439:]
5434:+
5430:H
5426:[
5421:]
5410:[
5403:=
5398:1
5394:K
5388::
5382:+
5378:H
5374:+
5321:A
5313:2
5309:H
5290:2
5286:2
5259:2
5255:]
5251:O
5248:C
5245:[
5240:]
5235:2
5231:O
5227:C
5224:[
5218:=
5212:c
5207:K
5189:2
5170:w
5167:K
5160:w
5157:K
5131:]
5122:H
5118:O
5115:[
5112:]
5107:+
5103:H
5099:[
5095:=
5089:w
5084:K
5066:3
5062:2
5049:.
5034:c
5029:K
5025:=
5019:]
5015:H
5010:2
5006:O
5002:C
4997:3
4993:H
4989:C
4985:[
4980:]
4975:+
4970:O
4965:3
4961:H
4955:[
4952:]
4940:2
4936:O
4932:C
4927:3
4923:H
4919:C
4914:[
4908:=
4905:K
4876:]
4872:O
4867:2
4863:H
4858:[
4855:]
4851:H
4846:2
4842:O
4838:C
4833:3
4829:H
4825:C
4821:[
4816:]
4811:+
4806:O
4801:3
4797:H
4791:[
4788:]
4776:2
4772:O
4768:C
4763:3
4759:H
4755:C
4750:[
4744:=
4738:c
4733:K
4720:O
4718:3
4714:2
4710:3
4706:2
4702:2
4698:3
4669:O
4667:3
4662:3
4659:−
4654:2
4650:2
4615:3
4611:2
4607:2
4598:3
4583:2
4581:O
4576:2
4558:c
4555:K
4533:K
4528:=
4522:c
4517:K
4502:Γ
4496:N
4492:i
4487:i
4485:z
4480:i
4478:c
4459:2
4454:i
4450:z
4444:i
4440:c
4434:N
4429:1
4426:=
4423:i
4413:2
4410:1
4405:=
4402:I
4385:4
4377:3
4339:T
4336:R
4333:+
4329:)
4323:r
4320:a
4317:b
4313:p
4308:(
4298:T
4295:R
4292:+
4279:=
4275:)
4269:r
4266:a
4263:b
4259:f
4254:(
4244:T
4241:R
4238:+
4225:=
4205:f
4178:Γ
4140:c
4135:K
4131:=
4125:.
4122:.
4119:.
4106:B
4085:A
4072:.
4069:.
4066:.
4053:T
4032:S
4012:.
4009:.
4006:.
3997:]
3992:B
3988:[
3979:]
3974:A
3970:[
3965:.
3962:.
3959:.
3950:]
3945:T
3941:[
3932:]
3927:S
3923:[
3917:=
3914:K
3901:Γ
3893:c
3890:K
3861:0
3853:p
3850:,
3847:T
3842:)
3833:d
3828:G
3825:d
3819:(
3791:q
3788:e
3783:K
3773:r
3768:Q
3757:j
3737:0
3729:p
3726:,
3723:T
3718:)
3709:d
3704:G
3701:d
3695:(
3667:q
3664:e
3659:K
3649:r
3644:Q
3623:,
3610:i
3601:)
3595:i
3591:a
3587:(
3575:j
3566:)
3560:j
3556:a
3552:(
3543:=
3537:r
3532:Q
3521:i
3501:)
3493:q
3490:e
3485:K
3478:r
3473:Q
3467:(
3457:T
3454:R
3451:=
3446:p
3443:,
3440:T
3435:)
3426:d
3421:G
3418:d
3412:(
3385:q
3382:e
3378:K
3368:T
3365:R
3359:=
3350:G
3343:r
3311:r
3306:Q
3296:T
3293:R
3290:+
3281:G
3274:r
3265:=
3260:p
3257:,
3254:T
3249:)
3240:d
3235:G
3232:d
3226:(
3212:K
3208:r
3205:Q
3194:ξ
3190:ξ
3183:K
3179:r
3176:Q
3141:q
3138:e
3133:K
3123:T
3120:R
3114:=
3105:G
3098:r
3063:q
3060:e
3055:K
3045:T
3042:R
3039:+
3030:G
3023:r
3014:=
3011:0
2985:0
2982:=
2977:p
2974:,
2971:T
2967:G
2960:r
2951:=
2946:p
2943:,
2940:T
2935:)
2926:d
2921:G
2918:d
2912:(
2881:r
2876:Q
2866:T
2863:R
2860:+
2851:G
2844:r
2835:=
2830:p
2827:,
2824:T
2820:G
2813:r
2804:=
2799:p
2796:,
2793:T
2788:)
2779:d
2774:G
2771:d
2765:(
2728:}
2723:B
2719:{
2710:}
2705:A
2701:{
2690:}
2685:T
2681:{
2672:}
2667:S
2663:{
2657:=
2651:r
2646:Q
2622::
2604:G
2597:r
2588:=
2583:i
2568:i
2558:k
2553:1
2550:=
2547:i
2512:}
2507:B
2503:{
2494:}
2489:A
2485:{
2474:}
2469:T
2465:{
2456:}
2451:S
2447:{
2435:T
2432:R
2429:+
2424:i
2409:i
2399:k
2394:1
2391:=
2388:i
2380:=
2375:p
2372:,
2369:T
2365:G
2358:r
2337:,
2325:)
2322:}
2318:B
2314:{
2305:T
2302:R
2296:+
2293:}
2289:A
2285:{
2276:T
2273:R
2267:(
2261:)
2258:}
2254:T
2250:{
2241:T
2238:R
2232:+
2229:}
2225:S
2221:{
2212:T
2209:R
2203:(
2200:+
2197:)
2186:B
2174:+
2163:A
2151:(
2145:)
2134:T
2122:+
2111:S
2099:(
2096:=
2091:p
2088:,
2085:T
2081:G
2074:r
2053:.
2037:B
2019:A
2001:T
1989:+
1983:S
1971:=
1966:p
1963:,
1960:T
1956:G
1949:r
1912:p
1909:,
1906:T
1902:G
1895:r
1886:=
1881:i
1871:i
1861:k
1856:1
1853:=
1850:i
1842:=
1837:p
1834:,
1831:T
1826:)
1817:d
1812:G
1809:d
1803:(
1769:i
1756:(
1748:i
1746:ν
1741:i
1733:.
1719:i
1715:N
1711:d
1706:i
1696:k
1691:1
1688:=
1685:i
1677:+
1674:T
1671:d
1668:S
1662:p
1659:d
1656:V
1653:=
1650:G
1647:d
1617:A
1611:μ
1593:}
1589:A
1585:{
1576:T
1573:R
1570:+
1560:A
1552:=
1546:A
1518:μ
1496:T
1484:+
1478:S
1466:=
1460:B
1448:+
1442:A
1415:ξ
1411:G
1401::
1386:0
1383:=
1378:p
1375:,
1372:T
1367:)
1358:d
1353:G
1350:d
1344:(
1329:ξ
1325:G
1313:ξ
1305:G
1264:S
1260:A
1252:G
1231:p
1229:K
1220:c
1218:K
1176:]
1171:B
1167:[
1158:]
1153:A
1149:[
1138:]
1133:T
1129:[
1120:]
1115:S
1111:[
1105:=
1100:c
1096:K
1082:c
1079:K
1052:T
1044:R
1024:q
1021:e
1016:K
1006:T
1003:R
997:=
988:G
982:r
915:2
909:2
906:−
901:3
895:2
891:3
887:3
866:}
863:H
855:2
842:3
834:{
828:}
822:+
818:O
809:3
805:H
800:{
797:}
786:2
773:3
764:{
758:=
755:K
714:O
712:3
707:2
704:−
699:3
695:2
691:2
687:3
626:N
572:}
567:B
563:{
554:}
549:A
545:{
534:}
529:T
525:{
516:}
511:S
507:{
501:=
490:k
484:+
480:k
474:=
469:c
465:K
427:}
423:T
419:{
407:}
403:S
399:{
388:k
384:=
374:}
370:B
366:{
354:}
350:A
346:{
339:+
335:k
317:−
314:k
310:+
307:k
275:T
263:S
252:k
248:=
225:B
213:A
206:+
202:k
198:=
153:τ
149:σ
145:β
141:α
129:τ
123:σ
117:β
111:α
20:)
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