171:, then the solution will be almost ideal. Since the interaction energies between A and B are almost equal, it follows that there is only a very small overall energy (enthalpy) change when the substances are mixed. The more dissimilar the nature of A and B, the more strongly the solution is expected to deviate from ideality.
2790:
1306:
822:
2184:
2543:
1693:
2051:
538:
3889:
1966:
1122:
1490:
3620:
4363:
In contrast to ideal solutions, where volumes are strictly additive and mixing is always complete, the volume of a non-ideal solution is not, in general, the simple sum of the volumes of the component pure liquids and
830:
However, the vapor above the solution may not actually behave as a mixture of ideal gases. Some authors therefore define an ideal solution as one for which each component obeys the fugacity analogue of Raoult's law
3057:
1385:
3392:
1127:
this definition leads to ideal values of the chemical potential and other thermodynamic properties even when the component vapors above the solution are not ideal gases. An equivalent statement uses thermodynamic
3500:
3299:
3218:
2327:
3961:
2868:
1191:
633:
93:, with the important difference that intermolecular interactions in liquids are strong and cannot simply be neglected as they can for ideal gases. Instead we assume that the mean strength of the
4225:
4129:
3135:
2398:
1758:
which means that the partial molar volumes in an ideal mix are independent of composition. Consequently, the total volume is the sum of the volumes of the components in their pure forms:
2960:
2527:
2785:{\displaystyle {\bar {g_{i}}}=\mu _{i}=g_{i}^{\mathrm {gas} }+RT\ln {\frac {f_{i}}{p^{u}}}=g_{i}^{\mathrm {gas} }+RT\ln {\frac {f_{i}^{*}}{p^{u}}}+RT\ln x_{i}=\mu _{i}^{*}+RT\ln x_{i}}
2458:
2059:
2241:
1753:
4268:
1810:
884:
235:
3402:
Solvent–solute interactions are the same as solute–solute and solvent–solvent interactions, on average. Consequently, the enthalpy of mixing (solution) is zero and the change in
1585:
374:
This definition depends on vapor pressure, which is a directly measurable property, at least for volatile components. The thermodynamic properties may then be obtained from the
1573:
4033:
3781:
3748:
3715:
1974:
967:
349:
4316:
394:
179:
Different related definitions of an ideal solution have been proposed. The simplest definition is that an ideal solution is a solution for which each component obeys
3650:
2898:
911:
625:
595:
568:
313:
262:
4354:. A single Margules parameter may be sufficient to describe the properties of the solution if the deviations from ideality are modest; such solutions are termed
50:
is zero as is the volume change on mixing by definition; the closer to zero the enthalpy of mixing is, the more "ideal" the behavior of the solution becomes. The
4336:
4288:
4152:
4053:
4001:
3981:
3670:
1838:
1537:
1513:
1408:
1183:
1163:
987:
935:
369:
286:
3800:
1850:
995:
1416:
4936:
4512:
3511:
139:
and the longer-range interactions must be nil (or at least indistinguishable). If the molecular forces are the same between AA, AB and BB, i.e.,
2968:
1317:
3305:
4638:
3416:
3225:
3140:
2249:
2903:
3897:
1301:{\displaystyle \left({\frac {\partial g(T,P)}{\partial P}}\right)_{T}=RT\left({\frac {\partial \ln f}{\partial P}}\right)_{T}.}
2801:
817:{\displaystyle \mu (T,p_{i})=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {p_{i}^{*}}{p^{u}}}+RT\ln x_{i}=\mu _{i}^{*}+RT\ln x_{i}.}
4164:
4061:
4497:
4453:
4683:
4476:
3069:
2332:
5007:
4631:
2179:{\displaystyle -{\frac {{\bar {h_{i}}}-h_{i}^{\mathrm {gas} }}{R}}=-{\frac {h_{i}^{*}-h_{i}^{\mathrm {gas} }}{R}}}
2469:
4773:
2406:
2192:
1704:
17:
4926:
4233:
1764:
1688:{\displaystyle \left({\frac {\partial \ln f_{i}}{\partial P}}\right)_{T,x_{i}}={\frac {\bar {v_{i}}}{RT}}.}
834:
185:
4856:
4624:
4911:
827:
This equation for the chemical potential can be used as an alternate definition for an ideal solution.
4803:
1542:
4788:
4723:
4006:
2046:{\displaystyle \left({\frac {\partial {\frac {g}{T}}}{\partial T}}\right)_{P}=-{\frac {h}{T^{2}}}}
100:
More formally, for a mix of molecules of A and B, then the interactions between unlike neighbors (
5002:
4743:
4406:
4401:
74:
3753:
533:{\displaystyle \mu (T,p_{i})=g(T,p_{i})=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {p_{i}}{p^{u}}}.}
4841:
4836:
4693:
4445:
4369:
3720:
3675:
940:
379:
322:
78:
4941:
4921:
4293:
1495:
Since all this, done as a pure substance, is valid in an ideal mix just adding the subscript
4437:
4655:
4647:
4381:
4351:
3628:
2876:
1576:
1129:
889:
603:
573:
546:
291:
240:
94:
63:
39:
8:
4768:
4738:
3884:{\displaystyle \Delta G_{\mathrm {m,mix} }=\sum _{i}x_{i}\Delta \mu _{i,\mathrm {mix} }}
1961:{\displaystyle {\frac {g(T,P)-g^{\mathrm {gas} }(T,p^{u})}{RT}}=\ln {\frac {f}{p^{u}}}.}
4997:
4416:
4321:
4273:
4137:
4038:
3986:
3966:
3791:
3655:
1823:
1522:
1516:
1498:
1393:
1168:
1148:
1117:{\displaystyle \mu (T,P)=g(T,P)=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {f_{i}}{p^{u}}}}
972:
920:
375:
354:
271:
47:
1485:{\displaystyle \left({\frac {\partial \ln f}{\partial P}}\right)_{T}={\frac {v}{RT}}.}
4946:
4905:
4808:
4493:
4472:
4449:
4438:
4411:
4391:
4386:
4347:
3407:
3403:
3063:
4522:
4881:
4876:
4708:
4668:
4526:
4517:
4396:
4356:
3625:
where m denotes molar, i.e., change in Gibbs free energy per mole of solution, and
2243:
and that the enthalpy of the mix is equal to the sum of its component enthalpies.
4866:
4851:
4783:
4748:
4733:
4728:
4713:
4678:
4368:
is not guaranteed over the whole composition range. By measurement of densities,
4155:
180:
55:
4916:
4871:
4861:
4778:
4673:
265:
70:
59:
51:
4488:
Felder, Richard M.; Rousseau, Ronald W.; Bullard, Lisa G. (15 December 2004).
4991:
4961:
4798:
4758:
4703:
4521:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
3615:{\displaystyle \Delta G_{\mathrm {m,mix} }=RT(x_{A}\ln x_{A}+x_{B}\ln x_{B})}
316:
66:(which measures deviation from ideality) is equal to one for each component.
4530:
4818:
4813:
1698:
Applying the first equation of this section to this last equation we find:
382:
42:
that exhibits thermodynamic properties analogous to those of a mixture of
4971:
4886:
3052:{\displaystyle \Delta G_{\mathrm {m,mix} }=RT\sum _{i}{x_{i}\ln x_{i}}.}
1380:{\displaystyle \left({\frac {\partial g(T,P)}{\partial P}}\right)_{T}=v}
4966:
4956:
4951:
4828:
4365:
3672:. Note that this free energy of mixing is always negative (since each
3387:{\displaystyle \Delta S_{\mathrm {m,mix} }=-R\sum _{i}x_{i}\ln x_{i}.}
1820:
Proceeding in a similar way but taking the derivative with respect to
4976:
4931:
4846:
4616:
3495:{\displaystyle \Delta G_{\mathrm {m,mix} }=RT\sum _{i}x_{i}\ln x_{i}}
168:
164:
90:
43:
989:
as a pure substance. Since the fugacity is defined by the equation
4793:
1841:
914:
4436:
Felder, Richard M.; Rousseau, Ronald W.; Bullard, Lisa G. (2005).
4896:
4698:
4688:
3294:{\displaystyle \Delta s_{i,\mathrm {mix} }=-R\sum _{i}\ln x_{i}}
597:= 1 bar, or as the pressure of the mix, whichever is simpler.
4718:
3213:{\displaystyle {\bar {g_{i}}}={\bar {h_{i}}}-T{\bar {s_{i}}}}
2322:{\displaystyle {\bar {u_{i}}}={\bar {h_{i}}}-p{\bar {v_{i}}}}
3956:{\displaystyle \Delta \mu _{i,\mathrm {mix} }=RT\ln x_{i}}
4346:
Deviations from ideality can be described by the use of
2863:{\displaystyle \Delta g_{i,\mathrm {mix} }=RT\ln x_{i}.}
163:
If the molecules are almost identical chemically, e.g.,
97:
are the same between all the molecules of the solution.
69:
The concept of an ideal solution is fundamental to both
1145:
If we differentiate this last equation with respect to
1311:
Since we know from the Gibbs potential equation that:
4487:
4435:
4324:
4296:
4276:
4236:
4167:
4140:
4064:
4041:
4009:
3989:
3969:
3900:
3803:
3756:
3723:
3678:
3658:
3631:
3514:
3419:
3308:
3228:
3143:
3072:
2971:
2906:
2879:
2804:
2546:
2472:
2409:
2335:
2252:
2195:
2062:
1977:
1853:
1826:
1767:
1707:
1588:
1545:
1525:
1501:
1419:
1396:
1320:
1194:
1171:
1151:
998:
975:
943:
923:
892:
837:
636:
606:
576:
549:
397:
357:
325:
294:
274:
243:
188:
4937:
List of boiling and freezing information of solvents
4608:
4270:
is the equilibrium vapor pressure of pure component
3983:
on mixing. If the chemical potential of pure liquid
2873:
Since the Gibbs free energy per mole of the mixture
388:) of each component. If the vapor is an ideal gas,
77:and their applications, such as the explanation of
4330:
4310:
4282:
4262:
4220:{\displaystyle \ p_{i}=(p_{i})_{\text{pure}}x_{i}}
4219:
4146:
4124:{\displaystyle \mu _{i}=\mu _{i}^{*}+RT\ln x_{i}.}
4123:
4047:
4027:
3995:
3975:
3955:
3883:
3775:
3742:
3709:
3664:
3644:
3614:
3494:
3386:
3293:
3212:
3129:
3051:
2954:
2892:
2862:
2784:
2521:
2452:
2392:
2321:
2235:
2178:
2045:
1960:
1832:
1804:
1747:
1687:
1567:
1531:
1507:
1484:
1402:
1379:
1300:
1177:
1157:
1116:
981:
961:
929:
905:
878:
816:
619:
589:
562:
532:
363:
343:
307:
280:
256:
229:
3410:. Hence the molar Gibbs free energy of mixing is
4989:
3790:The equation above can be expressed in terms of
3785:ideal solutions are miscible at any composition
3130:{\displaystyle g_{i}^{*}=h_{i}^{*}-Ts_{i}^{*}}
2393:{\displaystyle u_{i}^{*}=h_{i}^{*}-pv_{i}^{*}}
1410:, these last two equations put together give:
121:must be of the same average strength, i.e., 2
4632:
1815:
351:is the vapor pressure of the pure substance
160:, then the solution is automatically ideal.
27:Solution exhibiting thermodynamic properties
4490:Elementary Principles of Chemical Processes
4440:Elementary Principles of Chemical Processes
2955:{\displaystyle G_{m}=\sum _{i}x_{i}{g_{i}}}
2522:{\displaystyle C_{pi}^{*}={\bar {C_{pi}}}.}
1135:
4639:
4625:
4307:
2453:{\displaystyle u_{i}^{*}={\bar {u_{i}}}.}
2236:{\displaystyle {\bar {h_{i}}}=h_{i}^{*}}
1748:{\displaystyle v_{i}^{*}={\bar {v}}_{i}}
3963:is the change in chemical potential of
3505:or for a two-component ideal solution
14:
4990:
4646:
3406:on mixing is determined solely by the
1575:, with optional overbar, standing for
89:Ideality of solutions is analogous to
4620:
4263:{\displaystyle (p_{i})_{\text{pure}}}
1805:{\displaystyle V=\sum _{i}V_{i}^{*}.}
3787:and no phase separation will occur.
3783:must be negative (infinite)), i.e.,
2532:
879:{\displaystyle f_{i}=x_{i}f_{i}^{*}}
230:{\displaystyle p_{i}=x_{i}p_{i}^{*}}
174:
4580:R.S. Berry, S.A. Rice and J. Ross,
4158:over the entire composition range:
3062:At last we can calculate the molar
2463:It is also easily verifiable that
24:
4545:(8th edn, W.H.Freeman 2006), p.144
4518:Compendium of Chemical Terminology
4318:is the mole fraction of component
3922:
3919:
3916:
3901:
3875:
3872:
3869:
3854:
3825:
3822:
3819:
3813:
3804:
3652:is the mole fraction of component
3536:
3533:
3530:
3524:
3515:
3441:
3438:
3435:
3429:
3420:
3330:
3327:
3324:
3318:
3309:
3250:
3247:
3244:
3229:
2993:
2990:
2987:
2981:
2972:
2826:
2823:
2820:
2805:
2664:
2661:
2658:
2599:
2596:
2593:
2164:
2161:
2158:
2108:
2105:
2102:
2001:
1986:
1890:
1887:
1884:
1840:we get a similar result for molar
1618:
1597:
1442:
1428:
1352:
1329:
1276:
1262:
1226:
1203:
1047:
671:
460:
84:
25:
5019:
4372:of components can be determined.
4035:, then the chemical potential of
4571:(Benjamin-Cummings 1982), p. 180
4600:
4341:
3397:
54:of the solvent and solute obey
4587:
4574:
4561:
4548:
4535:
4506:
4481:
4462:
4429:
4251:
4237:
4198:
4184:
3767:
3704:
3692:
3609:
3551:
3204:
3179:
3157:
2560:
2510:
2441:
2313:
2288:
2266:
2209:
2082:
1915:
1896:
1872:
1860:
1733:
1667:
1568:{\displaystyle {\bar {v_{i}}}}
1559:
1347:
1335:
1221:
1209:
1072:
1053:
1035:
1023:
1014:
1002:
696:
677:
659:
640:
485:
466:
448:
429:
420:
401:
13:
1:
4567:K.J. Laidler and J.H. Meiser
4422:
3794:of the individual components
600:On substituting the value of
4927:Inorganic nonaqueous solvent
4028:{\displaystyle \mu _{i}^{*}}
7:
4541:P. Atkins and J. de Paula,
4375:
4154:of an ideal solution obeys
237:for all compositions. Here
10:
5024:
4912:Acid dissociation constant
4543:Atkins’ Physical Chemistry
3776:{\displaystyle x_{i}\to 0}
1816:Enthalpy and heat capacity
4895:
4827:
4757:
4654:
3743:{\displaystyle \ln x_{i}}
3710:{\displaystyle x_{i}\in }
2189:which in turn means that
1140:
962:{\displaystyle f_{i}^{*}}
371:at the same temperature.
344:{\displaystyle p_{i}^{*}}
4469:A to Z of Thermodynamics
4055:in an ideal solution is
1136:Thermodynamic properties
62:, respectively, and the
5008:Chemical thermodynamics
4877:Solubility table (data)
4744:Apparent molar property
4610:(Macmillan 1969), p.261
4595:Chemical Thermodynamics
4531:10.1351/goldbook.I02938
4407:Apparent molar property
4402:Coil-globule transition
4311:{\displaystyle x_{i}\,}
543:The reference pressure
75:chemical thermodynamics
4842:Total dissolved solids
4837:Solubility equilibrium
4762:and related quantities
4492:. Wiley. p. 293.
4370:thermodynamic activity
4332:
4312:
4284:
4264:
4221:
4148:
4125:
4049:
4029:
3997:
3977:
3957:
3885:
3777:
3744:
3711:
3666:
3646:
3616:
3496:
3388:
3295:
3214:
3131:
3053:
2956:
2894:
2864:
2786:
2523:
2454:
2394:
2323:
2237:
2180:
2047:
1962:
1834:
1806:
1749:
1689:
1569:
1533:
1509:
1486:
1404:
1390:with the molar volume
1381:
1302:
1179:
1159:
1118:
983:
963:
931:
907:
880:
818:
621:
591:
564:
534:
365:
345:
309:
282:
258:
231:
79:colligative properties
4942:Partition coefficient
4922:Polar aprotic solvent
4597:(Benjamin 1964) p.322
4558:(Pearson 2006), p.194
4554:T. Engel and P. Reid
4352:activity coefficients
4333:
4313:
4285:
4265:
4222:
4149:
4126:
4050:
4030:
3998:
3978:
3958:
3886:
3778:
3745:
3712:
3667:
3647:
3645:{\displaystyle x_{i}}
3617:
3497:
3389:
3296:
3215:
3132:
3054:
2957:
2895:
2893:{\displaystyle G_{m}}
2865:
2787:
2524:
2455:
2395:
2324:
2238:
2181:
2048:
1963:
1835:
1807:
1750:
1690:
1570:
1534:
1510:
1487:
1405:
1382:
1303:
1180:
1160:
1132:instead of fugacity.
1119:
984:
964:
932:
908:
906:{\displaystyle f_{i}}
881:
819:
622:
620:{\displaystyle p_{i}}
592:
590:{\displaystyle P^{o}}
565:
563:{\displaystyle p^{u}}
535:
366:
346:
310:
308:{\displaystyle x_{i}}
283:
259:
257:{\displaystyle p_{i}}
232:
107:) and like neighbors
4857:Enthalpy of solution
4784:Volume concentration
4779:Number concentration
4382:Activity coefficient
4322:
4294:
4274:
4234:
4165:
4138:
4062:
4039:
4007:
3987:
3967:
3898:
3801:
3754:
3721:
3676:
3656:
3629:
3512:
3417:
3306:
3226:
3141:
3070:
2969:
2904:
2877:
2802:
2544:
2470:
2407:
2333:
2250:
2193:
2060:
1975:
1851:
1824:
1765:
1705:
1586:
1577:partial molar volume
1543:
1523:
1499:
1417:
1394:
1318:
1192:
1169:
1149:
996:
973:
941:
921:
890:
835:
634:
627:from Raoult's law,
604:
574:
547:
395:
355:
323:
292:
288:above the solution,
272:
241:
186:
64:activity coefficient
4769:Molar concentration
4739:Dilution (equation)
4092:
4024:
3792:chemical potentials
3126:
3105:
3087:
2756:
2701:
2669:
2604:
2490:
2424:
2389:
2368:
2350:
2232:
2169:
2143:
2113:
1798:
1722:
1517:intensive variables
969:is the fugacity of
958:
875:
785:
730:
340:
226:
4809:Isotopic abundance
4774:Mass concentration
4648:Chemical solutions
4584:(Wiley 1980) p.750
4582:Physical Chemistry
4569:Physical Chemistry
4556:Physical Chemistry
4417:Virial coefficient
4348:Margules functions
4328:
4308:
4280:
4260:
4217:
4144:
4121:
4078:
4045:
4025:
4010:
3993:
3973:
3953:
3881:
3843:
3773:
3740:
3707:
3662:
3642:
3612:
3492:
3465:
3384:
3354:
3291:
3274:
3210:
3127:
3112:
3091:
3073:
3049:
3017:
2952:
2929:
2890:
2860:
2782:
2742:
2687:
2647:
2582:
2519:
2473:
2450:
2410:
2390:
2375:
2354:
2336:
2319:
2233:
2218:
2176:
2147:
2129:
2091:
2043:
1958:
1830:
1802:
1784:
1783:
1745:
1708:
1685:
1565:
1529:
1505:
1482:
1400:
1377:
1298:
1175:
1155:
1114:
979:
959:
944:
927:
903:
876:
861:
814:
771:
716:
617:
587:
560:
530:
376:chemical potential
361:
341:
326:
305:
278:
254:
227:
212:
91:ideality for gases
48:enthalpy of mixing
4985:
4984:
4444:. Wiley. p.
4412:Dilution equation
4392:Margules function
4387:Entropy of mixing
4331:{\displaystyle i}
4283:{\displaystyle i}
4257:
4204:
4170:
4147:{\displaystyle i}
4048:{\displaystyle i}
3996:{\displaystyle i}
3976:{\displaystyle i}
3834:
3750:or its limit for
3665:{\displaystyle i}
3456:
3408:entropy of mixing
3404:Gibbs free energy
3345:
3265:
3207:
3182:
3160:
3064:entropy of mixing
3008:
2920:
2712:
2642:
2563:
2533:Entropy of mixing
2513:
2444:
2316:
2291:
2269:
2212:
2174:
2118:
2085:
2041:
2008:
1997:
1971:Remembering that
1953:
1927:
1833:{\displaystyle T}
1774:
1736:
1680:
1670:
1625:
1562:
1532:{\displaystyle v}
1508:{\displaystyle i}
1477:
1449:
1403:{\displaystyle v}
1359:
1283:
1233:
1185:constant we get:
1178:{\displaystyle T}
1158:{\displaystyle p}
1112:
982:{\displaystyle i}
930:{\displaystyle i}
741:
525:
364:{\displaystyle i}
281:{\displaystyle i}
175:Formal definition
16:(Redirected from
5015:
4882:Solubility chart
4709:Phase separation
4669:Aqueous solution
4641:
4634:
4627:
4618:
4617:
4611:
4604:
4598:
4591:
4585:
4578:
4572:
4565:
4559:
4552:
4546:
4539:
4533:
4510:
4504:
4503:
4485:
4479:
4466:
4460:
4459:
4443:
4433:
4397:Regular solution
4337:
4335:
4334:
4329:
4317:
4315:
4314:
4309:
4306:
4305:
4289:
4287:
4286:
4281:
4269:
4267:
4266:
4261:
4259:
4258:
4255:
4249:
4248:
4226:
4224:
4223:
4218:
4216:
4215:
4206:
4205:
4202:
4196:
4195:
4180:
4179:
4168:
4153:
4151:
4150:
4145:
4130:
4128:
4127:
4122:
4117:
4116:
4091:
4086:
4074:
4073:
4054:
4052:
4051:
4046:
4034:
4032:
4031:
4026:
4023:
4018:
4002:
4000:
3999:
3994:
3982:
3980:
3979:
3974:
3962:
3960:
3959:
3954:
3952:
3951:
3927:
3926:
3925:
3890:
3888:
3887:
3882:
3880:
3879:
3878:
3853:
3852:
3842:
3830:
3829:
3828:
3782:
3780:
3779:
3774:
3766:
3765:
3749:
3747:
3746:
3741:
3739:
3738:
3716:
3714:
3713:
3708:
3688:
3687:
3671:
3669:
3668:
3663:
3651:
3649:
3648:
3643:
3641:
3640:
3621:
3619:
3618:
3613:
3608:
3607:
3592:
3591:
3579:
3578:
3563:
3562:
3541:
3540:
3539:
3501:
3499:
3498:
3493:
3491:
3490:
3475:
3474:
3464:
3446:
3445:
3444:
3393:
3391:
3390:
3385:
3380:
3379:
3364:
3363:
3353:
3335:
3334:
3333:
3300:
3298:
3297:
3292:
3290:
3289:
3273:
3255:
3254:
3253:
3219:
3217:
3216:
3211:
3209:
3208:
3203:
3202:
3193:
3184:
3183:
3178:
3177:
3168:
3162:
3161:
3156:
3155:
3146:
3136:
3134:
3133:
3128:
3125:
3120:
3104:
3099:
3086:
3081:
3058:
3056:
3055:
3050:
3045:
3044:
3043:
3028:
3027:
3016:
2998:
2997:
2996:
2961:
2959:
2958:
2953:
2951:
2950:
2949:
2939:
2938:
2928:
2916:
2915:
2899:
2897:
2896:
2891:
2889:
2888:
2869:
2867:
2866:
2861:
2856:
2855:
2831:
2830:
2829:
2791:
2789:
2788:
2783:
2781:
2780:
2755:
2750:
2738:
2737:
2713:
2711:
2710:
2700:
2695:
2686:
2668:
2667:
2655:
2643:
2641:
2640:
2631:
2630:
2621:
2603:
2602:
2590:
2578:
2577:
2565:
2564:
2559:
2558:
2549:
2528:
2526:
2525:
2520:
2515:
2514:
2509:
2508:
2496:
2489:
2484:
2459:
2457:
2456:
2451:
2446:
2445:
2440:
2439:
2430:
2423:
2418:
2399:
2397:
2396:
2391:
2388:
2383:
2367:
2362:
2349:
2344:
2328:
2326:
2325:
2320:
2318:
2317:
2312:
2311:
2302:
2293:
2292:
2287:
2286:
2277:
2271:
2270:
2265:
2264:
2255:
2242:
2240:
2239:
2234:
2231:
2226:
2214:
2213:
2208:
2207:
2198:
2185:
2183:
2182:
2177:
2175:
2170:
2168:
2167:
2155:
2142:
2137:
2127:
2119:
2114:
2112:
2111:
2099:
2087:
2086:
2081:
2080:
2071:
2067:
2052:
2050:
2049:
2044:
2042:
2040:
2039:
2027:
2019:
2018:
2013:
2009:
2007:
1999:
1998:
1990:
1984:
1967:
1965:
1964:
1959:
1954:
1952:
1951:
1939:
1928:
1926:
1918:
1914:
1913:
1895:
1894:
1893:
1855:
1839:
1837:
1836:
1831:
1811:
1809:
1808:
1803:
1797:
1792:
1782:
1754:
1752:
1751:
1746:
1744:
1743:
1738:
1737:
1729:
1721:
1716:
1694:
1692:
1691:
1686:
1681:
1679:
1671:
1666:
1665:
1656:
1654:
1649:
1648:
1647:
1646:
1630:
1626:
1624:
1616:
1615:
1614:
1595:
1574:
1572:
1571:
1566:
1564:
1563:
1558:
1557:
1548:
1538:
1536:
1535:
1530:
1514:
1512:
1511:
1506:
1491:
1489:
1488:
1483:
1478:
1476:
1465:
1460:
1459:
1454:
1450:
1448:
1440:
1426:
1409:
1407:
1406:
1401:
1386:
1384:
1383:
1378:
1370:
1369:
1364:
1360:
1358:
1350:
1327:
1307:
1305:
1304:
1299:
1294:
1293:
1288:
1284:
1282:
1274:
1260:
1244:
1243:
1238:
1234:
1232:
1224:
1201:
1184:
1182:
1181:
1176:
1164:
1162:
1161:
1156:
1123:
1121:
1120:
1115:
1113:
1111:
1110:
1101:
1100:
1091:
1071:
1070:
1052:
1051:
1050:
988:
986:
985:
980:
968:
966:
965:
960:
957:
952:
937:in solution and
936:
934:
933:
928:
912:
910:
909:
904:
902:
901:
885:
883:
882:
877:
874:
869:
860:
859:
847:
846:
823:
821:
820:
815:
810:
809:
784:
779:
767:
766:
742:
740:
739:
729:
724:
715:
695:
694:
676:
675:
674:
658:
657:
626:
624:
623:
618:
616:
615:
596:
594:
593:
588:
586:
585:
570:may be taken as
569:
567:
566:
561:
559:
558:
539:
537:
536:
531:
526:
524:
523:
514:
513:
504:
484:
483:
465:
464:
463:
447:
446:
419:
418:
378:ÎĽ (which is the
370:
368:
367:
362:
350:
348:
347:
342:
339:
334:
314:
312:
311:
306:
304:
303:
287:
285:
284:
279:
263:
261:
260:
255:
253:
252:
236:
234:
233:
228:
225:
220:
211:
210:
198:
197:
21:
5023:
5022:
5018:
5017:
5016:
5014:
5013:
5012:
4988:
4987:
4986:
4981:
4891:
4852:Solvation shell
4823:
4761:
4753:
4749:Miscibility gap
4734:Serial dilution
4729:Supersaturation
4679:Buffer solution
4650:
4645:
4615:
4614:
4605:
4601:
4592:
4588:
4579:
4575:
4566:
4562:
4553:
4549:
4540:
4536:
4511:
4507:
4500:
4486:
4482:
4467:
4463:
4456:
4434:
4430:
4425:
4378:
4344:
4323:
4320:
4319:
4301:
4297:
4295:
4292:
4291:
4275:
4272:
4271:
4254:
4250:
4244:
4240:
4235:
4232:
4231:
4211:
4207:
4201:
4197:
4191:
4187:
4175:
4171:
4166:
4163:
4162:
4139:
4136:
4135:
4112:
4108:
4087:
4082:
4069:
4065:
4063:
4060:
4059:
4040:
4037:
4036:
4019:
4014:
4008:
4005:
4004:
3988:
3985:
3984:
3968:
3965:
3964:
3947:
3943:
3915:
3908:
3904:
3899:
3896:
3895:
3868:
3861:
3857:
3848:
3844:
3838:
3812:
3811:
3807:
3802:
3799:
3798:
3761:
3757:
3755:
3752:
3751:
3734:
3730:
3722:
3719:
3718:
3683:
3679:
3677:
3674:
3673:
3657:
3654:
3653:
3636:
3632:
3630:
3627:
3626:
3603:
3599:
3587:
3583:
3574:
3570:
3558:
3554:
3523:
3522:
3518:
3513:
3510:
3509:
3486:
3482:
3470:
3466:
3460:
3428:
3427:
3423:
3418:
3415:
3414:
3400:
3375:
3371:
3359:
3355:
3349:
3317:
3316:
3312:
3307:
3304:
3303:
3285:
3281:
3269:
3243:
3236:
3232:
3227:
3224:
3223:
3198:
3194:
3192:
3191:
3173:
3169:
3167:
3166:
3151:
3147:
3145:
3144:
3142:
3139:
3138:
3121:
3116:
3100:
3095:
3082:
3077:
3071:
3068:
3067:
3039:
3035:
3023:
3019:
3018:
3012:
2980:
2979:
2975:
2970:
2967:
2966:
2945:
2941:
2940:
2934:
2930:
2924:
2911:
2907:
2905:
2902:
2901:
2884:
2880:
2878:
2875:
2874:
2851:
2847:
2819:
2812:
2808:
2803:
2800:
2799:
2776:
2772:
2751:
2746:
2733:
2729:
2706:
2702:
2696:
2691:
2685:
2657:
2656:
2651:
2636:
2632:
2626:
2622:
2620:
2592:
2591:
2586:
2573:
2569:
2554:
2550:
2548:
2547:
2545:
2542:
2541:
2537:Finally since
2535:
2501:
2497:
2495:
2494:
2485:
2477:
2471:
2468:
2467:
2435:
2431:
2429:
2428:
2419:
2414:
2408:
2405:
2404:
2384:
2379:
2363:
2358:
2345:
2340:
2334:
2331:
2330:
2307:
2303:
2301:
2300:
2282:
2278:
2276:
2275:
2260:
2256:
2254:
2253:
2251:
2248:
2247:
2227:
2222:
2203:
2199:
2197:
2196:
2194:
2191:
2190:
2157:
2156:
2151:
2138:
2133:
2128:
2126:
2101:
2100:
2095:
2076:
2072:
2070:
2069:
2068:
2066:
2061:
2058:
2057:
2035:
2031:
2026:
2014:
2000:
1989:
1985:
1983:
1979:
1978:
1976:
1973:
1972:
1947:
1943:
1938:
1919:
1909:
1905:
1883:
1882:
1878:
1856:
1854:
1852:
1849:
1848:
1825:
1822:
1821:
1818:
1793:
1788:
1778:
1766:
1763:
1762:
1739:
1728:
1727:
1726:
1717:
1712:
1706:
1703:
1702:
1672:
1661:
1657:
1655:
1653:
1642:
1638:
1631:
1617:
1610:
1606:
1596:
1594:
1590:
1589:
1587:
1584:
1583:
1553:
1549:
1547:
1546:
1544:
1541:
1540:
1524:
1521:
1520:
1500:
1497:
1496:
1469:
1464:
1455:
1441:
1427:
1425:
1421:
1420:
1418:
1415:
1414:
1395:
1392:
1391:
1365:
1351:
1328:
1326:
1322:
1321:
1319:
1316:
1315:
1289:
1275:
1261:
1259:
1255:
1254:
1239:
1225:
1202:
1200:
1196:
1195:
1193:
1190:
1189:
1170:
1167:
1166:
1150:
1147:
1146:
1143:
1138:
1106:
1102:
1096:
1092:
1090:
1066:
1062:
1046:
1045:
1041:
997:
994:
993:
974:
971:
970:
953:
948:
942:
939:
938:
922:
919:
918:
897:
893:
891:
888:
887:
870:
865:
855:
851:
842:
838:
836:
833:
832:
805:
801:
780:
775:
762:
758:
735:
731:
725:
720:
714:
690:
686:
670:
669:
665:
653:
649:
635:
632:
631:
611:
607:
605:
602:
601:
581:
577:
575:
572:
571:
554:
550:
548:
545:
544:
519:
515:
509:
505:
503:
479:
475:
459:
458:
454:
442:
438:
414:
410:
396:
393:
392:
356:
353:
352:
335:
330:
324:
321:
320:
299:
295:
293:
290:
289:
273:
270:
269:
248:
244:
242:
239:
238:
221:
216:
206:
202:
193:
189:
187:
184:
183:
177:
159:
152:
145:
138:
134:
127:
120:
113:
106:
87:
85:Physical origin
52:vapor pressures
28:
23:
22:
15:
12:
11:
5:
5021:
5011:
5010:
5005:
5003:Thermodynamics
5000:
4983:
4982:
4980:
4979:
4974:
4969:
4964:
4959:
4954:
4949:
4944:
4939:
4934:
4929:
4924:
4919:
4917:Protic solvent
4914:
4909:
4901:
4899:
4893:
4892:
4890:
4889:
4884:
4879:
4874:
4869:
4864:
4862:Lattice energy
4859:
4854:
4849:
4844:
4839:
4833:
4831:
4825:
4824:
4822:
4821:
4816:
4811:
4806:
4801:
4796:
4791:
4786:
4781:
4776:
4771:
4765:
4763:
4755:
4754:
4752:
4751:
4746:
4741:
4736:
4731:
4726:
4721:
4716:
4714:Eutectic point
4711:
4706:
4701:
4696:
4691:
4686:
4681:
4676:
4674:Solid solution
4671:
4666:
4664:Ideal solution
4660:
4658:
4652:
4651:
4644:
4643:
4636:
4629:
4621:
4613:
4612:
4599:
4586:
4573:
4560:
4547:
4534:
4505:
4499:978-0471687573
4498:
4480:
4471:Pierre Perrot
4461:
4455:978-0471687573
4454:
4427:
4426:
4424:
4421:
4420:
4419:
4414:
4409:
4404:
4399:
4394:
4389:
4384:
4377:
4374:
4343:
4340:
4327:
4304:
4300:
4279:
4253:
4247:
4243:
4239:
4228:
4227:
4214:
4210:
4200:
4194:
4190:
4186:
4183:
4178:
4174:
4143:
4134:Any component
4132:
4131:
4120:
4115:
4111:
4107:
4104:
4101:
4098:
4095:
4090:
4085:
4081:
4077:
4072:
4068:
4044:
4022:
4017:
4013:
3992:
3972:
3950:
3946:
3942:
3939:
3936:
3933:
3930:
3924:
3921:
3918:
3914:
3911:
3907:
3903:
3892:
3891:
3877:
3874:
3871:
3867:
3864:
3860:
3856:
3851:
3847:
3841:
3837:
3833:
3827:
3824:
3821:
3818:
3815:
3810:
3806:
3772:
3769:
3764:
3760:
3737:
3733:
3729:
3726:
3706:
3703:
3700:
3697:
3694:
3691:
3686:
3682:
3661:
3639:
3635:
3623:
3622:
3611:
3606:
3602:
3598:
3595:
3590:
3586:
3582:
3577:
3573:
3569:
3566:
3561:
3557:
3553:
3550:
3547:
3544:
3538:
3535:
3532:
3529:
3526:
3521:
3517:
3503:
3502:
3489:
3485:
3481:
3478:
3473:
3469:
3463:
3459:
3455:
3452:
3449:
3443:
3440:
3437:
3434:
3431:
3426:
3422:
3399:
3396:
3395:
3394:
3383:
3378:
3374:
3370:
3367:
3362:
3358:
3352:
3348:
3344:
3341:
3338:
3332:
3329:
3326:
3323:
3320:
3315:
3311:
3301:
3288:
3284:
3280:
3277:
3272:
3268:
3264:
3261:
3258:
3252:
3249:
3246:
3242:
3239:
3235:
3231:
3206:
3201:
3197:
3190:
3187:
3181:
3176:
3172:
3165:
3159:
3154:
3150:
3124:
3119:
3115:
3111:
3108:
3103:
3098:
3094:
3090:
3085:
3080:
3076:
3060:
3059:
3048:
3042:
3038:
3034:
3031:
3026:
3022:
3015:
3011:
3007:
3004:
3001:
2995:
2992:
2989:
2986:
2983:
2978:
2974:
2948:
2944:
2937:
2933:
2927:
2923:
2919:
2914:
2910:
2887:
2883:
2871:
2870:
2859:
2854:
2850:
2846:
2843:
2840:
2837:
2834:
2828:
2825:
2822:
2818:
2815:
2811:
2807:
2795:we find that
2793:
2792:
2779:
2775:
2771:
2768:
2765:
2762:
2759:
2754:
2749:
2745:
2741:
2736:
2732:
2728:
2725:
2722:
2719:
2716:
2709:
2705:
2699:
2694:
2690:
2684:
2681:
2678:
2675:
2672:
2666:
2663:
2660:
2654:
2650:
2646:
2639:
2635:
2629:
2625:
2619:
2616:
2613:
2610:
2607:
2601:
2598:
2595:
2589:
2585:
2581:
2576:
2572:
2568:
2562:
2557:
2553:
2534:
2531:
2530:
2529:
2518:
2512:
2507:
2504:
2500:
2493:
2488:
2483:
2480:
2476:
2461:
2460:
2449:
2443:
2438:
2434:
2427:
2422:
2417:
2413:
2387:
2382:
2378:
2374:
2371:
2366:
2361:
2357:
2353:
2348:
2343:
2339:
2315:
2310:
2306:
2299:
2296:
2290:
2285:
2281:
2274:
2268:
2263:
2259:
2230:
2225:
2221:
2217:
2211:
2206:
2202:
2187:
2186:
2173:
2166:
2163:
2160:
2154:
2150:
2146:
2141:
2136:
2132:
2125:
2122:
2117:
2110:
2107:
2104:
2098:
2094:
2090:
2084:
2079:
2075:
2065:
2038:
2034:
2030:
2025:
2022:
2017:
2012:
2006:
2003:
1996:
1993:
1988:
1982:
1969:
1968:
1957:
1950:
1946:
1942:
1937:
1934:
1931:
1925:
1922:
1917:
1912:
1908:
1904:
1901:
1898:
1892:
1889:
1886:
1881:
1877:
1874:
1871:
1868:
1865:
1862:
1859:
1829:
1817:
1814:
1813:
1812:
1801:
1796:
1791:
1787:
1781:
1777:
1773:
1770:
1756:
1755:
1742:
1735:
1732:
1725:
1720:
1715:
1711:
1696:
1695:
1684:
1678:
1675:
1669:
1664:
1660:
1652:
1645:
1641:
1637:
1634:
1629:
1623:
1620:
1613:
1609:
1605:
1602:
1599:
1593:
1561:
1556:
1552:
1528:
1504:
1493:
1492:
1481:
1475:
1472:
1468:
1463:
1458:
1453:
1447:
1444:
1439:
1436:
1433:
1430:
1424:
1399:
1388:
1387:
1376:
1373:
1368:
1363:
1357:
1354:
1349:
1346:
1343:
1340:
1337:
1334:
1331:
1325:
1309:
1308:
1297:
1292:
1287:
1281:
1278:
1273:
1270:
1267:
1264:
1258:
1253:
1250:
1247:
1242:
1237:
1231:
1228:
1223:
1220:
1217:
1214:
1211:
1208:
1205:
1199:
1174:
1154:
1142:
1139:
1137:
1134:
1125:
1124:
1109:
1105:
1099:
1095:
1089:
1086:
1083:
1080:
1077:
1074:
1069:
1065:
1061:
1058:
1055:
1049:
1044:
1040:
1037:
1034:
1031:
1028:
1025:
1022:
1019:
1016:
1013:
1010:
1007:
1004:
1001:
978:
956:
951:
947:
926:
900:
896:
873:
868:
864:
858:
854:
850:
845:
841:
825:
824:
813:
808:
804:
800:
797:
794:
791:
788:
783:
778:
774:
770:
765:
761:
757:
754:
751:
748:
745:
738:
734:
728:
723:
719:
713:
710:
707:
704:
701:
698:
693:
689:
685:
682:
679:
673:
668:
664:
661:
656:
652:
648:
645:
642:
639:
614:
610:
584:
580:
557:
553:
541:
540:
529:
522:
518:
512:
508:
502:
499:
496:
493:
490:
487:
482:
478:
474:
471:
468:
462:
457:
453:
450:
445:
441:
437:
434:
431:
428:
425:
422:
417:
413:
409:
406:
403:
400:
360:
338:
333:
329:
302:
298:
277:
266:vapor pressure
251:
247:
224:
219:
215:
209:
205:
201:
196:
192:
176:
173:
157:
150:
143:
136:
132:
125:
118:
111:
104:
86:
83:
71:thermodynamics
32:ideal solution
26:
9:
6:
4:
3:
2:
5020:
5009:
5006:
5004:
5001:
4999:
4996:
4995:
4993:
4978:
4975:
4973:
4970:
4968:
4965:
4963:
4960:
4958:
4955:
4953:
4950:
4948:
4945:
4943:
4940:
4938:
4935:
4933:
4930:
4928:
4925:
4923:
4920:
4918:
4915:
4913:
4910:
4907:
4903:
4902:
4900:
4898:
4894:
4888:
4885:
4883:
4880:
4878:
4875:
4873:
4870:
4868:
4865:
4863:
4860:
4858:
4855:
4853:
4850:
4848:
4845:
4843:
4840:
4838:
4835:
4834:
4832:
4830:
4826:
4820:
4817:
4815:
4812:
4810:
4807:
4805:
4804:Mass fraction
4802:
4800:
4799:Mole fraction
4797:
4795:
4792:
4790:
4787:
4785:
4782:
4780:
4777:
4775:
4772:
4770:
4767:
4766:
4764:
4760:
4759:Concentration
4756:
4750:
4747:
4745:
4742:
4740:
4737:
4735:
4732:
4730:
4727:
4725:
4722:
4720:
4717:
4715:
4712:
4710:
4707:
4705:
4704:Phase diagram
4702:
4700:
4697:
4695:
4692:
4690:
4687:
4685:
4684:Flory–Huggins
4682:
4680:
4677:
4675:
4672:
4670:
4667:
4665:
4662:
4661:
4659:
4657:
4653:
4649:
4642:
4637:
4635:
4630:
4628:
4623:
4622:
4619:
4609:
4603:
4596:
4590:
4583:
4577:
4570:
4564:
4557:
4551:
4544:
4538:
4532:
4528:
4524:
4523:ideal mixture
4520:
4519:
4514:
4509:
4501:
4495:
4491:
4484:
4478:
4477:0-19-856556-9
4474:
4470:
4465:
4457:
4451:
4447:
4442:
4441:
4432:
4428:
4418:
4415:
4413:
4410:
4408:
4405:
4403:
4400:
4398:
4395:
4393:
4390:
4388:
4385:
4383:
4380:
4379:
4373:
4371:
4367:
4361:
4359:
4358:
4353:
4349:
4339:
4338:in solution.
4325:
4302:
4298:
4277:
4245:
4241:
4212:
4208:
4192:
4188:
4181:
4176:
4172:
4161:
4160:
4159:
4157:
4141:
4118:
4113:
4109:
4105:
4102:
4099:
4096:
4093:
4088:
4083:
4079:
4075:
4070:
4066:
4058:
4057:
4056:
4042:
4020:
4015:
4011:
3990:
3970:
3948:
3944:
3940:
3937:
3934:
3931:
3928:
3912:
3909:
3905:
3865:
3862:
3858:
3849:
3845:
3839:
3835:
3831:
3816:
3808:
3797:
3796:
3795:
3793:
3788:
3786:
3770:
3762:
3758:
3735:
3731:
3727:
3724:
3701:
3698:
3695:
3689:
3684:
3680:
3659:
3637:
3633:
3604:
3600:
3596:
3593:
3588:
3584:
3580:
3575:
3571:
3567:
3564:
3559:
3555:
3548:
3545:
3542:
3527:
3519:
3508:
3507:
3506:
3487:
3483:
3479:
3476:
3471:
3467:
3461:
3457:
3453:
3450:
3447:
3432:
3424:
3413:
3412:
3411:
3409:
3405:
3381:
3376:
3372:
3368:
3365:
3360:
3356:
3350:
3346:
3342:
3339:
3336:
3321:
3313:
3302:
3286:
3282:
3278:
3275:
3270:
3266:
3262:
3259:
3256:
3240:
3237:
3233:
3222:
3221:
3220:
3199:
3195:
3188:
3185:
3174:
3170:
3163:
3152:
3148:
3122:
3117:
3113:
3109:
3106:
3101:
3096:
3092:
3088:
3083:
3078:
3074:
3065:
3046:
3040:
3036:
3032:
3029:
3024:
3020:
3013:
3009:
3005:
3002:
2999:
2984:
2976:
2965:
2964:
2963:
2946:
2942:
2935:
2931:
2925:
2921:
2917:
2912:
2908:
2885:
2881:
2857:
2852:
2848:
2844:
2841:
2838:
2835:
2832:
2816:
2813:
2809:
2798:
2797:
2796:
2777:
2773:
2769:
2766:
2763:
2760:
2757:
2752:
2747:
2743:
2739:
2734:
2730:
2726:
2723:
2720:
2717:
2714:
2707:
2703:
2697:
2692:
2688:
2682:
2679:
2676:
2673:
2670:
2652:
2648:
2644:
2637:
2633:
2627:
2623:
2617:
2614:
2611:
2608:
2605:
2587:
2583:
2579:
2574:
2570:
2566:
2555:
2551:
2540:
2539:
2538:
2516:
2505:
2502:
2498:
2491:
2486:
2481:
2478:
2474:
2466:
2465:
2464:
2447:
2436:
2432:
2425:
2420:
2415:
2411:
2403:
2402:
2401:
2385:
2380:
2376:
2372:
2369:
2364:
2359:
2355:
2351:
2346:
2341:
2337:
2308:
2304:
2297:
2294:
2283:
2279:
2272:
2261:
2257:
2244:
2228:
2223:
2219:
2215:
2204:
2200:
2171:
2152:
2148:
2144:
2139:
2134:
2130:
2123:
2120:
2115:
2096:
2092:
2088:
2077:
2073:
2063:
2056:
2055:
2054:
2036:
2032:
2028:
2023:
2020:
2015:
2010:
2004:
1994:
1991:
1980:
1955:
1948:
1944:
1940:
1935:
1932:
1929:
1923:
1920:
1910:
1906:
1902:
1899:
1879:
1875:
1869:
1866:
1863:
1857:
1847:
1846:
1845:
1843:
1827:
1799:
1794:
1789:
1785:
1779:
1775:
1771:
1768:
1761:
1760:
1759:
1740:
1730:
1723:
1718:
1713:
1709:
1701:
1700:
1699:
1682:
1676:
1673:
1662:
1658:
1650:
1643:
1639:
1635:
1632:
1627:
1621:
1611:
1607:
1603:
1600:
1591:
1582:
1581:
1580:
1578:
1554:
1550:
1526:
1519:and changing
1518:
1502:
1479:
1473:
1470:
1466:
1461:
1456:
1451:
1445:
1437:
1434:
1431:
1422:
1413:
1412:
1411:
1397:
1374:
1371:
1366:
1361:
1355:
1344:
1341:
1338:
1332:
1323:
1314:
1313:
1312:
1295:
1290:
1285:
1279:
1271:
1268:
1265:
1256:
1251:
1248:
1245:
1240:
1235:
1229:
1218:
1215:
1212:
1206:
1197:
1188:
1187:
1186:
1172:
1152:
1133:
1131:
1107:
1103:
1097:
1093:
1087:
1084:
1081:
1078:
1075:
1067:
1063:
1059:
1056:
1042:
1038:
1032:
1029:
1026:
1020:
1017:
1011:
1008:
1005:
999:
992:
991:
990:
976:
954:
949:
945:
924:
917:of component
916:
898:
894:
871:
866:
862:
856:
852:
848:
843:
839:
828:
811:
806:
802:
798:
795:
792:
789:
786:
781:
776:
772:
768:
763:
759:
755:
752:
749:
746:
743:
736:
732:
726:
721:
717:
711:
708:
705:
702:
699:
691:
687:
683:
680:
666:
662:
654:
650:
646:
643:
637:
630:
629:
628:
612:
608:
598:
582:
578:
555:
551:
527:
520:
516:
510:
506:
500:
497:
494:
491:
488:
480:
476:
472:
469:
455:
451:
443:
439:
435:
432:
426:
423:
415:
411:
407:
404:
398:
391:
390:
389:
387:
384:
381:
380:partial molar
377:
372:
358:
336:
331:
327:
318:
317:mole fraction
300:
296:
275:
268:of component
267:
249:
245:
222:
217:
213:
207:
203:
199:
194:
190:
182:
172:
170:
166:
161:
156:
149:
142:
131:
124:
117:
110:
103:
98:
96:
92:
82:
80:
76:
72:
67:
65:
61:
57:
53:
49:
45:
41:
37:
36:ideal mixture
33:
19:
18:Ideal mixture
4867:Raoult's law
4819:Ternary plot
4814:Mixing ratio
4663:
4607:
4602:
4594:
4593:I.M. Klotz,
4589:
4581:
4576:
4568:
4563:
4555:
4550:
4542:
4537:
4516:
4508:
4489:
4483:
4468:
4464:
4439:
4431:
4362:
4355:
4345:
4342:Non-ideality
4229:
4156:Raoult's Law
4133:
3893:
3789:
3784:
3624:
3504:
3401:
3398:Consequences
3061:
2872:
2794:
2536:
2462:
2400:, similarly
2245:
2188:
1970:
1819:
1757:
1697:
1494:
1389:
1310:
1144:
1126:
829:
826:
599:
542:
385:
383:Gibbs energy
373:
181:Raoult's law
178:
162:
154:
147:
140:
129:
122:
115:
108:
101:
99:
95:interactions
88:
68:
56:Raoult's law
35:
31:
29:
4972:Lyonium ion
4887:Miscibility
4872:Henry's law
4606:P.A. Rock,
4003:is denoted
1515:to all the
60:Henry's law
44:ideal gases
4992:Categories
4967:Amphiphile
4962:Lipophilic
4957:Hydrophile
4952:Hydrophobe
4829:Solubility
4724:Saturation
4694:Suspension
4423:References
4366:solubility
1842:enthalpies
4998:Solutions
4977:Lyate ion
4932:Solvation
4847:Solvation
4789:Normality
4106:
4089:∗
4080:μ
4067:μ
4021:∗
4012:μ
3941:
3906:μ
3902:Δ
3859:μ
3855:Δ
3836:∑
3805:Δ
3768:→
3728:
3690:∈
3597:
3568:
3516:Δ
3480:
3458:∑
3421:Δ
3369:
3347:∑
3340:−
3310:Δ
3279:
3267:∑
3260:−
3230:Δ
3205:¯
3186:−
3180:¯
3158:¯
3123:∗
3107:−
3102:∗
3084:∗
3033:
3010:∑
2973:Δ
2922:∑
2845:
2806:Δ
2770:
2753:∗
2744:μ
2727:
2698:∗
2683:
2618:
2571:μ
2561:¯
2511:¯
2487:∗
2442:¯
2421:∗
2386:∗
2370:−
2365:∗
2347:∗
2314:¯
2295:−
2289:¯
2267:¯
2229:∗
2210:¯
2145:−
2140:∗
2124:−
2089:−
2083:¯
2064:−
2024:−
2002:∂
1987:∂
1936:
1876:−
1795:∗
1776:∑
1734:¯
1719:∗
1668:¯
1619:∂
1604:
1598:∂
1560:¯
1443:∂
1435:
1429:∂
1353:∂
1330:∂
1277:∂
1269:
1263:∂
1227:∂
1204:∂
1088:
1000:μ
955:∗
872:∗
799:
782:∗
773:μ
756:
727:∗
712:
638:μ
501:
399:μ
337:∗
223:∗
169:2-butanol
165:1-butanol
4947:Polarity
4906:Category
4794:Molality
4656:Solution
4376:See also
2053:we get:
1130:activity
915:fugacity
40:solution
4897:Solvent
4699:Colloid
4689:Mixture
4357:regular
3717:, each
3066:since
913:is the
886:. Here
315:is its
264:is the
4496:
4475:
4452:
4230:where
4169:
3894:where
2246:Since
1141:Volume
46:. The
4719:Alloy
4513:IUPAC
2962:then
38:is a
4494:ISBN
4473:ISBN
4450:ISBN
4290:and
4256:pure
4203:pure
3137:and
2329:and
319:and
167:and
114:and
73:and
58:and
4527:doi
4525:".
4446:293
4350:or
2900:is
1539:to
1165:at
135:+ U
34:or
30:An
4994::
4515:,
4448:.
4360:.
4103:ln
3938:ln
3725:ln
3594:ln
3565:ln
3477:ln
3366:ln
3276:ln
3030:ln
2842:ln
2767:ln
2724:ln
2680:ln
2615:ln
1933:ln
1844::
1601:ln
1579::
1432:ln
1266:ln
1085:ln
796:ln
753:ln
709:ln
498:ln
158:BB
153:=
151:AA
146:=
144:AB
137:BB
133:AA
128:=
126:AB
119:BB
112:AA
105:AB
81:.
4908:)
4904:(
4640:e
4633:t
4626:v
4529::
4502:.
4458:.
4326:i
4303:i
4299:x
4278:i
4252:)
4246:i
4242:p
4238:(
4213:i
4209:x
4199:)
4193:i
4189:p
4185:(
4182:=
4177:i
4173:p
4142:i
4119:.
4114:i
4110:x
4100:T
4097:R
4094:+
4084:i
4076:=
4071:i
4043:i
4016:i
3991:i
3971:i
3949:i
3945:x
3935:T
3932:R
3929:=
3923:x
3920:i
3917:m
3913:,
3910:i
3876:x
3873:i
3870:m
3866:,
3863:i
3850:i
3846:x
3840:i
3832:=
3826:x
3823:i
3820:m
3817:,
3814:m
3809:G
3771:0
3763:i
3759:x
3736:i
3732:x
3705:]
3702:1
3699:,
3696:0
3693:[
3685:i
3681:x
3660:i
3638:i
3634:x
3610:)
3605:B
3601:x
3589:B
3585:x
3581:+
3576:A
3572:x
3560:A
3556:x
3552:(
3549:T
3546:R
3543:=
3537:x
3534:i
3531:m
3528:,
3525:m
3520:G
3488:i
3484:x
3472:i
3468:x
3462:i
3454:T
3451:R
3448:=
3442:x
3439:i
3436:m
3433:,
3430:m
3425:G
3382:.
3377:i
3373:x
3361:i
3357:x
3351:i
3343:R
3337:=
3331:x
3328:i
3325:m
3322:,
3319:m
3314:S
3287:i
3283:x
3271:i
3263:R
3257:=
3251:x
3248:i
3245:m
3241:,
3238:i
3234:s
3200:i
3196:s
3189:T
3175:i
3171:h
3164:=
3153:i
3149:g
3118:i
3114:s
3110:T
3097:i
3093:h
3089:=
3079:i
3075:g
3047:.
3041:i
3037:x
3025:i
3021:x
3014:i
3006:T
3003:R
3000:=
2994:x
2991:i
2988:m
2985:,
2982:m
2977:G
2947:i
2943:g
2936:i
2932:x
2926:i
2918:=
2913:m
2909:G
2886:m
2882:G
2858:.
2853:i
2849:x
2839:T
2836:R
2833:=
2827:x
2824:i
2821:m
2817:,
2814:i
2810:g
2778:i
2774:x
2764:T
2761:R
2758:+
2748:i
2740:=
2735:i
2731:x
2721:T
2718:R
2715:+
2708:u
2704:p
2693:i
2689:f
2677:T
2674:R
2671:+
2665:s
2662:a
2659:g
2653:i
2649:g
2645:=
2638:u
2634:p
2628:i
2624:f
2612:T
2609:R
2606:+
2600:s
2597:a
2594:g
2588:i
2584:g
2580:=
2575:i
2567:=
2556:i
2552:g
2517:.
2506:i
2503:p
2499:C
2492:=
2482:i
2479:p
2475:C
2448:.
2437:i
2433:u
2426:=
2416:i
2412:u
2381:i
2377:v
2373:p
2360:i
2356:h
2352:=
2342:i
2338:u
2309:i
2305:v
2298:p
2284:i
2280:h
2273:=
2262:i
2258:u
2224:i
2220:h
2216:=
2205:i
2201:h
2172:R
2165:s
2162:a
2159:g
2153:i
2149:h
2135:i
2131:h
2121:=
2116:R
2109:s
2106:a
2103:g
2097:i
2093:h
2078:i
2074:h
2037:2
2033:T
2029:h
2021:=
2016:P
2011:)
2005:T
1995:T
1992:g
1981:(
1956:.
1949:u
1945:p
1941:f
1930:=
1924:T
1921:R
1916:)
1911:u
1907:p
1903:,
1900:T
1897:(
1891:s
1888:a
1885:g
1880:g
1873:)
1870:P
1867:,
1864:T
1861:(
1858:g
1828:T
1800:.
1790:i
1786:V
1780:i
1772:=
1769:V
1741:i
1731:v
1724:=
1714:i
1710:v
1683:.
1677:T
1674:R
1663:i
1659:v
1651:=
1644:i
1640:x
1636:,
1633:T
1628:)
1622:P
1612:i
1608:f
1592:(
1555:i
1551:v
1527:v
1503:i
1480:.
1474:T
1471:R
1467:v
1462:=
1457:T
1452:)
1446:P
1438:f
1423:(
1398:v
1375:v
1372:=
1367:T
1362:)
1356:P
1348:)
1345:P
1342:,
1339:T
1336:(
1333:g
1324:(
1296:.
1291:T
1286:)
1280:P
1272:f
1257:(
1252:T
1249:R
1246:=
1241:T
1236:)
1230:P
1222:)
1219:P
1216:,
1213:T
1210:(
1207:g
1198:(
1173:T
1153:p
1108:u
1104:p
1098:i
1094:f
1082:T
1079:R
1076:+
1073:)
1068:u
1064:p
1060:,
1057:T
1054:(
1048:u
1043:g
1039:=
1036:)
1033:P
1030:,
1027:T
1024:(
1021:g
1018:=
1015:)
1012:P
1009:,
1006:T
1003:(
977:i
950:i
946:f
925:i
899:i
895:f
867:i
863:f
857:i
853:x
849:=
844:i
840:f
812:.
807:i
803:x
793:T
790:R
787:+
777:i
769:=
764:i
760:x
750:T
747:R
744:+
737:u
733:p
722:i
718:p
706:T
703:R
700:+
697:)
692:u
688:p
684:,
681:T
678:(
672:u
667:g
663:=
660:)
655:i
651:p
647:,
644:T
641:(
613:i
609:p
583:o
579:P
556:u
552:p
528:.
521:u
517:p
511:i
507:p
495:T
492:R
489:+
486:)
481:u
477:p
473:,
470:T
467:(
461:u
456:g
452:=
449:)
444:i
440:p
436:,
433:T
430:(
427:g
424:=
421:)
416:i
412:p
408:,
405:T
402:(
386:g
359:i
332:i
328:p
301:i
297:x
276:i
250:i
246:p
218:i
214:p
208:i
204:x
200:=
195:i
191:p
155:U
148:U
141:U
130:U
123:U
116:U
109:U
102:U
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.