306:. This theory was very successful for dilute solutions of 1:1 electrolytes and, as discussed below, the Debye–Hückel expressions are still valid at sufficiently low concentrations. The values calculated with Debye–Hückel theory diverge more and more from observed values as the concentrations and/or ionic charges increases. Moreover, Debye–Hückel theory takes no account of the specific properties of ions such as size or shape.
1246:
1927:
929:
2862:
Ge et al. modified this model, and obtained the TCPC parameters for a larger number of single salt aqueous solutions. This model was also extended for a number of electrolytes dissolved in methanol, ethanol, 2-propanol, and so on. Temperature dependent parameters for a number of common single salts
2830:
Besides the set of parameters obtained by Pitzer et al. in the 1970s mentioned in the previous section. Kim and
Frederick published the Pitzer parameters for 304 single salts in aqueous solutions at 298.15 K, extended the model to the concentration range up to the saturation point. Those parameters
2842:
Besides the well-known Pitzer-like equations, there is a simple and easy-to-use semi-empirical model, which is called the three-characteristic-parameter correlation (TCPC) model. It was first proposed by Lin et al. It is a combination of the Pitzer long-range interaction and short-range solvation
701:
2794:
These equations were applied to an extensive range of experimental data at 25 °C with excellent agreement to about 6 mol kg for various types of electrolyte. The treatment can be extended to mixed electrolytes and to include association equilibria. Values for the parameters
2821:
Pitzer parameters and SIT theory have been extensively compared. There are more parameters in the Pitzer equations than in the SIT equations. Because of this the Pitzer equations provide for more precise modelling of mean activity coefficient data and equilibrium constants. However, the
2789:
1717:
2466:
1241:{\displaystyle \ln \gamma _{i}={\frac {\partial ({\frac {G^{ex}}{W_{w}RT}})}{\partial b_{i}}}={\frac {z_{i}^{2}}{2}}f'+2\sum _{j}\lambda _{ij}b_{j}+{\frac {z_{i}^{2}}{2}}\sum _{j}\sum _{k}\lambda '_{jk}b_{j}b_{k}+3\sum _{j}\sum _{k}\mu _{ijk}b_{j}b_{k}+\cdots }
918:
2242:
2566:
489:
3461:
Ge, Xinlei; Zhang, Mei; Guo, Min; Wang, Xidong (April 2008). "Correlation and
Prediction of Thermodynamic Properties of Some Complex Aqueous Electrolytes by the Modified Three-Characteristic-Parameter Correlation Model".
2043:
468:. It was further developed by Guggenheim. Scatchard extended the theory to allow the interaction coefficients to vary with ionic strength. Note that the second form of Brønsted's equation is an expression for the
37:, which characterise interactions amongst ions and solvent. The derivation is thermodynamically rigorous at a given level of expansion. The parameters may be derived from various experimental data such as the
3516:
Ge, Xinlei; Wang, Xidong; Zhang, Mei; Seetharaman, Seshadri (March 2007). "Correlation and
Prediction of Activity and Osmotic Coefficients of Aqueous Electrolytes at 298.15 K by the Modified TCPC Model".
2572:
1711:
1520:
1922:{\displaystyle B_{MX}^{\phi }=\lambda _{MX}+I\lambda '_{MX}+\left({\frac {p}{2q}}\right)\left(\lambda _{MM}+I\lambda '_{MM}\right)+\left({\frac {q}{2p}}\right)\left(\lambda _{XX}+I\lambda '_{XX}\right)}
377:
451:
2253:
142:
2831:
are widely used, however, many complex electrolytes including ones with organic anions or cations, which are very significant in some related fields, were not summarized in their paper.
3434:
Kim, Hee Taik; Frederick, William J. (July 1988). "Evaluation of Pitzer ion interaction parameters of aqueous mixed electrolyte solutions at 25.degree.C. 2. Ternary mixing parameters".
781:
2834:
For some complex electrolytes, Ge et al. obtained the new set of Pitzer parameters using up-to-date measured or critically reviewed osmotic coefficient or activity coefficient data.
3544:
Ge, Xinlei; Zhang, Mei; Guo, Min; Wang, Xidong (January 2008). "Correlation and
Prediction of Thermodynamic Properties of Nonaqueous Electrolytes by the Modified TCPC Model".
1648:
1613:
2116:
2083:
3407:
Kim, Hee Taik; Frederick, William J. (April 1988). "Evaluation of Pitzer ion interaction parameters of aqueous electrolytes at 25.degree.C. 1. Single salt parameters".
1578:
237:
2866:
The performance of the TCPC model in correlation with the measured activity coefficient or osmotic coefficients is found to be comparable with Pitzer-like models.
2814:
measured as concentration quotients. Both SIT and Pitzer parameters have been used in this context, For example, both sets of parameters were calculated for some
2135:
269:
205:
185:
165:
3571:
Ge, Xinlei; Wang, Xidong (12 February 2009). "A Simple Two-Parameter
Correlation Model for Aqueous Electrolyte Solutions across a Wide Range of Temperatures".
22:
are important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water. They were first described by
2477:
696:{\displaystyle {\frac {G^{ex}}{W_{w}RT}}=f(I)+\sum _{i}\sum _{j}b_{i}b_{j}\lambda _{ij}(I)+\sum _{i}\sum _{j}\sum _{k}b_{i}b_{j}b_{k}\mu _{ijk}+\cdots }
279:
of molecules, the third virial coefficient involves interactions between three molecules, etc. This theory was developed by McMillan and Mayer.
1933:
2784:{\displaystyle \ln \gamma _{\pm }=|z^{+}z^{-}|f^{\gamma }+m\left({\frac {2pq}{p+q}}\right)B_{MX}^{\gamma }+m^{2}\leftC_{MX}^{\gamma }}
2118:
are not included as interactions between three ions of the same charge are unlikely to occur except in very concentrated solutions.
1253:
282:
Solutions of uncharged molecules can be treated by a modification of the McMillan-Mayer theory. However, when a solution contains
923:
and an expression for the activity coefficient is obtained by differentiating the virial expansion with respect to a molality b.
1656:
2807:
for inorganic and organic acids, bases and salts have been tabulated. Temperature and pressure variation is also discussed.
315:
383:
3489:
Lin, Cheng-Long; Lee, Liang-Sun; Tseng, Hsieng-Cheng (September 1993). "Thermodynamic behavior of electrolyte solutions".
3619:
2461:{\displaystyle \phi -1=|z^{+}z^{-}|f^{\phi }+b\left({\frac {2pq}{p+q}}\right)B_{MX}^{\phi }+m^{2}\leftC_{MX}^{\phi }.}
751:. This binary interaction parameter or second virial coefficient depends on ionic strength, on the particular species
3390:
3019:
2994:
2969:
2907:
3609:
3604:
3354:
Crea, F.; Foti, C.; Sammartano, S. (2008). "Sequestering ability of polycarboxylic acids towards dioxouranium(V)".
913:{\displaystyle G=\sum _{i}\mu _{i}\cdot N_{i}=\sum _{i}\left(\mu _{i}^{0}+RT\ln b_{i}\gamma _{i}\right)\cdot N_{i}}
71:
50:
3614:
3329:
3211:
2940:
2818:
complexes and were found to account equally well for the ionic strength dependence of the stability constants.
768:
represent the interactions between three particles. Higher terms may also be included in the virial expansion.
2822:
determination of the greater number of Pitzer parameters means that they are more difficult to determine.
53:(SIT theory), but Pitzer parameters are more difficult to determine experimentally than SIT parameters.
3229:"Thermodynamics of Electrolytes, II. Activity and osmotic coefficients with one or both ions univalent"
456:
in which the activity coefficient depended not only on ionic strength, but also on the concentration,
291:
46:
472:. Measurement of osmotic coefficients provides one means for determining mean activity coefficients.
3035:
E. Connick, Robert E. Connick (December 2000). "Kenneth Pitzer, 6 January 1914 · 26 December 1997".
1618:
1583:
298:
made up of ions of the opposite charge. Expressions were derived for the variation of single-ion
3062:
McMillan, W.G.; Mayer, J.E. (1945). "The statistical thermodynamics of multicomponent systems".
2088:
2055:
41:, mixed ion activity coefficients, and salt solubility. They can be used to calculate mixed ion
1556:
3291:"Thermodynamics of electrolytes. IV. Activity and osmotic coefficients for mixed electrolytes"
3260:"Thermodynamics of Electrolytes. III. Activity and osmotic coefficients for 2–2 electrolytes"
272:
2810:
One area of application of Pitzer parameters is to describe the ionic strength variation of
3072:
2811:
743:
represent the short-range interactions in the presence of solvent between solute particles
299:
210:
42:
2237:{\displaystyle B_{MX}^{\phi }=\beta _{MX}^{(0)}+\beta _{MX}^{(1)}e^{-\alpha {\sqrt {I}}}.}
8:
2885:
469:
240:
38:
3076:
2125:
parameter was found empirically to show an ionic strength dependence (in the absence of
3044:
2958:
772:
254:
190:
170:
150:
3502:
3386:
3325:
3207:
3015:
2990:
2965:
2936:
2903:
481:
34:
29:. The parameters of the Pitzer equations are linear combinations of parameters, of a
3580:
3553:
3526:
3498:
3471:
3443:
3416:
3363:
3302:
3271:
3240:
3184:
3157:
3130:
3080:
2875:
2561:{\displaystyle \ln \gamma _{\pm }={\frac {p\ln \gamma _{M}+q\ln \gamma _{X}}{p+q}}}
295:
294:
was based on the assumption that each ion was surrounded by a spherical "cloud" or
62:
30:
23:
3367:
2880:
275:
that the second virial coefficient arises from the intermolecular forces between
3290:
3259:
3064:
303:
26:
3598:
3119:"Studies on solubility IV. The principle of the specific interaction of ions"
287:
248:
3228:
2247:
With these definitions, the expression for the osmotic coefficient becomes
3161:
2038:{\displaystyle C_{MX}^{\phi }=\left\left(p\mu _{MMX}+q\mu _{MXX}\right).}
283:
3447:
3420:
3306:
3244:
3188:
3148:
Guggenheim, E.A.; Turgeon, J.C. (1955). "Specific interaction of ions".
3134:
3275:
3175:
Scatchard, G. (1936). "Concentrated solutions of strong electrolytes".
3048:
465:
45:
and water activities in solutions of high ionic strength for which the
3584:
3557:
3530:
3475:
3084:
244:
3118:
2471:
A similar expression is obtained for the mean activity coefficient.
49:
is no longer adequate. They are more rigorous than the equations of
2126:
2987:
Aquatic
Chemistry: Chemical Equilibria and Rates in Natural Waters
2815:
3397:
Chapter 9, Estimation of medium effects on thermodynamic data
3098:
Debye, P.; Hückel, E. (1923). "Zur
Theorie der Electrolyte".
1515:{\displaystyle \phi -1=\left(\sum _{i}b_{i}\right)^{-1}\left}
724:
480:
The exposition begins with a virial expansion of the excess
309:
Brønsted had independently proposed an empirical equation,
3353:
735:
represents the Debye–Hückel limiting law. The quantities
61:
A starting point for the development can be taken as the
1706:{\displaystyle f^{\phi }={\frac {f'-{\frac {f}{I}}}{2}}}
3380:
3147:
3515:
2052:
is essentially the Debye–Hückel term. Terms involving
372:{\displaystyle \ln {\gamma }=-\alpha m^{1/2}-2\beta m}
247:. The remaining terms quantify the departure from the
2916:
Ion interaction approach: theory and data correlation
2575:
2480:
2256:
2138:
2091:
2058:
1936:
1720:
1659:
1621:
1586:
1559:
1256:
932:
784:
492:
446:{\displaystyle 1-\varphi =(\alpha /3)m^{1/2}+\beta m}
386:
318:
257:
213:
193:
173:
153:
74:
3324:(2nd ed.). Boca Raton: CRC Press. p. 93.
3206:(2nd ed.). Boca Raton: CRC Press. p. 84.
3061:
2984:
2825:
2957:
2783:
2560:
2460:
2236:
2110:
2077:
2037:
1921:
1705:
1642:
1607:
1572:
1514:
1240:
912:
695:
445:
371:
290:interactions must also be taken into account. The
263:
243:. The first term on the right-hand side is for an
231:
199:
179:
159:
136:
3257:
3226:
3037:Proceedings of the American Philosophical Society
2955:
771:Next, the free energy is expressed as the sum of
759:and the temperature and pressure. The quantities
3596:
3288:
3097:
3543:
3460:
3322:Activity coefficients in electrolyte solutions
3204:Activity coefficients in electrolyte solutions
2933:Activity coefficients in electrolyte solutions
2900:Activity coefficients in electrolyte solutions
16:Thermodynamic extension of Debye–Hückel theory
3433:
3406:
3014:(3rd ed.). London: Taylor and Francis.
460:, of the specific ion through the parameter
137:{\displaystyle PV=RT+BP+CP^{2}+DP^{3}\dots }
3488:
2949:
3573:Journal of Chemical & Engineering Data
3546:Journal of Chemical & Engineering Data
3519:Journal of Chemical & Engineering Data
3464:Journal of Chemical & Engineering Data
3436:Journal of Chemical & Engineering Data
3409:Journal of Chemical & Engineering Data
3034:
2837:
3174:
56:
3116:
475:
3374:
3009:
2935:(2nd ed.). Boca Raton: CRC Press.
731:is the ionic strength. The first term,
3597:
3570:
3381:Grenthe, I.; Puigdomenech, I. (1997).
3319:
3201:
3028:
2978:
2930:
2897:
712:is the mass of the water in kilograms,
2985:Snoeyink, V.L.; Jenkins, D. (1980).
13:
3385:. Nuclear Energy Agency, O.E.C.D.
3258:Pitzer, K.S.; Mayorga, G. (1974).
3227:Pitzer, K.S.; Mayorga, G. (1973).
2863:were also compiled, available at.
1001:
955:
14:
3631:
775:, or partial molal free energy,
3289:Pitzer, K.S.; Kim, J.J. (1974).
3141:
2956:Stumm, W.; Morgan, J.J. (1996).
2826:Compilation of Pitzer parameters
3564:
3537:
3509:
3482:
3454:
3427:
3400:
3347:
3338:
3313:
3282:
3251:
3220:
3195:
3168:
51:specific ion interaction theory
3383:Modelling in aquatic chemistry
3110:
3091:
3055:
3003:
2924:
2902:(2nd ed.). C.R.C. Press.
2727:
2717:
2621:
2596:
2401:
2391:
2295:
2270:
2206:
2200:
2179:
2173:
2129:) which could be expressed as
1643:{\displaystyle C_{MX}^{\phi }}
1608:{\displaystyle B_{MX}^{\phi }}
996:
958:
605:
599:
540:
534:
413:
399:
1:
3368:10.1016/j.talanta.2007.12.009
2891:
65:equation of state for a gas.
3503:10.1016/0378-3812(93)85004-6
7:
3320:Pitzer, Kenneth S. (1991).
3202:Pitzer, Kenneth S. (1991).
2931:Pitzer, Kenneth S. (1991).
2869:
10:
3636:
3344:Pitzer (1991), Tables 2-11
2898:Pitzer, K.S., ed. (1991).
2111:{\displaystyle \mu _{XXX}}
2078:{\displaystyle \mu _{MMM}}
3620:Electrochemical equations
2914:Chapter 3. *Pitzer, K.S.
1573:{\displaystyle f^{\phi }}
1524:For a simple electrolyte
251:with changing pressure,
3610:Chemical thermodynamics
3605:Thermodynamic equations
3117:Brønsted, J.N. (1922).
2838:A comparable TCPC model
464:. This is the basis of
207:is the temperature and
3491:Fluid Phase Equilibria
3010:Millero, F.J. (2006).
2785:
2562:
2462:
2238:
2112:
2079:
2039:
1923:
1707:
1644:
1609:
1574:
1516:
1242:
914:
697:
447:
373:
265:
233:
201:
181:
161:
138:
57:Historical development
3615:Equilibrium chemistry
3012:Chemical Oceanography
2812:equilibrium constants
2786:
2563:
2463:
2239:
2113:
2080:
2040:
1924:
1708:
1645:
1610:
1575:
1541:, at a concentration
1517:
1243:
915:
698:
476:The Pitzer parameters
448:
374:
300:activity coefficients
273:statistical mechanics
271:. It can be shown by
266:
234:
232:{\displaystyle B,C,D}
202:
182:
162:
139:
43:activity coefficients
3162:10.1039/TF9555100747
2573:
2478:
2254:
2136:
2089:
2056:
1934:
1718:
1657:
1619:
1584:
1557:
1254:
930:
782:
490:
384:
316:
255:
211:
191:
171:
151:
72:
3448:10.1021/je00053a017
3421:10.1021/je00052a035
3307:10.1021/ja00825a004
3245:10.1021/j100638a009
3189:10.1021/cr60064a008
3135:10.1021/ja01426a001
3077:1945JChPh..13..276M
2989:. New York: Wiley.
2964:. New York: Wiley.
2886:Osmotic coefficient
2780:
2692:
2454:
2366:
2210:
2183:
2156:
1954:
1913:
1842:
1776:
1738:
1639:
1604:
1393:
1149:
1108:
1036:
856:
773:chemical potentials
470:osmotic coefficient
292:Debye–Hückel theory
241:virial coefficients
47:Debye–Hückel theory
39:osmotic coefficient
3276:10.1007/BF00648138
3150:Trans. Faraday Soc
2918:, pp. 75–153.
2781:
2763:
2675:
2558:
2458:
2437:
2349:
2234:
2187:
2160:
2139:
2108:
2075:
2035:
1937:
1919:
1898:
1827:
1761:
1721:
1703:
1640:
1622:
1605:
1587:
1570:
1545:, made up of ions
1512:
1454:
1444:
1434:
1378:
1353:
1343:
1284:
1238:
1195:
1185:
1134:
1133:
1123:
1094:
1065:
1022:
910:
842:
836:
800:
693:
640:
630:
620:
565:
555:
443:
369:
261:
229:
197:
177:
157:
134:
3585:10.1021/je800483q
3558:10.1021/je700446q
3531:10.1021/je060451k
3476:10.1021/je7006499
3301:(18): 5701–5707.
3264:J. Solution. Chem
3239:(19): 2300–2308.
3085:10.1063/1.1724036
2756:
2669:
2556:
2430:
2343:
2227:
1975:
1974:
1868:
1797:
1701:
1695:
1553:, the parameters
1445:
1435:
1425:
1344:
1334:
1275:
1186:
1176:
1124:
1114:
1112:
1056:
1040:
1015:
994:
827:
791:
631:
621:
611:
556:
546:
526:
482:Gibbs free energy
302:as a function of
264:{\displaystyle P}
239:... are known as
200:{\displaystyle T}
180:{\displaystyle V}
167:is the pressure,
160:{\displaystyle P}
35:Gibbs free energy
3627:
3589:
3588:
3568:
3562:
3561:
3541:
3535:
3534:
3513:
3507:
3506:
3486:
3480:
3479:
3458:
3452:
3451:
3431:
3425:
3424:
3404:
3398:
3396:
3378:
3372:
3371:
3351:
3345:
3342:
3336:
3335:
3317:
3311:
3310:
3295:J. Am. Chem. Soc
3286:
3280:
3279:
3255:
3249:
3248:
3224:
3218:
3217:
3199:
3193:
3192:
3172:
3166:
3165:
3145:
3139:
3138:
3123:J. Am. Chem. Soc
3114:
3108:
3107:
3095:
3089:
3088:
3059:
3053:
3052:
3032:
3026:
3025:
3007:
3001:
3000:
2982:
2976:
2975:
2963:
2953:
2947:
2946:
2928:
2913:
2876:Bromley equation
2790:
2788:
2787:
2782:
2779:
2774:
2762:
2758:
2757:
2755:
2744:
2743:
2742:
2738:
2715:
2705:
2704:
2691:
2686:
2674:
2670:
2668:
2657:
2646:
2634:
2633:
2624:
2619:
2618:
2609:
2608:
2599:
2591:
2590:
2567:
2565:
2564:
2559:
2557:
2555:
2544:
2543:
2542:
2521:
2520:
2501:
2496:
2495:
2467:
2465:
2464:
2459:
2453:
2448:
2436:
2432:
2431:
2429:
2418:
2417:
2416:
2412:
2389:
2379:
2378:
2365:
2360:
2348:
2344:
2342:
2331:
2320:
2308:
2307:
2298:
2293:
2292:
2283:
2282:
2273:
2243:
2241:
2240:
2235:
2230:
2229:
2228:
2223:
2209:
2198:
2182:
2171:
2155:
2150:
2117:
2115:
2114:
2109:
2107:
2106:
2084:
2082:
2081:
2076:
2074:
2073:
2044:
2042:
2041:
2036:
2031:
2027:
2026:
2025:
2004:
2003:
1980:
1976:
1967:
1963:
1953:
1948:
1928:
1926:
1925:
1920:
1918:
1914:
1909:
1891:
1890:
1873:
1869:
1867:
1856:
1847:
1843:
1838:
1820:
1819:
1802:
1798:
1796:
1785:
1772:
1754:
1753:
1737:
1732:
1712:
1710:
1709:
1704:
1702:
1697:
1696:
1688:
1683:
1674:
1669:
1668:
1649:
1647:
1646:
1641:
1638:
1633:
1614:
1612:
1611:
1606:
1603:
1598:
1579:
1577:
1576:
1571:
1569:
1568:
1521:
1519:
1518:
1513:
1511:
1507:
1500:
1499:
1490:
1489:
1480:
1479:
1470:
1469:
1453:
1443:
1433:
1418:
1417:
1408:
1407:
1398:
1394:
1389:
1371:
1370:
1352:
1342:
1324:
1308:
1307:
1299:
1295:
1294:
1293:
1283:
1247:
1245:
1244:
1239:
1231:
1230:
1221:
1220:
1211:
1210:
1194:
1184:
1169:
1168:
1159:
1158:
1145:
1132:
1122:
1113:
1107:
1102:
1093:
1088:
1087:
1078:
1077:
1064:
1049:
1041:
1035:
1030:
1021:
1016:
1014:
1013:
1012:
999:
995:
993:
986:
985:
975:
974:
962:
953:
948:
947:
919:
917:
916:
911:
909:
908:
896:
892:
891:
890:
881:
880:
855:
850:
835:
823:
822:
810:
809:
799:
727:of the ions and
702:
700:
699:
694:
686:
685:
670:
669:
660:
659:
650:
649:
639:
629:
619:
598:
597:
585:
584:
575:
574:
564:
554:
527:
525:
518:
517:
507:
506:
494:
452:
450:
449:
444:
433:
432:
428:
409:
378:
376:
375:
370:
356:
355:
351:
329:
296:ionic atmosphere
270:
268:
267:
262:
238:
236:
235:
230:
206:
204:
203:
198:
186:
184:
183:
178:
166:
164:
163:
158:
143:
141:
140:
135:
130:
129:
114:
113:
31:virial expansion
24:physical chemist
20:Pitzer equations
3635:
3634:
3630:
3629:
3628:
3626:
3625:
3624:
3595:
3594:
3593:
3592:
3569:
3565:
3542:
3538:
3514:
3510:
3487:
3483:
3459:
3455:
3432:
3428:
3405:
3401:
3393:
3379:
3375:
3352:
3348:
3343:
3339:
3332:
3318:
3314:
3287:
3283:
3256:
3252:
3225:
3221:
3214:
3200:
3196:
3173:
3169:
3146:
3142:
3115:
3111:
3096:
3092:
3060:
3056:
3033:
3029:
3022:
3008:
3004:
2997:
2983:
2979:
2972:
2960:Water Chemistry
2954:
2950:
2943:
2929:
2925:
2910:
2894:
2881:Davies equation
2872:
2840:
2828:
2775:
2767:
2745:
2734:
2730:
2726:
2716:
2714:
2710:
2706:
2700:
2696:
2687:
2679:
2658:
2647:
2645:
2641:
2629:
2625:
2620:
2614:
2610:
2604:
2600:
2595:
2586:
2582:
2574:
2571:
2570:
2545:
2538:
2534:
2516:
2512:
2502:
2500:
2491:
2487:
2479:
2476:
2475:
2449:
2441:
2419:
2408:
2404:
2400:
2390:
2388:
2384:
2380:
2374:
2370:
2361:
2353:
2332:
2321:
2319:
2315:
2303:
2299:
2294:
2288:
2284:
2278:
2274:
2269:
2255:
2252:
2251:
2222:
2215:
2211:
2199:
2191:
2172:
2164:
2151:
2143:
2137:
2134:
2133:
2096:
2092:
2090:
2087:
2086:
2063:
2059:
2057:
2054:
2053:
2015:
2011:
1993:
1989:
1985:
1981:
1962:
1958:
1949:
1941:
1935:
1932:
1931:
1902:
1883:
1879:
1878:
1874:
1860:
1855:
1851:
1831:
1812:
1808:
1807:
1803:
1789:
1784:
1780:
1765:
1746:
1742:
1733:
1725:
1719:
1716:
1715:
1687:
1676:
1675:
1673:
1664:
1660:
1658:
1655:
1654:
1650:are defined as
1634:
1626:
1620:
1617:
1616:
1599:
1591:
1585:
1582:
1581:
1564:
1560:
1558:
1555:
1554:
1540:
1532:
1495:
1491:
1485:
1481:
1475:
1471:
1459:
1455:
1449:
1439:
1429:
1413:
1409:
1403:
1399:
1382:
1363:
1359:
1358:
1354:
1348:
1338:
1317:
1313:
1309:
1300:
1289:
1285:
1279:
1274:
1270:
1269:
1255:
1252:
1251:
1226:
1222:
1216:
1212:
1200:
1196:
1190:
1180:
1164:
1160:
1154:
1150:
1138:
1128:
1118:
1103:
1098:
1092:
1083:
1079:
1070:
1066:
1060:
1042:
1031:
1026:
1020:
1008:
1004:
1000:
981:
977:
976:
967:
963:
961:
954:
952:
943:
939:
931:
928:
927:
904:
900:
886:
882:
876:
872:
851:
846:
841:
837:
831:
818:
814:
805:
801:
795:
783:
780:
779:
767:
740:
721:
717:
710:
675:
671:
665:
661:
655:
651:
645:
641:
635:
625:
615:
590:
586:
580:
576:
570:
566:
560:
550:
513:
509:
508:
499:
495:
493:
491:
488:
487:
478:
424:
420:
416:
405:
385:
382:
381:
347:
343:
339:
325:
317:
314:
313:
256:
253:
252:
212:
209:
208:
192:
189:
188:
187:is the volume,
172:
169:
168:
152:
149:
148:
125:
121:
109:
105:
73:
70:
69:
59:
17:
12:
11:
5:
3633:
3623:
3622:
3617:
3612:
3607:
3591:
3590:
3579:(2): 179–186.
3563:
3552:(1): 149–159.
3536:
3525:(2): 538–547.
3508:
3481:
3470:(4): 950–958.
3453:
3442:(3): 278–283.
3426:
3415:(2): 177–184.
3399:
3391:
3373:
3362:(3): 775–778.
3346:
3337:
3330:
3312:
3281:
3270:(7): 539–546.
3250:
3219:
3212:
3194:
3183:(3): 309–327.
3167:
3140:
3129:(5): 877–898.
3109:
3090:
3065:J. Chem. Phys.
3054:
3043:(4): 479–483.
3027:
3020:
3002:
2995:
2977:
2970:
2948:
2941:
2922:
2921:
2920:
2919:
2908:
2893:
2890:
2889:
2888:
2883:
2878:
2871:
2868:
2860:
2859:
2839:
2836:
2827:
2824:
2792:
2791:
2778:
2773:
2770:
2766:
2761:
2754:
2751:
2748:
2741:
2737:
2733:
2729:
2725:
2722:
2719:
2713:
2709:
2703:
2699:
2695:
2690:
2685:
2682:
2678:
2673:
2667:
2664:
2661:
2656:
2653:
2650:
2644:
2640:
2637:
2632:
2628:
2623:
2617:
2613:
2607:
2603:
2598:
2594:
2589:
2585:
2581:
2578:
2568:
2554:
2551:
2548:
2541:
2537:
2533:
2530:
2527:
2524:
2519:
2515:
2511:
2508:
2505:
2499:
2494:
2490:
2486:
2483:
2469:
2468:
2457:
2452:
2447:
2444:
2440:
2435:
2428:
2425:
2422:
2415:
2411:
2407:
2403:
2399:
2396:
2393:
2387:
2383:
2377:
2373:
2369:
2364:
2359:
2356:
2352:
2347:
2341:
2338:
2335:
2330:
2327:
2324:
2318:
2314:
2311:
2306:
2302:
2297:
2291:
2287:
2281:
2277:
2272:
2268:
2265:
2262:
2259:
2245:
2244:
2233:
2226:
2221:
2218:
2214:
2208:
2205:
2202:
2197:
2194:
2190:
2186:
2181:
2178:
2175:
2170:
2167:
2163:
2159:
2154:
2149:
2146:
2142:
2105:
2102:
2099:
2095:
2072:
2069:
2066:
2062:
2046:
2045:
2034:
2030:
2024:
2021:
2018:
2014:
2010:
2007:
2002:
1999:
1996:
1992:
1988:
1984:
1979:
1973:
1970:
1966:
1961:
1957:
1952:
1947:
1944:
1940:
1929:
1917:
1912:
1908:
1905:
1901:
1897:
1894:
1889:
1886:
1882:
1877:
1872:
1866:
1863:
1859:
1854:
1850:
1846:
1841:
1837:
1834:
1830:
1826:
1823:
1818:
1815:
1811:
1806:
1801:
1795:
1792:
1788:
1783:
1779:
1775:
1771:
1768:
1764:
1760:
1757:
1752:
1749:
1745:
1741:
1736:
1731:
1728:
1724:
1713:
1700:
1694:
1691:
1686:
1682:
1679:
1672:
1667:
1663:
1637:
1632:
1629:
1625:
1602:
1597:
1594:
1590:
1567:
1563:
1536:
1528:
1510:
1506:
1503:
1498:
1494:
1488:
1484:
1478:
1474:
1468:
1465:
1462:
1458:
1452:
1448:
1442:
1438:
1432:
1428:
1424:
1421:
1416:
1412:
1406:
1402:
1397:
1392:
1388:
1385:
1381:
1377:
1374:
1369:
1366:
1362:
1357:
1351:
1347:
1341:
1337:
1333:
1330:
1327:
1323:
1320:
1316:
1312:
1306:
1303:
1298:
1292:
1288:
1282:
1278:
1273:
1268:
1265:
1262:
1259:
1249:
1248:
1237:
1234:
1229:
1225:
1219:
1215:
1209:
1206:
1203:
1199:
1193:
1189:
1183:
1179:
1175:
1172:
1167:
1163:
1157:
1153:
1148:
1144:
1141:
1137:
1131:
1127:
1121:
1117:
1111:
1106:
1101:
1097:
1091:
1086:
1082:
1076:
1073:
1069:
1063:
1059:
1055:
1052:
1048:
1045:
1039:
1034:
1029:
1025:
1019:
1011:
1007:
1003:
998:
992:
989:
984:
980:
973:
970:
966:
960:
957:
951:
946:
942:
938:
935:
921:
920:
907:
903:
899:
895:
889:
885:
879:
875:
871:
868:
865:
862:
859:
854:
849:
845:
840:
834:
830:
826:
821:
817:
813:
808:
804:
798:
794:
790:
787:
763:
738:
719:
715:
708:
704:
703:
692:
689:
684:
681:
678:
674:
668:
664:
658:
654:
648:
644:
638:
634:
628:
624:
618:
614:
610:
607:
604:
601:
596:
593:
589:
583:
579:
573:
569:
563:
559:
553:
549:
545:
542:
539:
536:
533:
530:
524:
521:
516:
512:
505:
502:
498:
477:
474:
454:
453:
442:
439:
436:
431:
427:
423:
419:
415:
412:
408:
404:
401:
398:
395:
392:
389:
379:
368:
365:
362:
359:
354:
350:
346:
342:
338:
335:
332:
328:
324:
321:
304:ionic strength
260:
228:
225:
222:
219:
216:
196:
176:
156:
145:
144:
133:
128:
124:
120:
117:
112:
108:
104:
101:
98:
95:
92:
89:
86:
83:
80:
77:
58:
55:
33:of the excess
27:Kenneth Pitzer
15:
9:
6:
4:
3:
2:
3632:
3621:
3618:
3616:
3613:
3611:
3608:
3606:
3603:
3602:
3600:
3586:
3582:
3578:
3574:
3567:
3559:
3555:
3551:
3547:
3540:
3532:
3528:
3524:
3520:
3512:
3504:
3500:
3496:
3492:
3485:
3477:
3473:
3469:
3465:
3457:
3449:
3445:
3441:
3437:
3430:
3422:
3418:
3414:
3410:
3403:
3394:
3392:92-64-15569-4
3388:
3384:
3377:
3369:
3365:
3361:
3357:
3350:
3341:
3333:
3327:
3323:
3316:
3308:
3304:
3300:
3296:
3292:
3285:
3277:
3273:
3269:
3265:
3261:
3254:
3246:
3242:
3238:
3234:
3233:J. Phys. Chem
3230:
3223:
3215:
3209:
3205:
3198:
3190:
3186:
3182:
3178:
3171:
3163:
3159:
3155:
3151:
3144:
3136:
3132:
3128:
3124:
3120:
3113:
3105:
3101:
3094:
3086:
3082:
3078:
3074:
3070:
3067:
3066:
3058:
3050:
3046:
3042:
3038:
3031:
3023:
3021:0-8493-2280-4
3017:
3013:
3006:
2998:
2996:0-471-51185-4
2992:
2988:
2981:
2973:
2971:0-471-05196-9
2967:
2962:
2961:
2952:
2944:
2938:
2934:
2927:
2923:
2917:
2911:
2909:0-8493-5415-3
2905:
2901:
2896:
2895:
2887:
2884:
2882:
2879:
2877:
2874:
2873:
2867:
2864:
2858:
2854:
2850:
2846:
2845:
2844:
2835:
2832:
2823:
2819:
2817:
2813:
2808:
2806:
2802:
2798:
2776:
2771:
2768:
2764:
2759:
2752:
2749:
2746:
2739:
2735:
2731:
2723:
2720:
2711:
2707:
2701:
2697:
2693:
2688:
2683:
2680:
2676:
2671:
2665:
2662:
2659:
2654:
2651:
2648:
2642:
2638:
2635:
2630:
2626:
2615:
2611:
2605:
2601:
2592:
2587:
2583:
2579:
2576:
2569:
2552:
2549:
2546:
2539:
2535:
2531:
2528:
2525:
2522:
2517:
2513:
2509:
2506:
2503:
2497:
2492:
2488:
2484:
2481:
2474:
2473:
2472:
2455:
2450:
2445:
2442:
2438:
2433:
2426:
2423:
2420:
2413:
2409:
2405:
2397:
2394:
2385:
2381:
2375:
2371:
2367:
2362:
2357:
2354:
2350:
2345:
2339:
2336:
2333:
2328:
2325:
2322:
2316:
2312:
2309:
2304:
2300:
2289:
2285:
2279:
2275:
2266:
2263:
2260:
2257:
2250:
2249:
2248:
2231:
2224:
2219:
2216:
2212:
2203:
2195:
2192:
2188:
2184:
2176:
2168:
2165:
2161:
2157:
2152:
2147:
2144:
2140:
2132:
2131:
2130:
2128:
2124:
2119:
2103:
2100:
2097:
2093:
2070:
2067:
2064:
2060:
2051:
2032:
2028:
2022:
2019:
2016:
2012:
2008:
2005:
2000:
1997:
1994:
1990:
1986:
1982:
1977:
1971:
1968:
1964:
1959:
1955:
1950:
1945:
1942:
1938:
1930:
1915:
1910:
1906:
1903:
1899:
1895:
1892:
1887:
1884:
1880:
1875:
1870:
1864:
1861:
1857:
1852:
1848:
1844:
1839:
1835:
1832:
1828:
1824:
1821:
1816:
1813:
1809:
1804:
1799:
1793:
1790:
1786:
1781:
1777:
1773:
1769:
1766:
1762:
1758:
1755:
1750:
1747:
1743:
1739:
1734:
1729:
1726:
1722:
1714:
1698:
1692:
1689:
1684:
1680:
1677:
1670:
1665:
1661:
1653:
1652:
1651:
1635:
1630:
1627:
1623:
1600:
1595:
1592:
1588:
1565:
1561:
1552:
1548:
1544:
1539:
1535:
1531:
1527:
1522:
1508:
1504:
1501:
1496:
1492:
1486:
1482:
1476:
1472:
1466:
1463:
1460:
1456:
1450:
1446:
1440:
1436:
1430:
1426:
1422:
1419:
1414:
1410:
1404:
1400:
1395:
1390:
1386:
1383:
1379:
1375:
1372:
1367:
1364:
1360:
1355:
1349:
1345:
1339:
1335:
1331:
1328:
1325:
1321:
1318:
1314:
1310:
1304:
1301:
1296:
1290:
1286:
1280:
1276:
1271:
1266:
1263:
1260:
1257:
1235:
1232:
1227:
1223:
1217:
1213:
1207:
1204:
1201:
1197:
1191:
1187:
1181:
1177:
1173:
1170:
1165:
1161:
1155:
1151:
1146:
1142:
1139:
1135:
1129:
1125:
1119:
1115:
1109:
1104:
1099:
1095:
1089:
1084:
1080:
1074:
1071:
1067:
1061:
1057:
1053:
1050:
1046:
1043:
1037:
1032:
1027:
1023:
1017:
1009:
1005:
990:
987:
982:
978:
971:
968:
964:
949:
944:
940:
936:
933:
926:
925:
924:
905:
901:
897:
893:
887:
883:
877:
873:
869:
866:
863:
860:
857:
852:
847:
843:
838:
832:
828:
824:
819:
815:
811:
806:
802:
796:
792:
788:
785:
778:
777:
776:
774:
769:
766:
762:
758:
754:
750:
746:
742:
734:
730:
726:
722:
711:
690:
687:
682:
679:
676:
672:
666:
662:
656:
652:
646:
642:
636:
632:
626:
622:
616:
612:
608:
602:
594:
591:
587:
581:
577:
571:
567:
561:
557:
551:
547:
543:
537:
531:
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288:electrostatic
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2127:ion-pairing
3599:Categories
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3213:0849354153
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2942:0849354153
2892:References
725:molalities
466:SIT theory
3177:Chem. Rev
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