Activity coefficients 3.9.6



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3.9.6 Activity coefficients

Activity coefficients of some strong electrolytes in aqueous solution at 25 °C

The mean ionic activity coefficient γ_± of an electrolyte, consisting of v₊ cations R and v₋ anions X, is related to the chemical potential μ of one mole of electrolyte by

μ = μ^θ + v₊RT ln m_R + v₋RT ln m_X + (v₊ + v₋)RT ln γ_±

where m_R and m_X denote the molalities of the cation R and anion X respectively while μ is independent of the composition of the solution and is chosen so that γ_±→ 1 at infinite dilution.

In the following table of γ_± for some typical 1–1 electrolytes at 25°C the values at molalities 0.1 upwards have been interpolated by a Debye–Hückel type of formula. All γ_± values are considered to be accurate to within ±0.002.

Some 1-1 electrolytes at 25 °C

m/(mol kg ^-¹)	HCl	LiCl	NaCl	KCl	CsCl	LiNO₃	NaNO₃	KNO₃	CsNO₃

0.01^{. . .}	0.904	0.903	0.902	0.901	0.899	0.903	0.900	0.897	0.896
0.02^{. . .}	0.875	0.873	0.870	0.868	0.865	0.872	0.866	0.861	0.860
0.05^{. . .}	0.830	0.825	0.820	0.816	0.807	0.825	0.811	0.799	0.795
0.10^{. . .}	0.796	0.790	0.778	0.770	0.756	0.788	0.762	0.739	0.733
0.2^{. . .}	0.767	0.757	0.735	0.718	0.694	0.752	0.703	0.663	0.655
0.4 ^{. . .}	0.755	0.740	0.693	0.666	0.628	0.728	0.638	0.576	0.561
0.6 ^{. . .}	0.763	0.743	0.673	0.637	0.589	0.727	0.599	0.519	0.501
0.8 ^{. . .}	0.783	0.755	0.662	0.618	0.563	0.733	0.570	0.476	0.458
1.0 ^{. . .}	0.809	0.774	0.657	0.604	0.544	0.743	0.548	0.443	0.422
1.2 ^{. . .}	0.840	0.796	0.654	0.593	0.529	0.757	0.530	0.414	0.393
1.4 ^{. . .}	0.876	0.823	0.655	0.586	0.518	0.774	0.514	0.390	0.368
1.6 ^{. . .}	0.916	0.853	0.657	0.580	0.509	0.792	0.501	0.369
1.8 ^{. . .}	0.960	0.885	0.662	0.576	0.501	0.812	0.489	0.350
2.0 ^{. . .}	1.009	0.921	0.668	0.573	0.495	0.835	0.478	0.333
2.5 ^{. . .}	1.147	1.026	0.688	0.569	0.484	0.896	0.455	0.297
3.0 ^{. . .}	1.316	1.156	0.714	0.569	0.478	0.966	0.437	0.269
3.5 ^{. . .}	1.518	1.317	0.746	0.572	0.474	1.044	0.422	0.246
4.0 ^{. . .}	1.762	1.510	0.783	0.577	0.473	1.125	0.408
4.5 ^{. . .}	2.04	1.741	0.826	0.583	0.473	1.215	0.396
5.0 ^{. . .}	2.38	2.02	0.874		0.474	1.310	0.386

The values of γ for typical 2–1 and 1–2 electrolytes in the following table are from Hamer and Wu (1972). They are principally derived from experimental values of relative water vapour pressures by use of the Gibbs–Duhem relation.

Some 2–1 and 1–2 electrolytes at 25 °C

m/(mol kg⁻¹)	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0

MgCl₂ . .	0.535	0.494	0.481	0.480	0.485	0.496	0.511	0.530	0.552	0.577
CaCl₂ . .	0.517	0.469	0.451	0.442	0.444	0.449	0.456	0.467	0.480	0.496
SrCl₂ . .	0.510	0.459	0.438	0.428	0.425	0.426	0.430	0.437	0.445	0.456
BaCl₂ . .	0.492	0.436	0.412	0.398	0.391	0.388	0.387	0.388	0.390	0.393
MnCl₂^{. . .}	0.511	0.464	0.445	0.438	0.436	0.440	0.445	0.453	0.464	0.476
FeCl₂^{. . .}	0.509	0.463	0.446	0.441	0.443	0.449	0.458	0.470	0.484	0.500
ZnCl₂^{. . .}	0.499	0.447	0.419	0.400	0.384	0.371	0.359	0.348	0.339	0.330
CoCl₂^{. . .}	0.529	0.483	0.467	0.463	0.465	0.472	0.482	0.496	0.513	0.532
NiCl₂^{. . .}	0.527	0.482	0.466	0.462	0.465	0.473	0.484	0.499	0.517	0.538
CuCl₂^{. . .}	0.495	0.441	0.418	0.407	0.407	0.398	0.398	0.399	0.402	0.405
MgBr₂^{. . .}	0.540	0.512	0.511	0.522	0.540	0.565	0.595	0.629	0.669	0.715
CaBr₂^{. . .}	0.540	0.502	0.491	0.492	0.500	0.513	0.530	0.551	0.576	0.604
SrBr₂^{. . .}	0.535	0.492	0.477	0.473	0.476	0.483	0.494	0.508	0.525	0.545
BaBr₂^{. . .}	0.512	0.463	0.444	0.437	0.436	0.438	0.443	0.451	0.460	0.471
Mg(NO₃)₂^.	0.526	0.484	0.470	0.467	0.471	0.479	0.491	0.508	0.521	0.540
Ca(NO₃)₂.	0.494	0.433	0.402	0.382	0.369	0.359	0.352	0.348	0.344	0.342
Sr(NO₃)₂.	0.482	0.414	0.376	0.350	0.331	0.316	0.304	0.294	0.285	0.278
Co(NO₃)₂ .	0.515	0.469	0.452	0.445	0.446	0.450	0.457	0.467	0.478	0.492
Cu(NO₃)₂ .	0.516	0.466	0.445	0.435	0.431	0.431	0.434	0.440	0.447	0.456
Li₂SO₄^{. .}	0.469	0.400	0.364	0.341	0.325	0.312	0.303	0.296	0.289	0.285
Na₂SO₄^{. .}	0.446	0.366	0.321	0.291	0.268	0.251	0.236	0.224	0.213	0.204
K₂SO₄^{. .}	0.424	0.343	0.300	0.272	0.251	0.236	0.224	—	—	—
Rb₂SO₄^{. .}	0.443	0.365	0.323	0.295	0.274	0.258	0.245	0.234	0.225	0.217
Cs₂SO₄^{. .}	0.444	0.369	0.329	0.304	0.285	0.270	0.259	0.249	0.241	0.234
H₂SO₄^{. .}	0.251	0.195	0.171	0.156	0.147	0.140	0.135	0.130	0.127	0.125

Values are compiled from NIST (formerly NBS) tabulations of Goldberg et al. (1977, 1978, 1979a, 1979b, 1981) and the computer compilation GAMPHI (Goldberg, 1985). Experimental values have also been compiled by Lobo (1989).

References

R. N. Goldberg and R. L. Nuttall (1977) J. Phys. Chem. Ref. Data, 6, 385.
R. N. Goldberg and R. L. Nuttall (1978) J. Phys. Chem. Ref. Data, 7, 263.
R. N. Goldberg, R. L. Nuttall and B. R. Staples (1979a) J. Phys. Chem. Ref. Data, 8, 923.
R. N. Goldberg (1979b) J. Phys. Chem. Ref. Data, 8, 1005.
R. N. Goldberg (1981) J. Phys. Chem. Ref. Data, 10, 1.
R. N. Goldberg (1985) GAMPHI—a Database of Activity and Osmotic Coefficients for Aqueous Electrolyte Solutions, NBS Technical Note 1206.
W. J. Hamer and Y.-C. Wu (1972) J. Phys. Chem. Ref. Data, 1, 1047.
V. M. M. Lobo (1989) Handbook of Electrolyte Solutions, Parts A & B, Elsevier, Amsterdam.

A.K. Covington

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