Appendix IV
Debye-Hückel Equation and Kielland Table For Ion-Activity Coefficients
Debye-Hückel expression for individual ion-activities:
å × 108 | Ion |
2.5 | ![]() |
3.0 | ![]() ![]() ![]() |
3.5 | ![]() ![]() ![]() ![]() |
4.0 | ![]() ![]() ![]() |
4.0–4.5 | ![]() ![]() ![]() ![]() |
4.5 | ![]() ![]() |
5 | ![]() ![]() ![]() |
6 | ![]() ![]() ![]() |
8 | ![]() |
9 | ![]() ![]() ![]() |
Temperature (°C) | A | B (× 10–8) |
0 | 0.4883 | 0.3241 |
5 | 0.4921 | 0.3249 |
10 | 0.4960 | 0.3258 |
15 | 0.5000 | 0.3262 |
20 | 0.5042 | 0.3273 |
25 | 0.5085 | 0.3281 |
30 | 0.5130 | 0.3290 |
35 | 0.5175 | 0.3297 |
40 | 0.5221 | 0.3305 |
50 | 0.5319 | 0.3321 |
60 | 0.5425 | 0.3338 |
Charge | Size,* å | Ions | l = 0.0005 |
0.001 | 0.0025 | 0.005 | 0.01 | 0.025 | 0.05 | 0.1 |
1 | 2.5 | ![]() ![]() ![]() ![]() ![]() |
0.975 | 0.964 | 0.945 | 0.924 | 0.898 | 0.85 | 0.80 | 0.75 |
3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
0.975 | 0.964 | 0.945 | 0.925 | 0.899 | 0.85 | 0.805 | 0.755 | |
4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
0.975 | 0.964 | 0.947 | 0.928 | 0.902 | 0.86 | 0.82 | 0.775 | |
6 | ![]() ![]() |
0.975 | 0.965 | 0.948 | 0.929 | 0.907 | 0.87 | 0.835 | 0.80 | |
9 | ![]() |
0.975 | 0.967 | 0.950 | 0.933 | 0.914 | 0.88 | 0.86 | 0.83 | |
2 | 4.5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
0.903 | 0.867 | 0.805 | 0.742 | 0.665 | 0.55 | 0.455 | 0.37 |
5 | ![]() ![]() ![]() ![]() ![]() ![]() |
0.903 | 0.868 | 0.805 | 0.744 | 0.67 | 0.555 | 0.465 | 0.38 | |
6 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
0.905 | 0.870 | 0.809 | 0.749 | 0.675 | 0.57 | 0.485 | 0.405 | |
8 | ![]() ![]() |
0.906 | 0.872 | 0.813 | 0.755 | 0.69 | 0.595 | 0.52 | 0.45 | |
3 | 4 | ![]() ![]() |
0.796 | 0.725 | 0.612 | 0.505 | 0.395 | 0.25 | 0.16 | 0.095 |
9 | ![]() ![]() ![]() ![]() ![]() |
0.802 | 0.738 | 0.632 | 0.54 | 0.445 | 0.325 | 0.245 | 0.18 |
*Note that these sizes are rounded values for the effective size in water solution and are not the size of the simple ions, unhydrated. For a more detailed discussion, see the original paper from which these values were taken [J. Kielland, J. Amer. Chem. Soc., 59, 1675 (1973)].
References
BERNER, R. A. 1971. Principles of Chemical Sedimentology. McGraw-Hill, New York, 240 pp.
KLOTZ, I. M. 1950. Chemical Thermodynamics. Prentice-Hall, Eaglewood Cliffs, N.J., 369 pp.
MANOV, G. G., R. G. BATES, W. J HAMER, and S. F. ACREE. 1943. Values of the constants in the Debye-Hückel equation for activity coefficients. J. Amer. Chem. Soc., 65, pp. 1765–1767.