activity of a solute in solution at 25°C =
= (activity coefficient) * (molar concentration of the solute)
(-1) * LOG10 (activity coefficient) =
= (0.509 * ((electric charge)^2)) * SQRT(ionic strength of the solution) / (1 + (0.328 * (effective diameter of the hydrated ion in Angstrom units) * SQRT(ionic strength of the solution)))
activity coefficient =
= 10^(-0.509 * ((electric charge)^2) * SQRT(ionic strength) / (1 + (0.328 * (effective diameter of the hydrated ion in Angstrom units) * SQRT(ionic strength)))
Points:
(1) The effective diameter of most singly charged hydrated ions is in the range of 3-4 Angstrom units. For ions with a charge of 2+ it is often 5-6 Angstrom, while ions with charges of 3-4+ may have a diameter of 9-11 Angstrom. A table of effective diameters is in Table A4-1, page A-56 in Skoog and Leary (page A-56); this is based on the data of J. Kielland published in J American Chem Soc. 1937; 59: 1675.
(2) The effective diameter of the hydrated ion usually is insignificant in the equation when the ionic strength is < 0.10.
(3) The equation works well for ionic strengths up to 0.01, fairly well up to 0.1 but variably above that level.
(4) The activity coefficients for various solutes are listed in the CRC Handbook of Chemistry and Physics.
(5) The activity coefficient is dimensionless.
