The Activity Coefficient for Other Composition Measures - Mixing Liquids: Molecular Solutions - Liquid-State Physical Chemistry: Fundamentals, Modeling, and Applications (2013)

Liquid-State Physical Chemistry: Fundamentals, Modeling, and Applications (2013)

11. Mixing Liquids: Molecular Solutions

11.7. The Activity Coefficient for Other Composition Measures*

So far, we have dealt with activity coefficients using the mole fraction x as a measure for composition. In practice, people use also molality m (m moles of solute per 1 kg of solvent) and molarity c (c moles per liter solution). Whichever measure is used, the difference μμ, where μ is the infinite dilution reference value, should be the same. Denoting with ax and am the activities using the mole fraction and molality scale we must have

(11.111) c11-math-0111

So we obtain

(11.112) c11-math-0112

with γ the activity coefficient. For the molality scale we have (see Chapter 2)

(11.113) c11-math-0113

where M1 is the molar mass of the solvent. For infinite dilution

c11-math-5046

Moreover, for infinite dilution,

c11-math-5047

In total, we thus obtain

(11.114) c11-math-0114

A similar calculation for the molarity scale yields γc/γx = x2ρ/c2M1 with ρ the mass density and c2 the molarity of the solute.

Problem 11.17

Calculate the relationship between the activity coefficients on the mole fraction scale and the molarity scale.