Page 182 - Chemical equilibria Volume 4

158 Chemical Equilibria
A1.2.6. Relation between conventions (II) and (III)
Let us examine the relation between the activity coefficients expressed on
the basis of the dilute solution reference (II), and those stemming from the
molar solution (convention (III)).
Let us write that the chemical potential does not depend on the chosen
reference state, and taking account of relation [A1.5], we find:

μ s = μ 0(III) + Rlnγ s (III) C ≅ μ s ∞ + R lnγ (II) x s [A1.15]
T
T
s
s
s
Thus, we can identify and write:
μ 0(III) = μ s ∞ [A1.16]
s
We find:

γ s (III) C =γ (II) x s [A1.17]
s
s
Thus, the chemical potential in infinite dilution is equal to that at the
concentration of 1 mol/l.

The product of the activity coefficient in convention (II) by the molar
fraction (i.e. the activity in reference (II)) is equal to the product of the
activity coefficient in convention (III) by the concentration expressed in
moles per liter (i.e. the activity in reference (III)).

If the solution is very dilute, from relations [A1.17] and [A1.5], we
deduce:

γ (III)
γ (II) = s [A1.18]
s
v 0 0
0
The molar volume of the solventv is expressed in liters per mole.
0
If the concentrations are sufficiently low for us to write thatγ s (II) = 1, then
γ s (III) = v .
0
0