Physical Chemistry Third Edition

6.3 Activity and Activity Coefficients 265

so that Eq. (6.3-36) can be written

μiμ◦i(m)+RTln

(

γi(m)mi

m◦

)

(6.3-40)

Sincex 1 ≈1 in dilute solutions, the molality activity coefficient and the mole fraction

activity coefficient are nearly equal to each other in a dilute solution.

Equation (6.3-40) is the same as Eq. (6.2-12) except for the presence of the activity

coefficient. All that is needed to convert an expression for a dilute solution into one for

an arbitrary solution is to insert the activity coefficient.

The Concentration Description

The molar concentration is given by

ci

ni

V



ni

nVm



xi

Vm

(6.3-41)

whereVmV/nis themean molar volume(nis the total amount of all substances).

We want to write an equation of the form

μiμ◦i(c)+RTln

(

γ(ic)ci

c◦

)

(6.3-42)

so that the activity in the concentration description is

a

(c)

i 

γi(c)ci

c◦

(6.3-43)

wherec◦is defined to be exactly equal to 1 mol L−^1 or 1 mol m−^3. Equation (6.3-42)

is valid if

μ◦i(c)μ(II)i +RTln(Vm,1∗ c◦) (6.3-44)

and

γi(c)

γi(II)Vm

Vm,1∗

(6.3-45)

The standard-state chemical potential is that of a solute with a concentration equal to

1 mol L−^1 or 1 mol m−^3 and obeying Henry’s law in the concentration description, as

in Eq. (6.2-16).

In all of our descriptions, a solvent is treated in the same way as in convention I. Its

activity is always its mole fraction times its activity coefficient and its standard state is

the pure liquid:

a 1 γ 1 x 1 (1solvent, all descriptions) (6.3-46)