Physical Chemistry Third Edition

258 6 The Thermodynamics of Solutions

6.3 Activity and Activity Coefficients

We have obtained several relations for the chemical potential that look quite similar.

For an ideal gas, either pure or in a mixture,

μiμ◦i+RTln

(

Pi

P◦

)

(ideal gas) (6.3-1)

For a component of an ideal solution or for the solvent in a dilute solution,

μiμ∗i+RTln(xi)

(component of an ideal solution

or solvent in a dilute solution) (6.3-2)

For a solute in a dilute solution we had a choice of three relations:

μiμ◦i(H)+RTln(xi) (solute in a dilute solution) (6.3-3)

μiμ

◦(m)

i +RTln(mi/m

◦) (solute in a dilute solution) (6.3-4)

μiμ

◦(c)

i +RTln(ci/c

◦) (solute in a dilute solution) (6.3-5)

The Definition of the Activity

In each of the preceding five equations the chemical potential is equal to a standard-state

chemical potential plus a term that consists ofRTtimes the logarithm of a composition

variable. We now want to write a single equation that will apply to all cases:

μiμ◦i+RTln(ai) (defines the activityai) (6.3-6)

whereμ◦iis the chemical potential of substanceiin the appropriate standard state and

where this equation definesai, theactivityof substancei.

Comparison of Eq. (6.3-6) with the preceding five equations shows that

ai

Pi

P◦

(ideal gas) (6.3-7)

aixi

(component of an ideal solution

or solvent in a dilute solution)

(6.3-8)

aixi (dilute solute, mole fraction description) (6.3-9)

ai

mi

m◦

(dilute solute, molality description) (6.3-10)

ai

ci

c◦

(dilute solute, concentration description) (6.3-11)