Physical Chemistry Third Edition

264 6 The Thermodynamics of Solutions

By convention II:

a( 2 II)

P 2

k 2



12 .45 torr

160 torr

 0. 0778

γ 2 (II)

a 2

x 2



0. 0778

0. 100

 0. 778

The activity coefficientγ( 2 II)is closer to unity than isγ 2 (I). The activity coefficient of the

solvent is the same in both conventions.

Exercise 6.15

Since diethyl ether is designated as the solvent in the previous example its activity and activity

coefficient are the same in convention II as in convention I. Find the activity and the activity

coefficient of diethyl ether in the previous example. The partial vapor pressure of diethyl ether at

this composition and pressure is equal to 408.6 torr and the vapor pressure of pure diethyl ether

at this temperature is equal to 442.6 torr.

The Molality Description

Activities and activity coefficients of solutes are also defined for the molality description.

The molality of solute numberiis given by

mi

ni

w 1



ni

n 1 M 1



xi

x 1 M 1

(6.3-35)

whereM 1 is the molar mass of the solvent andw 1 is the mass of the solvent in kilograms.

Once again, we want to have a version of Eq. (6.3-6). Using the relation of Eq. (6.3-35)

in Eq. (6.3-34), we write

μiμ

◦(II)

i +RTln(M^1 m

◦)+RTln

(

γi(II)x 1 mi

m◦

)

(6.3-36)

wherem◦is defined to equal 1 mol kg−^1 (exactly). This equation is in the form of

Eq. (6.3-6) if

a(m)i 

γ(II)i x 1 mi

m◦

(6.3-37)

and

μ◦i(m)μ◦i(II)+RTln(M 1 m◦) (6.3-38)

The standard state is the same as for the molality description of a dilute solute that

obeys Henry’s law: the hypothetical solution with molality equal to 1 mol kg−^1 and

obeying the molality version of Henry’s law, Eq. (6.2-11).

We define themolality activity coefficient

γ

(m)

i γ

(II)

i x^1 (6.3-39)