Physical Chemistry Third Edition

6.3 Activity and Activity Coefficients 263

This equation is the same as Henry’s law except for the occurrence of the

activity instead of the mole fraction. The activity is an “effective” mole fraction in

expressing the chemical potential and the partial vapor pressure. Equation (6.3-31) is

equivalent to

a(II)i 

Pi

ki

(componentisolute) (6.3-32)

Theactivity coefficientin convention II is again defined as the ratio of the activity to

the mole fraction. It is equal to the actual vapor pressure divided by the vapor pressure

predicted by Henry’s law and describes how the substance deviates from Henry’s law:

γi(II)

ai(II)

xi



Pi

kixi

(componentisolute) (6.3-33)

Equation (6.3-29) can now be written

μiμ

◦(II)

i +RTln(γ

(II)

i xi) (componentisolute) (6.3-34)

Convention II is sometimes referred to as the application of thesolute standard state

to the solutes and the application of thesolvent standard stateto the solvent. Conven-

tion I is called the application of the solvent standard state to every component. The

reason for having two conventions is that we would like to have activity coefficients

nearly equal to unity as often as possible. In convention I we describe the deviation

of each substance from Raoult’s law. If Raoult’s law is approximately obeyed by all

substances, the use of convention I gives an activity coefficient approximately equal

to unity for each substance. In convention II we describe the deviation of the sol-

vent from Raoult’s law and the deviation of a solute from Henry’s law. If Henry’s

law is approximately obeyed by a solute, the use of convention II gives an activity

coefficient approximately equal to unity for that solute, as well as an activity coeffi-

cient approximately equal to unity for the solvent, which would approximately obey

Raoult’s law.

EXAMPLE6.12

Henry’s law constant for ethanol in diethyl ether at 20◦C is equal to 160 torr. Find the activity

and activity coefficient of ethanol (component 2) in diethyl ether (component 1) at 20◦C for

a mole fraction of ethanol equal to 0.100, using both convention I and convention II. The

partial pressure of ethanol at this composition and temperature is equal to 12.45 torr, and the

vapor pressure of pure ethanol at this temperature is equal to 44.40 torr.

Solution

By convention I:

a( 2 I)

P 2

P 2 ∗



12 .45 torr

44 .40 torr

 0. 280

γ 2 (I)

0. 280

0. 100

 2. 80