Physical Chemistry Third Edition

330 7 Chemical Equilibrium

This equation represents a new version ofHenry’s law. If the activity coefficients

are equal to unity, the partial vapor pressure of HCl is proportional to the square of the

molality, not proportional to the molality as in Henry’s law. Figure 7.2 shows the partial

vapor pressure of HCl as a function of molality in an aqueous solution at 298.15 K.

Table A.12 gives the values of the partial pressure for larger molalities for the same

temperature. The table represents experimental data, and the graph represents values

calculated from values of the activity coefficient determined by other techniques.

0.020

0.015

0.010

0.005

1

P/torr

0 2 3 4

m/mol kg^21

Figure 7.2 The Partial Vapor Pressure
of HCl as a Function of Molality.

EXAMPLE7.15

The partial vapor pressure of a 5.00 mol kg−^1 aqueous solution of HCl at 298.15 K is equal

to 6. 97 × 10 −^5 atm.aThe mean ionic activity coefficient is equal to 2.38. Find the value of

k(±m)and ofμ◦++μ◦−−μ◦(HCl,g).

Solution

k(±m)

P(HCl)

γ±^2 m^2



6. 97 × 10 −^5 atm

( 2. 38 )^2

(

5 .00 mol kg−^1

) 2

 4. 92 × 10 −^7 atm kg^2 mol−^2

μ◦++μ◦−−μ◦(HCl,g)RTln

⎛

⎝k

(m)

± m

◦ 2

P◦

⎞

⎠

(8.3145 J K−^1 mol−^1 )(298.15 K)

×ln

⎛

⎜

⎝

(

4. 92 × 10 −^7 atm kg^2 mol−^2

)(

1 mol kg−^1

) 2

0 .98692 atm

⎞

⎟

⎠

− 3. 60 × 104 J mol−^1 − 36 .0kJmol−^1

where we have used the fact thatP◦ 0 .98692 atm.

aS. J. Bates and H. D. Kirschman,J. Am. Chem. Soc., 41 , 1991 (1919).

Equations (7.4-5) through (7.4-8) are valid for a nonvolatile strong electrolyte such

as NaCl, CaCl 2 , or KOH, as well as for a volatile strong electrolyte such as HCl. For

CaCl 2

a(CaCl 2 )(γ±m±/m◦)^3 (γ±ν±m/m◦)^3 (7.4-14)

wheremis the stoichiometric molality,γ±is defined in Eq. (6.4-6), andm±is defined

in Eq. (6.4-7). If the formula of an electrolyte is represented by Mν+Xν−and if there

is no other source of either ion,

a(Mν+Xν−)(γ±m±/m◦)ν(γ±ν±m/m◦)ν (7.4-15)

whereνis the total number of ions in the formula.

Some of the deviation from ideality of electrolyte solutes is due to ion pairing, which

means that two ions temporarily remain together as a unit. The ion pair equilibrates