Physical Chemistry Third Edition

332 7 Chemical Equilibrium

and

meq(A−)

ns

1 .000 kg

(7.5-2)

Assuming thatγHAequals unity, we obtain

Ka

γ(H+)(meq(H+)/m◦)γ(A−)(meq(A−)/m◦)

meq(HA)/m◦



a(H+)γ(A−)meq(A−)

meq(HA)



a(H+)γ(A−)ns

na

(7.5-3)

Ifγ(A−) is also assumed to equal unity, this equation can be written in the form known

as theHenderson–Hasselbalch equation:

pHpKa+log 10

(

ms

ma

)

pKa+log 10

(

ns

na

)

(7.5-4)

wherepKais defined by

pKa−log 10 (Ka) (definition ofpKa) (7.5-5)

and wheremsandmaare the stoichiometric molalities of the salt and the acid. If

greater accuracy is desired than this equation provides, one can use Eq. (7.5-3) with

experimental or theoretical values ofγ(A−).

EXAMPLE7.16

a.Using the Henderson–Hasselbalch equation, calculate the pH of a solution made from

0.400 mol of acetic acid and 0.600 mol of sodium acetate in 1.000 kg of water.

b.Repeat the calculation of part a using Eq. (7.5-3) and the Davies equation.

Solution

a.Using the valueKa 1. 75 × 10 −^5 ,

pH 4. 757 +log 10

(

0 .600 mol

0 .400 mol

)

 4. 932

b.Letmabe the molality of acid that would occur if the acid did not ionize andmsbe

the molality of the anion that would occur if the salt did not hydrolyze. We assume that

the salt dissociates completely, thatγ(H+),γ(A−), andγ(OH−) are equal and can be

approximated by the Davies equation, and thatγ(HA) 1 .The ionization of the acid is

represented by

HA
H++A−