The Foundations of Chemistry

Multiplying by
1 gives

log [H 3 O]
log Ka
log

Recalling that in Chapter 18 we defined
log [H 3 O] (or for the general expression
log
[H]) as pH and
log Kaas pKa, the preceding equation becomes

pHpKalog where pKa
log Ka (acid/salt buffer)

This equation is known as the Henderson–Hasselbalch equation.Workers in the biolog-
ical sciences use it frequently. In general terms, we write

pHpKalog (acid/salt buffer)

EXAMPLE 19-2 Weak Acid/Salt of Weak Acid Buffer Solution

(via the Henderson–Hasselbalch Equation)

Use the Henderson–Hasselbalch equation to calculate the pH of the buffer solution in
Example 19-1.

Plan

The Henderson–Hasselbalch equation is pHpKalog 

[conju

[a

g

c

a

i

t

d

e

]

base]

. The value for pKa

for acetic acid can be calculated from the value of Kafound in Example 19-1 and many other
places. The solution in Example 19-1 is 0.10 Min CH 3 COOH and 0.20 Min NaCH 3 COO.
The values used for [conjugate base] and [acid] are their initial concentrations after mixing but
before reaction.

Solution

The appropriate values needed for the Henderson–Hasselbalch equation are

pKa
log Ka
log 1.8 10 
^5 4.74

[conjugate base][CH 3 COO
][NaCH 3 COO]initial0.20 M

[acid][CH 3 COOH]initial0.10 M

pHpKalog 4.74log

4.74log 2.04.740.305.04

You should now work Exercise 9.

(0.20)



(0.10)

[conjugate base]



[acid]

[conjugate base]



[acid]

[salt]



[acid]

[acid]



[salt]

19-1 The Common Ion Effect and Buffer Solutions 797

The relationship is valid onlyfor

solutions that contain a weak

monoproticacid and a soluble, ionic

salt of the weak acid with a univalent

cation, both in reasonable

concentrations.

The values pKa4.74, the log of 2.0,

and pH5.04 all have two significant

figures.

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 18.9, pH of Buffer Solutions.