Page 109 - Basic physical chemistry for the atmospheric sciences

Acids and bases

Following the same convention as for pH , - l ogK3 can be written as
pK3• Therefore,

[base]
+
pH = pKa l og (5 . 2 8)
[acid]
For most buffers pH = pK3, and [base] = [acid] . Of course, the ca­
pacity of a buffer depends on the amounts of acid and base in the
solution. The buff ering capacity is defined as the number of moles of
H + (or OH - ) that would have to be added to a solution to change its
pH by one unit.
Exercise 5 . 4 . One liter l L) of a buffer solution contains 0 . 1 0 mole
(
of acetic acid , HC 2H302, and 0 . 1 0 mole of sodium acetate , NaC2H302•
If the acid-dissociation constant for acetic acid is l . 7 x 4 1 0 - 5 , what
is the pH of the solution? What is the acid buffering capacity of
the solution?
Solution. Since the molar concentrations of the acid and the base
are equal , we have from Eq. (5 .28)
pH = pKa = -log l . 7 x 4 1 0 - 5 )
(
or,
pH = 4 . 7 6

To lower the pH by one unit , enough H + must be added to convert
C 2H30 2 to H C 2H302 such that

(0. 1 0 - x )
pH = 3 . 76 = pK a + log
O. l O + x
Therefore,
(0. 1 0 - x )
3 . 76 = 4 . 7 6 + log 0
1 O . l O + x

and ,
x = 0.08 1
Thus , 0.08 1 mole of H + would have to be added to the solution to
lower its pH by one unit. The buffering capacity of the solution is
therefore 0.0 1 mole.
8
Exercise 5 .5. What will be the change in the pH of the buffer
solution in Exercise 5 . 4 if 0.020 mole of hydrochloric acid is added?