Page 99 - Instant notes

Acid-base titrations 85

at the end point the salt solution is weakly acidic (pH<7), as the conjugate acid of a weak
base is stronger than the conjugate base of a strong acid (Fig. 2b; see also Topic C3).
Again, before the end point, the fall in pH due to the addition of the strong acid is
partially offset by a shift in the weak base equilibrium:

to the right according to Le Chatelier’s principle (see Topic C1), so that the change in pH
with added acid is greatest at the end point.
Again, a graph of dpH/dV against V could be used to determine the endpoint, as this is
where a minimum in dpH/dV should occur. An alternative method for determining these
end points does not involve the measurement of pH, but instead involves the use of an
acid-base indicator.

Buffers

The ability of a weak acid to partially offset the rise in pH caused by the addition of a
base and of a weak base to partially offset the fall in pH due to the addition of an acid is
exploited in buffer solutions. These consist of a solution containing large and equal
−
concentrations of both a weak acid, HA, and its conjugate weak base, A , for which (see
Topic C3) pH=pK a+log 10(a A−/a HA), which in terms of concentrations is (see Topic C1):

where c HA and are the concentrations of acid and conjugate base, respectively, and
γ HA and are their respective activity coefficients. The concentrations of acid and base
are typically of the order of 0.1 M such that the activity coefficients cannot be
approximated to unity, but the effect of the activity term is generally small and hence:

This is known as the Henderson-Hasselbalch equation. For a buffer solution,
−
and so pH≈pK a. As large concentrations of HA and A are present, addition (or
production) of a relatively small amount of base compared with the amount of HA
−
−
present results in the reaction HA (aq)+OH (aq)→A (aq)+H 2O (1). This mops up the added
hydroxide ion, whilst causing little change to the large values of c HA or , and hence
little change to the solution pH. Similarly, addition (or pro duction) of a relatively small
+
−
amount of acid produces the reaction A (aq)+H 3O (aq)→HA (aq)+H 2O (1) which mops up the
added acid, whilst maintaining C HA, C A- and hence the solution pH constant. Judicious
choice of the acid/conjugate base pair therefore allows the pH of a solution to be
maintained at a desired value, determined by the pK a of the acid, even if relatively small
amounts of hydroxide or hydronium ions are being added to or removed from the solution
(Fig. 3). This is termed a buffered solution.