Example 1
A 25.00 cm^3 aliquot of a solution of a base of known concentration 0.1057 M is
titrated with an acid of unknown concentration. The reaction involved 1 mole of
base and 1 mole of acid. The end point was determined as 24.88 cm^3 of acid
added. What is the concentration of the acid?
25.00 cm^3 of the base solution contained 25.00¥ 0.1057 =2.6425 mmol base.
From the known reaction, this should be equivalent to 2.6425 mmol of acid.
Since the volume of acid at the end point was 24.88 cm^3 , the concentration must
be (2.6425/24.88) =0.1062 M.
In some cases, the end point detected does not correspond exactly with the
equivalence point. This may be due to problems with the reaction, or to the
small amount of reagent needed to react with additional materials (for example,
the added indicator) present in the titrand. In these cases, a blank titration must
be performed, or allowance made for the titration error.In order to achieve the highest accuracy, it is necessary to use well-established
standard materials as reagents in the primary calibration or standardization of
the reacting solutions (see Topic A5).
The most important of these are called primary standards, and should be
easy to obtain, purify and dry, should be stable and not hygroscopic, but should
be readily soluble and react rapidly and stoichiometrically. They should ideally
have a high relative molecular mass to minimize weighing errors.
The above criteria mean that reagents such as sodium hydroxide, which is
hygroscopic and may react with carbon dioxide from the air, and potassium
permanganate, which slowly decomposes in air, are unsuitable as primary
standards.
Solutions used for quantitative analysis need to be checked and calibrated
frequently. For example, hydrochloric acid solutions should be checked against
sodium carbonate solution and sodium hydroxide against potassium hydrogen
phthalate.The end point of a titration is based upon experimental observation, whereas
the equivalence point is the theoretical value dependent upon the reaction equa-
tion. In an ideal case, these should be the same, but a check may be needed to
ensure that factors such as blank errors do not affect the results.
In any titration, the end point corresponds to rapid changes in the concentra-
tion of species. This may be detected in many ways. Instrumental methods are
discussed later, and visual indicators are discussed below.
For reactions such as a strong acid neutralizing a strong base (Fig. 1), the
change at the end point is large, and the rate of change with volume is very
great, as shown by the derivative plot in Figure 2(b). In other cases, such as the
reaction of weak acids with weak bases, the titration curve shows a much less
pronounced change, and the derivative plot may be needed to confirm the end
point, as in Figure 2(b). The second derivative plot is also useful, but relies
greatly on very accurate measurements. Plots of the concentration of a species
(for example H+, or OH-), against the volume added, give straight lines inter-
secting at the end point.
If a mixture of acids, or a polybasic acid such as maleic acid, is titrated, then
twoend points are obtained. Similarly, for mixtures of two titrands, two end
points will be detected, provided the species have sufficiently different equilib-
rium constants for the reaction (e.g. Ka1Ka2).Equivalence
points and end
points
Standard
solutions
82 Section C – Analytical reactions in solution