Page 292 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

10 TITRIMETRIC ANALVSIS

pH = -log a,+ = pK,, + log- [In,] + log -
where ylnA and ylnB are the activity coefficients of the acidic and basic forms of
the indicator. Equation (3) may be written in the logarithmic form:
[In,]
Y1
Y ln,
The pH will depend upon the ionic strength of the solution (which is, of course,
related to the activity coefficient - see Section 2.5). Hence, when making a
colour comparison for the determination of the pH of a solution, not only must
the indicator concentration be the same in the two solutions but the ionic
strength must also be equal or approximately equal. The equation incidentally
provides an explanation of the so-called salt and solvent effects which are
observed with indicators. The colour-change equilibrium at any particular ionic
strength (constant activity-coefficient term) can be expressed by a condensed
form of equation (4):
pH = pK;, + [In,]
logm
where pK;, is termed the apparent indicator constant.
The value of the ratio [InB]/[InA] (i.e. [Basic form]/[Acidic form]) can
be determined by a visual colour comparison or, more accurately, by a
spectrophotometric method. Both forms of the indicator are present at any
hydrogen-ion concentration. It must be realised, however, that the human eye
has a limited ability to detect either of two colours when one of them
predominates. Experience shows that the solution will appear to have the 'acid'
colour, i.e. of In,, when the ratio of [In,] to [In,] is above approximately 10,
and the 'alkaline' colour, i.e. of In,, when the ratio of [In,] to [In,] is
above approximately 10. Thus only the 'acid' colour will be visible when
[InA]/[InB] > 10; the corresponding limit of pH given by equation (5) is:
pH = pK;, - 1
Only the alkaline colour will be visible when [InB]/[InA] > 10, and the
corresponding limit of pH is:
pH = pK;, + 1
The colour-change interval is accordingly pH = pK;, I 1, i.e. over approximately
two pH units. Within this range the indicator will appear to change from one
colour to the other. The change will be gradual, since it depends upon the ratio
of the concentrations of the two coloured forms (acidic form and basic form).
When the pH of the solution is equal to the apparent dissociation constant of
the indicator pK;,, the ratio [In,] to [In,] becomes equal to 1, and the
indicator will have a colour due to an equal mixture of the 'acid' and 'alkaline'
forms. This is sometimes known as the 'middle tint' of the indicator. This applies
strictly only if the two colours are of equal intensity. If one form is more intensely
coloured than the other or if the eye is more sensitive to one colour than the
other, then the middle tint will be slightly displaced along the pH range of the
indicator.
Table 10.1 contains a list of indicators suitable for titrimetric analysis and
for the colorimetric determination of pH. The colour-change intervals of most
ofthe various indicators listed in the table are represented graphically in Fig. 10.1.