Page 67 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

THE HVDROCEN ION EXPONENT 2.17

pH = log,, l/[H+] = log 1 -log[H+]
= log 1 -10g4.0 x 10-~
= O - 5.602
= 4.398
-
(ii) Find the hydrogen ion concentration corresponding to pH = 5.643.
pH = log,, l/[H+] = log 1 - log[H+] = 5.643
.'. log[H+] = -5.643
This must be written in the usual form containing a negative characteristic and
a positive mantissa:
log[H+] = -5.643 = 6.357
By reference to a calculator or to tables of antilogarithms we find CH+] =
2.28 x mol L- '.
(iii) Calculate the pH of a 0.01 M solution of acetic acid in which the degree
of dissociation is 12.5 percent.
The hydrogen ion concentration of the solution is 0.125 x 0.01
= 1.25 x mol L-'
pH = log,, l/[H+] = log 1 -log[H+]
= O - 3.097
= 2.903
The hydroxide ion concentration may be expressed in a similar way:
pOH = -log,,[OH-] = log,, l/[OH-1,. or [OH-] = 10-pOH
If we write the equation:

in the form:
log[H+] +log[OH-] = log Kw = - 14

This relationship should hold for al1 dilute solutions at about 25 OC.
Figure 2.1 will serve as a useful mnemonic for the relation between [H '1, pH,
[OH -1, and pOH in acid and alkaline solution.
The logarithmic or exponential form has also been found useful for expressing
other small quantities which arise in quantitative analysis. These include:
(i) dissociation constants (Section 2.13), (ii) other ionic concentrations, and
(iii) solubility products (Section 2.6).
(i) For any acid with a dissociation constant of Ka:
pKa = log l/Ka = -log K,
Similarly for any base with dissociation constant K,:
pKb = log l/Kb = -log Kb