Question

A buffer solution contains 0.1 mole of sodium acetate in 1000 cm3 of 0.1 M acetic acid, to the above buffer solution, 0.1 M of sodium acetate is further added and dissolved. The $pH$ of the resulting buffer is equal to:
A. $p{K_a} - \log 2$
B. $p{K_a}$
C. $p{K_a} + 2$
D. $p{K_a} + \log 2$

Answer 1

Hint: Any solution whose $pH$ is not altered to any extent by the addition of small quantities of acid or a base is called buffer solution. Or we can say a solution acidity or alkalinity which can resist change in $pH$ upon addition of a small amount of acid or base. For the given question we will use Henderson’s equation:
\[pH = pKa + \log \dfrac{{[salt]}}{{[acid]}}\]

Complete step by step answer:
According to the question the initial concentrations are:
\[\left[ {C{H_3}COONa} \right] = 0.1\;M\] and,
\[\left[ {C{H_2}COOH} \right] = 0.1\;M\]
After the addition of 0.1 mol \[C{H_3}COONa\] we get:
\[\left[ {C{H_3}COONa} \right] = 0.1 + 0.1 = 0.2\;M\] and,
\[\left[ {C{H_2}COOH} \right] = 0.1\;M\]
Now as we all know from Henderson’s equation ($pH$ of a buffer) of acidic buffer:
\[pH = pKa + \log \dfrac{{[salt]}}{{[acid]}}\]
$
   \Rightarrow pH = pKa + \log \dfrac{{[0.2]}}{{[0.1]}} \\
   \Rightarrow pH = pKa + \log 2 \\
$

So, the correct answer is Option D .

Additional Information:
The property of a buffer solution to resist changes in $pH$ value is known as buffer capacity. Experimentally it has been found that if ratio of \[\dfrac{{[salt]}}{{[acid]}}\] or \[\dfrac{{[salt]}}{{[base]}}\] is 1, then $pH$ of the buffer doesn’t change at all. So we can also say that, the number of moles of acid or base added to 1 litre of solution to change its $pH$ by unity is called buffer capacity.
Buffers are used in industrial processes such as manufacture of paper, ink, drugs etc.

Note:
Buffer solution can be obtained by
Mixing weak acid with its salt with strong base
Mixing weak base with its salt with strong acid
From a solution of ampholyte. (These are the substances which show properties of both an acid and a base. Proteins and amino acids are examples for ampholyte.)
From a mixture of an acid salt and a normal salt of a polybasic acid.