Question

When a solution of acetic acid was titrated with NaOH, the pH of the solution when half the acid neutralized was 4.74. Dissociation constant of the acid is:
(a) $1.8\text{ x }{{10}^{-5}}$
(b) $3.2\text{ x }{{10}^{-5}}$
(c) $8.7\text{ x }{{10}^{-8}}$
(d) $6.42\text{ x }{{10}^{-4}}$

Answer 1

Hint: Acetic acid is a weak acid and sodium hydroxide is a strong base. This will react together to give salt and water. A solution consisting of a weak acid and its salt with a strong base is known as an acid buffer. Use the relation between pH and dissociation constant to find the same.

Complete step by step answer:
According to the question, we have been provided with the following data –
A solution of acetic acid is titrated with Sodium Hydroxide (NaOH). This gives two products – sodium acetate and water. The reaction can be written as –
$C{{H}_{3}}COOH+NaOH\rightleftharpoons C{{H}_{3}}COONa+{{H}_{2}}O$
When a weak acid and strong base react, it gives salt and water, which is mildly basic in nature. This type of reaction is known as a neutralization reaction and the medium is known as an acidic buffer.
For acidic buffers, the value of pH can be written as –
pH = pKa + log([salt] / [acid])
where, pKa = -log (Ka)
Ka = dissociation constant
[salt] = concentration of salt (mol/L)
[acid] = concentration of weak acid (mol/L)
In the above reaction, we can see that 1 mole of acid (acetic acid) reacts with 1 mole of base (sodium hydroxide) of given 1 mole of salt (sodium acetate) and water respectively.
Given, half the acid was neutralized, therefore, 0.5 mole of acid was used and 0.5 mole of salt will be produced.
Therefore, we can assume the concentration of salt = acid = 0.5 = c
So, we can calculate the value of pH as –
pH = pKa + log([salt] / [acid])
pH = pKa + log (c / c)
pH = pKa + log 1
since log 1 = 0, the equation becomes,
pH = pKa
Given, pH of the solution = 4.74
Therefore, pKa = 4.74
- log Ka = 4.74
log Ka = - 4.74
Ka = $\text{ }{{10}^{-4.74}}$
Dissociation constant = Ka = $1.8\text{ x }{{10}^{-5}}$
Therefore, the answer is – option (a).

Note: A basic buffer solution consists of a mixture of a weak base and its salt with strong acid. For example – a mixture of ammonium hydroxide and ammonium chloride.
We can relate pOH and dissociation constant for a base by the equation –
pOH = pKb +log([salt] / [base]).