Question

500 mL of $ {\text{0}}{\text{.2M}} $ acetic acid are added to $ 500{\text{ mL}} $ of $ 0.30{\text{ M}} $ sodium acetate solution. If the dissociation constant of acetic acid is $ 1.5 \times {10^{ - 5}} $ then pH of the resulting solution is:
(A) 5
(B) 9
(C) 3
(D) 4

Answer 1

Hint: To answer this question, you must recall the formula for calculating the pH of a buffer solution. The pH of a buffer solution is given by the Henderson- Hasselbalch equation. We shall substitute the values in the equation below to calculate the pH.

Formula used: Henderson- Hasselbalch Equation:
 $ {\text{pH}} = {\text{p}}{{\text{K}}_{\text{a}}} + {\text{log}}\dfrac{{\left[ {{\text{salt}}} \right]}}{{\left[ {{\text{acid}}} \right]}} $
Where, $ {\text{pH}} $ denotes the negative logarithm of the hydrogen ion in the buffer solution
 $ {\text{p}}{{\text{K}}_{\text{a}}} $ denotes the negative logarithm of the dissociation constant of the weak acid.
 $ \left[ {{\text{salt}}} \right] $ denotes the concentration of the salt in the buffer solution
And, $ \left[ {{\text{acid}}} \right] $ denotes the concentration of the weak acid in the buffer solution.

Complete step by step solution:
The given solution of acetic acid and sodium acetate is an acidic buffer solution as acetic acid is a weak acid while sodium acetate is the salt of weak acid acetic acid and strong base sodium hydroxide.
500 ml of both the solutions are mixed in the question to form the given buffer solution. Using the Henderson- Hasselbalch equation, we can find the pH of the buffer solution easily. We know that the pH of an acidic buffer can be given as:
 $ {\text{pH}} = {\text{p}}{{\text{K}}_{\text{a}}} + {\text{log}}\dfrac{{\left[ {{\text{C}}{{\text{H}}_3}{\text{COONa}}} \right]}}{{\left[ {{\text{C}}{{\text{H}}_3}{\text{COOH}}} \right]}} $
Substituting the values, we get, $ {\text{pH}} = - \log \left( {1.5 \times {{10}^{ - 5}}} \right) + \log \left( {\dfrac{{0.3}}{{0.2}}} \right) $
 $ \Rightarrow pH = - \log \left( {1.5} \right) - \log {10^{ - 5}} + \log \left( {1.5} \right) $
 $ pH = 5 $
The correct answer is A.

Note:
A buffer solution is a solution that has the tendency to resist any changes in its pH in addition to a small amount of acid or base. A buffer can be either acidic or basic. A basic buffer is the solution of a weak base and its salt with a strong acid. Similarly an acidic buffer is the solution of a weak acid and its salt with a strong base.