Question

$20\text{ml}\text{of}0.1\text{M}$ acetic acid is mixed with $10\text{mL}$ of sodium acetate. ${\text{pK}}_a\text{of}C{H}_{3}COOH$ is $4.8$, then the concentration of sodium acetate, if pH of the mixture is $4.8$ is:

• A. $0.1\text{M}$
• B. $0.4\text{M}$
• C. $0.2\text{M}$
• D. $1\text{M}$

Answer 1

The correct option is C $0.2\text{M}$

The expression for the pH of the acidic buffer solution is as given below.
${\text{pH = pK}}_a+\log \frac{\left[\text{salt}\right]}{\text{[Acid]}}$
When ${\text{pH = pK}}_a,\text{[Salt] = [Acid]}$
$\text{[Acid]}=\frac{20\times 0.1}{30}=0.067\text{M}$
Hence, in the mixture of acetic acid and sodium acetate $\text{[Salt]}=0.067\text{M}$.
The total volume of the mixture is $30\text{mL}$. The volume of the original solution of sodium acetage is $10\text{mL}$.
$\text{Hence, in the original solution os sodium acetate [salt] =}0.067\times \frac{30}{10}=0.2\text{M}$