Question

A buffer solution is prepared by mixing 0.3 M NH$_3$ and 0.1 M NH$_4$NO$_3$. If $K_b$ of NH$_3$ is $1.6 \times 10^{-5}$ at 25°C, then the pH (rounded off to one decimal place) of the buffer solution at 25°C is ________.

Hint:

For weak base–conjugate acid buffers, use $\text{pOH} = pK_b + \log \frac{[\text{salt}]}{[\text{base}]}$ and $\text{pH} = 14 - \text{pOH}$.

Answer 1

Correct Answer: 9.7

Step 1: Write the buffer equation.
For an NH$_3$/NH$_4^+$ buffer, \[ \text{pOH} = pK_b + \log \frac{[\text{salt}]}{[\text{base}]} \] Given: $pK_b = -\log(1.6 \times 10^{-5}) = 4.8$. Step 2: Substitute concentrations.
\[ \text{pOH} = 4.8 + \log \frac{0.1}{0.3} = 4.8 + \log(0.333) = 4.8 - 0.48 = 4.32 \] \[ \text{pH} = 14 - 4.32 = 9.68 \approx 9.7 \] Rounding off to one decimal place gives pH = 9.7.
Step 3: Conclusion.
Hence, the buffer solution has pH = 9.7.