Question

The pK_b of dimethylamine and pK_a of acetic acid are 3.27 and 4.77 respectively at T (K). The correct option for the pH of dimethylammonium acetate solution is

• A. 6.25
• B. 8.5
• C. 5.5
• D. 7.75

Answer 1

The Correct Option is D

To find the pH of a dimethylammonium acetate solution, we need to consider the equilibrium between the conjugate acid and base forms of the species present.
Given:
- \( \text{p}K_b \) of dimethylamine = 3.27
- \( \text{p}K_a \) of acetic acid = 4.77
We will use the Henderson-Hasselbalch equation for the calculation. Since dimethylammonium acetate is a salt of a weak base (dimethylamine) and a weak acid (acetic acid), the pH can be determined by the following relationship:
\[ \text{pH} = \frac{1}{2} (\text{p}K_a + \text{p}K_b + 14) \]
Here is the detailed calculation:
1. Determine the \(\text{p}K_a\) of dimethylammonium ion:
  \[ \text{p}K_a (\text{dimethylammonium ion}) = 14 - \text{p}K_b (\text{dimethylamine}) \]
  \[ \text{p}K_a (\text{dimethylammonium ion}) = 14 - 3.27 = 10.73 \]
2. Calculate the pH using the above relationship:
  \[ \text{pH} = \frac{1}{2} (\text{p}K_a (\text{acetic acid}) + \text{p}K_a (\text{dimethylammonium ion})) \]
  \[ \text{pH} = \frac{1}{2} (4.77 + 10.73) \]
  \[ \text{pH} = \frac{1}{2} \times 15.5 \]
  \[ \text{pH} = 7.75 \]
Therefore, the correct pH of the dimethylammonium acetate solution is \( \textbf{7.75} \), which matches the given answer.
Conclusion:
The correct option for the pH of dimethylammonium acetate solution is option (D): 7.75.The correct answer is option (D): 7.75