In acid buffer solution `(pH = 4.4)`, the ratio of concentrations of acid to salt is `2 : 1`. The value of dissociation constant of weak acid may be

Options

A. `1.8 xx 10^(-4)`
B. `2 xx 10^(-7)`
C. `4 xx 10^(-5)`
D. `2 xx 10^(-8)`

Explanation

To solve the problem, we need to find the dissociation constant (Ka) of a weak acid in an acidic buffer solution with a given pH and concentration ratio of acid to salt.

### Step-by-step Solution:

1. **Identify the Given Information**:
- pH of the buffer solution = 4.4
- Ratio of concentrations of acid (HA) to salt (A-) = 2:1

2. **Determine the Ratio of Salt to Acid**:
- If the ratio of acid to salt is 2:1, then the ratio of salt to acid is:
\[ \frac{[A^-]}{[HA]} = \frac{1}{2} \]

3. **Use the Henderson-Hasselbalch Equation**:
The Henderson-Hasselbalch equation is:
\[ \text{pH} = \text{pKa} + \log\left(\frac{[A^-]}{[HA]}\right) \]
Substituting the known values:
\[ 4.4 = \text{pKa} + \log\left(\frac{1}{2}\right) \]

4. **Calculate the Logarithm**:
- The logarithm of \(\frac{1}{2}\) can be calculated as:
\[ \log\left(\frac{1}{2}\right) = -\log(2) \approx -0.3010 \]

5. **Substitute the Logarithm into the Equation**:
\[ 4.4 = \text{pKa} - 0.3010 \]

6. **Solve for pKa**:
\[ \text{pKa} = 4.4 + 0.3010 = 4.7010 \]

7. **Convert pKa to Ka**:
The relationship between Ka and pKa is given by:
\[ \text{pKa} = -\log(Ka) \implies Ka = 10^{-\text{pKa}} \]
Substituting the value of pKa:
\[ Ka = 10^{-4.7010} \]

8. **Calculate Ka**:
\[ Ka \approx 2 \times 10^{-5} \]

### Final Answer:
The dissociation constant (Ka) of the weak acid is approximately \(2 \times 10^{-5}\).

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