The degree of hydrolysis of 0.1 M solution of conjugate base of HA is 0.01.
Find the `H^+` concentation in 0.4 M solution of `A^-`:

Options

A. `5xx10^(-11) M`
B. `5xx10^(-12) M`
C. `2xx10^(-3) M`
D. `2xx10^(-4) M`

Answer

To solve the problem, we need to find the concentration of \( H^+ \) ions in a 0.4 M solution of the conjugate base \( A^- \) given that the degree of hydrolysis of a 0.1 M solution of \( A^- \) is 0.01.

### Step-by-Step Solution:

1. **Understanding Degree of Hydrolysis**:
The degree of hydrolysis (\( \alpha \)) is defined as the fraction of the solute that undergoes hydrolysis. For a 0.1 M solution of \( A^- \), the degree of hydrolysis is given as \( \alpha = 0.01 \).

2. **Calculate the Concentration of Hydrolyzed Species**:
The concentration of the hydrolyzed species \( HA \) can be calculated using the degree of hydrolysis:
\[ [HA] = \alpha \times C_0 \]
where \( C_0 \) is the initial concentration of \( A^- \).
\[ [HA] = 0.01 \times 0.1 = 0.001 \, \text{M} \]

3. **Calculate the Change in Concentration of \( A^- \)**:
The concentration of \( A^- \) that remains after hydrolysis can be calculated as:
\[ [A^-] = C_0 - [HA] = 0.1 - 0.001 = 0.099 \, \text{M} \]

4. **Determine \( H^+ \) Concentration**:
The hydrolysis reaction can be represented as:
\[ A^- + H_2O \rightleftharpoons HA + OH^- \]
From the hydrolysis, we know that the concentration of \( H^+ \) produced is equal to the concentration of \( OH^- \) produced, which is equal to \( [HA] \):
\[ [H^+] = [HA] = 0.001 \, \text{M} \]

5. **Scaling Up to 0.4 M Solution**:
Now, we need to find the \( H^+ \) concentration in a 0.4 M solution of \( A^- \). The degree of hydrolysis will remain the same (0.01) since it is a property of the conjugate base.
\[ [HA] = \alpha \times C_0 = 0.01 \times 0.4 = 0.004 \, \text{M} \]

6. **Final Calculation of \( H^+ \) Concentration**:
Therefore, the concentration of \( H^+ \) in the 0.4 M solution of \( A^- \) is:
\[ [H^+] = 0.004 \, \text{M} \]

### Final Answer:
The \( H^+ \) concentration in a 0.4 M solution of \( A^- \) is \( 0.004 \, \text{M} \).