The degree of ionisation of an acid HA is 0.00001 at 0.1 M concentration. Its dissociation constant will be

Options

A. a. `10^(-9)`
B. b. `10^(-11)`
C. c. `10^(-8)`
D. d. `10^(-7)`

Explanation

To find the dissociation constant (Ka) of the acid HA given its degree of ionization and concentration, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Degree of ionization (α) = 0.00001
- Concentration (C) = 0.1 M

2. **Understand the Relationship:**
- The dissociation constant (Ka) for a weak acid can be calculated using the formula:
\[ K_a = C \cdot \alpha^2 \]
where:
- \(C\) is the concentration of the acid,
- \(\alpha\) is the degree of ionization.

3. **Substitute the Values:**
- Substitute the values of \(C\) and \(\alpha\) into the formula:
\[ K_a = 0.1 \cdot (0.00001)^2 \]

4. **Calculate \(\alpha^2\):**
- Calculate \((0.00001)^2\):
\[ (0.00001)^2 = 0.0000000001 = 10^{-10} \]

5. **Calculate \(K_a\):**
- Now substitute this value back into the equation for \(K_a\):
\[ K_a = 0.1 \cdot 10^{-10} \]
- Convert 0.1 to scientific notation:
\[ 0.1 = 10^{-1} \]
- Therefore:
\[ K_a = 10^{-1} \cdot 10^{-10} = 10^{-11} \]

6. **Final Result:**
- The dissociation constant \(K_a\) is:
\[ K_a = 10^{-11} \]

### Conclusion:
The dissociation constant \(K_a\) for the acid HA is \(10^{-11}\).

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