The degree of dissociation of 0.1 M HCN solution is 0.01%. Its ionisation constant would be :

Options

A. `10^(-3)`
B. `10^(-7)`
C. `10^(-7)`
D. `10^(-9)`

Explanation

To find the ionization constant (Ka) of the HCN solution, we can follow these steps:

### Step 1: Understand the given data
We are given:
- Concentration of HCN (C) = 0.1 M
- Degree of dissociation (α) = 0.01%

### Step 2: Convert the degree of dissociation to a fraction
The degree of dissociation (α) is given in percentage. To convert it to a fraction:
\[ \alpha = \frac{0.01}{100} = 0.0001 \]

### Step 3: Calculate the concentration of ions produced
When HCN dissociates, it produces H⁺ and CN⁻ ions. The concentration of these ions at equilibrium can be expressed as:
\[ [\text{H}^+] = [\text{CN}^-] = \alpha \times C \]
Substituting the values:
\[ [\text{H}^+] = [\text{CN}^-] = 0.0001 \times 0.1 = 0.00001 \, \text{M} \]

### Step 4: Calculate the concentration of undissociated HCN
The concentration of undissociated HCN at equilibrium is:
\[ [\text{HCN}] = C - \alpha C = 0.1 - 0.0001 \times 0.1 \]
Since α is very small, we can approximate:
\[ [\text{HCN}] \approx 0.1 \, \text{M} \]

### Step 5: Write the expression for the ionization constant (Ka)
The ionization constant (Ka) is given by the formula:
\[ K_a = \frac{[\text{H}^+][\text{CN}^-]}{[\text{HCN}]} \]
Substituting the values we calculated:
\[ K_a = \frac{(0.00001)(0.00001)}{0.1} \]

### Step 6: Calculate Ka
Calculating the above expression:
\[ K_a = \frac{0.0000000001}{0.1} = 0.000000001 = 10^{-9} \, \text{M} \]

### Final Answer
Thus, the ionization constant (Ka) of HCN is:
\[ K_a = 10^{-9} \, \text{M} \]