A solution of weak acid HA containing 0.01 moles of acid per litre of solutions has pH = 4. The percentage degree of ionisation of the acid and the ionisation constant of acid are respectively

Options

A. `1%, 10^(-6)`
B. `0.01%, 10^(-4)`
C. `1%, 10^(-4)`
D. `0.01%, 10^(-6)`

Explanation

To solve the problem, we need to calculate the percentage degree of ionization (α) and the ionization constant (Ka) of the weak acid HA given the concentration and pH of the solution.

### Step 1: Determine the concentration of H⁺ ions
The pH of the solution is given as 4. We can calculate the concentration of hydrogen ions (H⁺) using the formula:
\[ \text{[H⁺]} = 10^{-\text{pH}} \]
Substituting the pH value:
\[ \text{[H⁺]} = 10^{-4} \, \text{mol/L} \]

### Step 2: Set up the ionization equilibrium
The weak acid HA ionizes as follows:
\[ HA \rightleftharpoons H^+ + A^- \]
Let the initial concentration of HA be \( C = 0.01 \, \text{mol/L} \) and the amount ionized be \( x \). At equilibrium, we have:
- [HA] = \( C - x \)
- [H⁺] = \( x \)
- [A⁻] = \( x \)

From Step 1, we know that \( x = [H⁺] = 10^{-4} \, \text{mol/L} \).

### Step 3: Calculate the concentration of HA at equilibrium
Using the initial concentration and the amount ionized:
\[ [HA] = C - x = 0.01 - 10^{-4} \]
Since \( 10^{-4} \) is much smaller than \( 0.01 \), we can approximate:
\[ [HA] \approx 0.01 \, \text{mol/L} \]

### Step 4: Calculate the ionization constant (Ka)
The ionization constant \( K_a \) is given by:
\[ K_a = \frac{[H^+][A^-]}{[HA]} \]
Substituting the equilibrium concentrations:
\[ K_a = \frac{x \cdot x}{C - x} = \frac{x^2}{C - x} \]
Substituting the values:
\[ K_a = \frac{(10^{-4})^2}{0.01 - 10^{-4}} \]
Using the approximation \( 0.01 - 10^{-4} \approx 0.01 \):
\[ K_a = \frac{10^{-8}}{0.01} = 10^{-6} \]

### Step 5: Calculate the percentage degree of ionization (α)
The degree of ionization \( \alpha \) is given by:
\[ \alpha = \frac{x}{C} \]
Substituting the values:
\[ \alpha = \frac{10^{-4}}{0.01} = 0.01 \]

To express this as a percentage:
\[ \text{Percentage degree of ionization} = \alpha \times 100 = 0.01 \times 100 = 1\% \]

### Final Results
- The percentage degree of ionization (α) is **1%**.
- The ionization constant (Ka) is **\( 10^{-6} \)**.