For solution of weak electrolytic, the degree of ionization

Options

A. Will be reciprocal to the dilution
B. Will be proportional to dilution
C. Will be proportional to the square root of dilution
D. Will be proportional to concentration of electrolyte

Answer

To solve the question regarding the degree of ionization for a solution of a weak electrolyte, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Weak Electrolytes**:
- A weak electrolyte is a substance that partially ionizes in solution. This means that not all of the solute dissociates into ions.

2. **Ostwald's Dilution Law**:
- Ostwald's dilution law relates the degree of ionization (α) of a weak electrolyte to its concentration (C) and its dissociation constant (K). It states that as the dilution of the solution increases, the degree of ionization also increases.

3. **Dissociation of a Binary Electrolyte**:
- Consider a binary electrolyte AB that dissociates into A⁺ and B⁻ ions:
\[ AB \rightleftharpoons A^+ + B^- \]

4. **Expression for the Dissociation Constant (K)**:
- The dissociation constant (K) for the reaction can be expressed as:
\[ K = \frac{[A^+][B^-]}{[AB]} \]

5. **Setting Up Initial and Equilibrium Concentrations**:
- Let the initial concentration of AB be C. At equilibrium:
- The concentration of A⁺ and B⁻ will be αC (where α is the degree of ionization).
- The concentration of AB will be \(C(1 - \alpha)\).

6. **Substituting into the Dissociation Constant Expression**:
- Substitute the equilibrium concentrations into the expression for K:
\[ K = \frac{(\alpha C)(\alpha C)}{C(1 - \alpha)} = \frac{\alpha^2 C^2}{C(1 - \alpha)} \]

7. **Simplifying the Expression**:
- Since α is very small for weak electrolytes, we can approximate \(1 - \alpha \approx 1\):
\[ K \approx \frac{\alpha^2 C}{1} \]
- Rearranging gives:
\[ \alpha^2 = \frac{K}{C} \]

8. **Finding the Degree of Ionization (α)**:
- Taking the square root of both sides, we find:
\[ \alpha = \sqrt{\frac{K}{C}} \]

9. **Conclusion**:
- This shows that the degree of ionization (α) is proportional to the square root of the dilution (or concentration) of the electrolyte. Therefore, the correct answer is that the degree of ionization is proportional to the square root of dilution.

### Final Answer:
The degree of ionization (α) of a weak electrolyte is proportional to the square root of its dilution.