If c is the molar concentration of the solution of a weak electrolyte, then its degree of dissociation is proportional to ............ .

Answer

To solve the question regarding the relationship between the molar concentration (C) of a weak electrolyte and its degree of dissociation (α), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Weak Electrolytes**:
- A weak electrolyte is a substance that partially dissociates into ions in solution. The degree of dissociation (α) is defined as the fraction of the total number of moles of the electrolyte that dissociates into ions.

2. **Setting Up the Reaction**:
- Consider a weak electrolyte represented as \( AB \) that dissociates into \( A \) and \( B \):
\[ AB \rightleftharpoons A + B \]
- Initially, if the concentration of \( AB \) is \( C \), then at equilibrium, the concentration of \( A \) and \( B \) will be \( C\alpha \) (where \( \alpha \) is the degree of dissociation).

3. **Equilibrium Concentrations**:
- At equilibrium, the concentration of the undissociated electrolyte \( AB \) will be:
\[ [AB] = C(1 - \alpha) \]
- The concentrations of the products \( A \) and \( B \) will both be \( C\alpha \).

4. **Expression for Equilibrium Constant (K)**:
- The equilibrium constant \( K \) for the dissociation can be expressed as:
\[ K = \frac{[A][B]}{[AB]} = \frac{(C\alpha)(C\alpha)}{C(1 - \alpha)} = \frac{C^2\alpha^2}{C(1 - \alpha)} \]
- Simplifying this gives:
\[ K = \frac{C\alpha^2}{1 - \alpha} \]

5. **Assuming Low Degree of Dissociation**:
- For weak electrolytes, \( \alpha \) is usually small, so \( 1 - \alpha \approx 1 \). Thus, we can simplify the equation to:
\[ K \approx C\alpha^2 \]

6. **Finding the Relationship**:
- Rearranging the above equation gives:
\[ \alpha^2 \approx \frac{K}{C} \]
- Taking the square root of both sides results in:
\[ \alpha \approx \sqrt{\frac{K}{C}} \]
- This shows that the degree of dissociation \( \alpha \) is inversely proportional to the square root of the concentration \( C \):
\[ \alpha \propto \frac{1}{\sqrt{C}} \]

### Conclusion:
The degree of dissociation \( \alpha \) of a weak electrolyte is inversely proportional to the square root of its molar concentration \( C \).