For the weak electrolyte , their degree of dissociation increase

Options

A. One increasing dilution
B. On decreasing diluation
C. On increasing pressure
D. None of these

Answer

To solve the question regarding the degree of dissociation of a weak electrolyte, we will follow these steps:

### Step 1: Understanding the Weak Electrolyte
A weak electrolyte, such as HA, partially dissociates in solution. The dissociation can be represented as:
\[ HA \rightleftharpoons H^+ + A^- \]

### Step 2: Setting Up the Equilibrium Expression
Let the initial concentration of the weak electrolyte HA be \( C \). If \( x \) is the amount that dissociates, then at equilibrium:
- Concentration of \( HA \) = \( C - x \)
- Concentration of \( H^+ \) = \( x \)
- Concentration of \( A^- \) = \( x \)

### Step 3: Defining Degree of Dissociation
The degree of dissociation \( \alpha \) is defined as the fraction of the original substance that has dissociated:
\[ \alpha = \frac{x}{C} \]

### Step 4: Writing the Equilibrium Constant Expression
The equilibrium constant \( K_a \) for the dissociation of the weak electrolyte can be expressed as:
\[ K_a = \frac{[H^+][A^-]}{[HA]} = \frac{x \cdot x}{C - x} = \frac{x^2}{C - x} \]

### Step 5: Applying the Assumption for Weak Electrolytes
For weak electrolytes, \( x \) (the amount dissociated) is usually much smaller than \( C \). Therefore, we can approximate:
\[ C - x \approx C \]
This simplifies our expression for \( K_a \):
\[ K_a \approx \frac{x^2}{C} \]

### Step 6: Relating Degree of Dissociation to Concentration
Substituting \( x = C \alpha \) into the equation gives:
\[ K_a \approx \frac{(C \alpha)^2}{C} = C \alpha^2 \]

### Step 7: Understanding the Effect of Dilution
According to the principle of dilution (L'Hospital's dilution law), as the concentration \( C \) decreases (i.e., when we dilute the solution), \( K_a \) remains constant. Therefore, if \( C \) decreases, \( \alpha \) must increase to keep \( K_a \) constant:
\[ K_a = C \alpha^2 \]
This implies:
\[ \alpha \propto \frac{1}{\sqrt{C}} \]
Thus, as the concentration decreases (or volume increases), the degree of dissociation \( \alpha \) increases.

### Conclusion
The degree of dissociation of a weak electrolyte increases with dilution.

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