The relationship between ionisation and change in concentration of any weak electrolyte is expressed as :

Options

A. `alpha = (K_(alpha))/(C )`
B. `alpha = sqrt((K_(a))/(C ))`
C. `alpha = K_(alpha) C`
D. `alpha = sqrt((K_(a))/(C^(2)))`

Answer

To solve the problem regarding the relationship between ionization and change in concentration of any weak electrolyte, we can follow these steps:

### Step 1: Define the weak electrolyte and its dissociation
Let’s consider a weak electrolyte represented as HA, which dissociates into H⁺ ions and A⁻ ions:
\[ HA \rightleftharpoons H^+ + A^- \]

### Step 2: Set up the initial concentrations
Assume the initial concentration of the weak electrolyte (HA) is \( C \). Initially, the concentrations of H⁺ and A⁻ ions are both zero:
- \([HA] = C\)
- \([H^+] = 0\)
- \([A^-] = 0\)

### Step 3: Define the change in concentration
Let \( \alpha \) be the degree of ionization. After ionization, the concentration of HA decreases, and the concentrations of H⁺ and A⁻ increase. The concentrations can be expressed as:
- \([HA] = C - C\alpha = C(1 - \alpha)\)
- \([H^+] = C\alpha\)
- \([A^-] = C\alpha\)

### Step 4: Write the expression for the ionization constant (Ka)
The ionization constant \( K_a \) for the dissociation of the weak electrolyte can be expressed as:
\[ K_a = \frac{[H^+][A^-]}{[HA]} \]
Substituting the concentrations we derived:
\[ K_a = \frac{(C\alpha)(C\alpha)}{C(1 - \alpha)} \]
This simplifies to:
\[ K_a = \frac{C^2\alpha^2}{C(1 - \alpha)} = \frac{C\alpha^2}{1 - \alpha} \]

### Step 5: Assume α is small
Since \( \alpha \) is small for weak electrolytes, we can assume \( 1 - \alpha \approx 1 \). Thus, the equation simplifies to:
\[ K_a \approx C\alpha^2 \]

### Step 6: Rearranging to find the relationship between α and C
From the equation \( K_a = C\alpha^2 \), we can express \( \alpha^2 \) as:
\[ \alpha^2 = \frac{K_a}{C} \]
Taking the square root gives us:
\[ \alpha = \sqrt{\frac{K_a}{C}} \]

### Conclusion
Thus, the relationship between ionization (\( \alpha \)) and the concentration (\( C \)) of a weak electrolyte is given by:
\[ \alpha = \sqrt{\frac{K_a}{C}} \]