The correct experssion for Ostwald's dilution law is

Options

A. `K_(a)= alpha^(2)V`
B. `K_(a)=(alpha^(2))/(V)`
C. `K_(a)=(alpha^(2))/((1-alpha)V)`
D. `K_(a)=(alpha^(2))/((1-alpha)C)`

Explanation

To derive the correct expression for Ostwald's dilution law, let's break down the concept step by step.

### Step 1: Understand Ostwald's Dilution Law
Ostwald's dilution law states that the degree of ionization (α) of a weak electrolyte is directly proportional to its dilution. This means that as the concentration of the electrolyte decreases (dilution increases), the degree of ionization increases.

### Step 2: Define Degree of Ionization
The degree of ionization (α) is defined as the fraction of the total amount of the electrolyte that dissociates into ions. For a weak electrolyte, if we have a concentration \( C \), then the degree of ionization can be expressed as:

\[ \alpha = \frac{\text{Number of moles ionized}}{\text{Total number of moles}} = \frac{x}{C} \]

where \( x \) is the number of moles that have ionized.

### Step 3: Relate to the Dissociation Constant
For a weak electrolyte, the dissociation constant \( K_a \) (for acids) or \( K_b \) (for bases) can be expressed in terms of the concentration and degree of ionization. For a weak acid, the dissociation can be represented as:

\[ HA \rightleftharpoons H^+ + A^- \]

The expression for the dissociation constant \( K_a \) is given by:

\[ K_a = \frac{[H^+][A^-]}{[HA]} \]

In terms of \( C \) and \( \alpha \):

\[ K_a = \frac{C\alpha^2}{C(1-\alpha)} \approx \frac{C\alpha^2}{C} \quad \text{(for very weak electrolytes, where } \alpha \text{ is small)} \]

### Step 4: Rearranging the Equation
From the above expression, we can rearrange to express \( \alpha^2 \):

\[ \alpha^2 = \frac{K_a}{C} \]

### Step 5: Final Expression
This leads us to the final expression of Ostwald's dilution law:

\[ \alpha^2 = K_a \cdot V \]

where \( V \) is the volume of the solution.

### Conclusion
Thus, the correct expression for Ostwald's dilution law is:

\[ \alpha^2 = K_a \cdot C \]