State and derive ostwald dilution law for weak electrolyte?

Question: State and derive ostwald dilution law for weak electrolyte?

Ostwald's dilution law is a formula that describes the relationship between the degree of dissociation and the concentration of a weak electrolyte. A weak electrolyte is a substance that partially breaks down into ions when dissolved in water, such as acetic acid or ammonia. The degree of dissociation is the fraction of molecules that dissociate into ions. The law states that the degree of dissociation is inversely proportional to the square root of the concentration of the weak electrolyte. Mathematically, the law can be expressed as:

$$K_d = \frac{\alpha^2}{1 - \alpha} \cdot c_0$$

where $K_d$ is the dissociation constant, $\alpha$ is the degree of dissociation, and $c_0$ is the initial concentration of the weak electrolyte. If $\alpha$ is very small, which is true for most weak electrolytes, then $1 - \alpha \approx 1$, and the law simplifies to:

$$K_d = \alpha^2 \cdot c_0$$

or

$$\alpha = \sqrt{\frac{K_d}{c_0}}$$

This shows that the degree of dissociation increases as the concentration decreases, or as the dilution increases.

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