# Ostwald’s Dilution Law

Ostwald’s Dilution Law:

It states that “The extent of ionization of a weak electrolyte increases with increase in dilution”.

Let us consider n mole of an electrolyte AB dissolve in ‘V’ litre of the solution. If α be the degree of ionization of a electrolyte. Then,

$$\alpha = \frac{\text{Number of moles ionized}}{\text{total number of moles}}$$

$$or, \alpha = \frac{\text{Number of moles ionized}}{\text{n}}$$

$$or, \text{Number of moles ionized} = {\text{n} \alpha }$$

$$\therefore \text{Number of moles unionized} = {\text{n – n} \alpha } = {\text{n(1-} \alpha) } $$

Let any electrolyte ionizes as follows:

$$AB{{\rightleftharpoons}}A^+ + B^-$$

Initially, let concentration of the electrolyte(AB) is n. The concentration of A and B are zero.

At equilibrium, concentration of AB becomes n(1-α) and concentration of A and B ions becomes nα.

We know, from the law of mass action:

$$\text{Rate of dissociation} \propto [AB]$$

$$or, \text{Rate of dissociation} = K_1\text{[AB]}…….(i)$$

Here K_{c} is the ionization constant. This remains constant at a particular temperature.

Similarly,

$$\text{Rate of dissociation} \propto [A^+]+ [B^-]$$

$$or, \text{Rate of dissociation} = K_2 [A^+]+ [B^-]…….(ii)$$

From equation (i) and (ii),

$$K_1 [AB] = K_2[A^+][B^-]$$

$$or, \frac{k_1}{K_2} = \frac{[A^+] + [B^-]}{AB}$$

$$or, K_c = \frac{[A^+] + [B^-]}{AB}…….(iii)$$

When 1 mole of electrolyte is dissolved in V litres of solution, then C = 1/v.

Now, putting the value of [AB], [A^{+}], [B^{–}] in equation (iii), we get:

$$K_c = \frac{\frac{n\alpha}{v} \times \frac{n\alpha}{v} }{\frac{n(1-\alpha)}{v}}$$

$$K_c = \frac{n\alpha ^2}{v(1-\alpha)}…….(iv)$$

Equation (iv) is called the Ostwald’s dilution law. Here K_{c} is the ionization constant. This remains constant at a particular temperature.

Two cases can be made from the the above equation.

**Ostwald’s dilution law for weak electrolyte:**

For weak electrolyte, degree of dissociation (α) is almost constant. Hence (1-α) can be written as 1.

Now, equation (iv) becomes,

$$K = \frac{\alpha ^2}{V}$$

$$or, \alpha = \sqrt{KV}$$

$$\text{Since} V = \frac{1}{n}, \text{we can write}:$$

$$or, \alpha = \sqrt{ \frac{K}{n}} $$

This is the expression of Ostwald’s dilution law for weak electrolyte.

**Ostwald’s dilution law for for strong electrolyte:**

The value of degree of dissociation (α) is very large in case of strong electrolyte, so, we take equation (iv) to find the degree of dissociation of strong electrolyte.

**Note:**This law is the application of the law of mass action to the ionic equilibrium.

**Limitations of Ostwald’s dilution law:**

- This law is applicable only for weak electrolyte.
- This law doesn’t hold true for concentrated solution.

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