0.004 M K$$_2$$SO$$_4$$ solution is isotonic with 0.01 M glucose solution. Percentage dissociation of K$$_2$$SO$$_4$$ is _______ (Nearest integer)

For isotonic solutions, the osmotic pressures are equal:

$$i_1 C_1 = i_2 C_2$$

For glucose (non-electrolyte): $$i_2 = 1$$, $$C_2 = 0.01$$ M

For K$$_2$$SO$$_4$$: $$C_1 = 0.004$$ M

$$i_1 \times 0.004 = 1 \times 0.01$$

$$i_1 = \frac{0.01}{0.004} = 2.5$$

K$$_2$$SO$$_4$$ dissociates as: $$\text{K}_2\text{SO}_4 \rightarrow 2\text{K}^+ + \text{SO}_4^{2-}$$

Number of ions $$n = 3$$

Using the van't Hoff factor formula:

$$i = 1 + \alpha(n - 1)$$

$$2.5 = 1 + \alpha(3 - 1)$$

$$2.5 = 1 + 2\alpha$$

$$\alpha = \frac{1.5}{2} = 0.75$$

Percentage dissociation = $$0.75 \times 100 = 75\%$$