The percentage dissociation of a salt (MX$$_3$$) solution at given temperature (van't Hoff factor i = 2) is .......... % (Nearest Integer)

Let the salt be written as $$MX_3$$. In water it dissociates as

$$MX_3 \;\rightarrow\; M^{3+} + 3\,X^-$$

Thus one formula unit produces $$n = 1 + 3 = 4$$ particles when the dissociation is complete.

For any electrolyte, the van’t Hoff factor $$i$$ is related to the degree of dissociation $$\alpha$$ by

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

In the present case, $$n = 4$$, and the experimental value is $$i = 2$$. Substitute these values in $$(1)$$:

$$2 = 1 + (4-1)\,\alpha$$

$$2 = 1 + 3\,\alpha$$

$$3\,\alpha = 1$$

$$\alpha = \frac{1}{3} = 0.333...$$

The percentage dissociation is therefore

$$\alpha \times 100\% = 0.333... \times 100\% \approx 33\%$$

Nearest integer = 33 %.