JEE MAIN - Chemistry (2025 - 7th April Morning Shift - No. 24)
Explanation
To determine the percentage dissociation of the salt $\text{MX}_3$, consider the following dissociation reaction:
$ \text{MX}_3 \rightarrow \text{M}^{+3} + 3\text{X}^{-} $
The van't Hoff factor, $\text{i}$, is given as 2. The formula relating $\text{i}$ to the degree of dissociation, $\alpha$, is:
$ \text{i} = 1 + (\text{n} - 1) \alpha $
Here, $\text{n}$ represents the total number of ions produced per formula unit of the salt. For $\text{MX}_3$, dissociation yields:
1 $\text{M}^{+3}$ ion
3 $\text{X}^{-}$ ions
Thus, $\text{n} = 4$. Substituting into the formula, we have:
$ 2 = 1 + (4 - 1) \alpha $
Simplifying, we solve for $\alpha$:
$ 2 = 1 + 3\alpha $
$ 3\alpha = 1 $
$ \alpha = \frac{1}{3} \approx 0.3333 $
As a percentage, this degree of dissociation is:
$ \alpha \times 100\% \approx 33.33\% $
Rounding to the nearest integer gives:
$ 33\% $
Therefore, the percentage dissociation of the salt $\text{MX}_3$ is approximately 33%.
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