Find Percentage Dissociation Using i Factor

❓ Question

The percentage dissociation of a salt:

$$MX_3$$

solution at a given temperature is to be calculated.

Given:

$$\text{van’t Hoff factor } i = 2$$

Find the percentage dissociation.

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🖼 Question Image

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✍️ Short Concept

For dissociation problems:

👉 First find total ions formed
👉 Then use van’t Hoff factor formula.

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🔷 Step 1 — Dissociation Reaction 💯

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

Total ions formed:

$$n = 4$$

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🔷 Step 2 — van’t Hoff Factor Formula

For dissociation:

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

Where:

• $i$ = van’t Hoff factor
• $n$ = total ions formed
• $\alpha$ = degree of dissociation

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🔷 Step 3 — Substitute Values

Given:

$$i = 2$$
$$n = 4$$

So:

$$2 = 1 + (4-1)\alpha$$
$$2 = 1 + 3\alpha$$
$$\alpha = \frac{1}{3}$$

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🔷 Step 4 — Percentage Dissociation

$$\%\text{ dissociation} = \alpha \times 100$$
$$= \frac{1}{3}\times 100$$
$$= 33.33\%$$

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✅ Final Answer

$$\boxed{33.33\%}$$

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⭐ Golden JEE Insight

For dissociation:

$$\boxed{i = 1 + (n-1)\alpha}$$

For association:

$$\boxed{i = 1 - (n-1)\alpha}$$

Always first count total particles formed after dissociation.