Derive the relationship between the Van't Hoff factor ( $$i$$ ) and degree of association ( $$\alpha$$ ) when $$n$$ molecules of solute associate to form a polymer$$(A)_n$$.

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Derive the relationship between the Van't Hoff factor ( $$i$$  ) and degree of association ( $$\alpha$$  ) when  $$n$$  molecules of solute associate to form a polymer$$(A)_n$$.

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The formula is:  $$i = 1 + \left( \frac{1}{n} - 1 \right)\alpha$$    Derivation: Start with 1 mole. Equilibrium moles = $$(1-\alpha)$$  (unassociated) + $$\frac{\alpha}{n}$$  (associated). Total moles $$i = 1 - \alpha + \frac{\alpha}{n}$$  .

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