A solution of 1.8 g of benzoic acid ( C₆H₅COOH ) in 30 g of benzene shows a freezing point depression of 1.2 K. What is

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Question

A solution of 1.8 g of benzoic acid ( C₆H₅COOH ) in 30 g of benzene shows a freezing point depression of 1.2 K. What is the van't Hoff factor if it dimerizes? ( K_f = 5.12 K kg/mol, Molar mass = 122 g/mol )

Options

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0.75 1.0 0.25 0.48 Correct

Explanation

Given: A solution of 1.8 g of benzoic acid ( C₆H₅COOH ) in 30 g of benzene shows a freezing point depression of 1.2 K. What is the van't Hoff factor if it dimerizes? ( K_f = 5.12 K kg/mol, Molar mass = 122 g/mol ) Formula: Molality = 1.8 / 122/0.03 = 0.492 mol/kg. Substitution & Calculation: Normal Δ T_f = 5.12 × 0.492 = 2.52 K . Observed Δ T_f = 1.2 K . i = 1.2/2.52 = 0.476 . Final Result: The computed value matches expected outcome and confirms correct choice as per latest NCERT 2026-27.

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