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Molecules of benzoic acid $$(C_6H_5COOH)$$ dimerise in benzene. '$$w$$' g of the acid dissolved in $$30$$g of benzene shows a depression in freezing point equal to $$2$$K. If the percentage association of the acid to form a dimer in the solution is $$80$$, then $$w$$ is:
(Given that $$K_f=5$$K kg $$mol^{-1}$$, Molar mass of benzoic acid $$=122$$ g $$mol^{-1}$$)


A
1.8g
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B
2.4g
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C
1.0g
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D
1.5g
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Solution

The correct option is B $$2.4$$g
$$\underset{Wg}{2(C_6H_5COOH)}\overset{C_6H_6}{\underset{(30g)}{\longrightarrow}}\underset{\text{diser}}{C_6H_5COOH)_2}$$

$$\Delta_fT=i\times k_f\times m$$

$$2=0.6\times 5\times \dfrac{w\times 1000}{122\times 30}$$

$$(i=1-0.8+0.4=0.6)$$

$$w=2.44$$ g.

Hence, the correct option is $$B$$

Chemistry

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