JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Solutions

Molecules of benzoic acid

(C_{6} H_{5} COOH)

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 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)2.4 g✓ Correct
(B)1.0 g
(C)1.5 g
(D)1.8 g

Answer: (A)

Solution

For dimerisation

2 A \to A_{2}

with

80%

association, the van't Hoff factor is

i = 1 - \frac{α}{2} = 1 - \frac{0.8}{2} = 0.6

. Using

Δ T_{f} = i K_{f} m

with

Δ T_{f} = 2

K_{f} = 5

and

30

g of solvent,

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

, which is

2 = \frac{3000 w}{3660}

. Solving,

w = \frac{2 \times 3660}{3000} \approx 2.4

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option

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