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van’t Hoff factor of a 0.5% (w/w) aqueous solution of KCl which freezes at –0.24⁰C is (K_f of water = 1.86K kgmol^–1, mol.wt.of KCl = 74.5)

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2.32

1.92

1.32

1.52

answer is C.

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Detailed Solution

(W/W)% of aq. KCl =0.5%

W_KCl = 0.5g

$\large W_{H_2O}=(100-0.5)=99.5g$

FP of KCl sol. = -0.24^oc

$\large \Delta T_f=0-(-0.24)=0.24^oc\\K_f\;of\;H_2O=1.86KKgmole^{-1}\\\Delta T_f=iK_fm\\0.24=iX1.86X\frac{0.5}{74.5}X\frac{1000}{99.5}$

$\large i=1.92$

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