A dilute solution contains ‘t’ moles of solute X in 1 kg of solvent with molal elevation constant $K_{b}$ , the solute dimerises in the solution according to the following equation. The degree of association is $α . 2 X ⇌ X_{2}$

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The degree of association $α = \frac{2 (K_{b} t - Δ T_{b})}{K_{b} T}$

The molecular mass observed will be lesser than actual molecular mass

The colligative properties observed will be

${(T_{b})}_{o b s} < {(T_{b})}_{t h e o r e t i c a l}; {(T_{f})}_{o b s} < {(T_{f})}_{t h e o r e t i c a l}; Δ P_{o b s} < Δ P_{t h e o r e t i c a l}$

The equilibrium constant for the process can be expressed as: $K = \frac{K_{b} (K_{b} t - Δ T_{b})}{{[2 Δ T_{b} - K_{b} t]}^{2}}$

answer is A, D.

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Detailed Solution

$\underset{1 - α}{2 X} ⇌ \underset{\frac{α}{2}}{X_{2}} i = 1 - \frac{α}{2} \frac{{(Δ t_{b})}_{0.65}}{K_{b} t} = i = 1 - \frac{α}{2} \frac{α}{2} = 1 - \frac{Δ t_{b}}{K_{b} t} = \frac{K_{b} t - Δ t_{b}}{K_{b} t} (A) α = \frac{2 (K_{b} t - Δ t_{b})}{K_{b} t}$