If the boiling point of an aqueous solution containing a non-volatile solute is 100.15∘C. What is its freezing point? Given latent heat of fusion and vapourization of water 80calg−1 and 540calg−1, respectively.
A
−0.542∘C
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B
−1.542∘C
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C
−2.542∘C
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D
−1.542∘C
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Solution
The correct option is A−0.542∘C For a given aqueous solution, ΔTf=Kf×m....(i) ΔTb=Kb×m....(ii) Kf=RT2f1000lf....(iii) Kb=RT2v1000lv....(iv)
Dividing Eq. (iii) by Eq. (iv), kfKb=T2f×lVT2b×lf ∴ΔTfΔTb=T2f×lvT2b×lf Tf=0+273=273K, Tb=100+273=373K lf=80calg−1,lv=540calg−1 ∴ΔTf0.15=273×273×540373×373×80 ΔTf=ΔTf0.15=273×273×540373×373×80×0.15=0.15=0.542 ∴TF=0−0.542=−0.542∘C