Q14 / 54 · JEE Advanced 2018 (Paper 1) · Chemistry

The plot given below shows P-T curves (where, P is the pressure and T is the temperature) for two solvents X and Y and isomolal solutions of NaCl in these solvents. NaCl is completely dissociates in both the solvents.
Figure
On the addition of equal number of moles of a non-volatile solute S in equal amount (in kg) of these solvents, the elevation of boiling point of solvent X is three times that of solvent Y. The solute S is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in the solvent Y, the degree of dimerization in the solvent X is _______.

Correct answer: 0.05

Solution

From the graph:
For the solvent X,    

∆Tbx=2
∆Tbx=mNaCl×Kbx  ...i
For the solvent Y,   

∆Tby=1
∆Tby=mNaCl×Kby  ...ii
From the equations (i) and (ii),
⇒ KbxKby=2
For the solute S,
Figure
i=1-α2
∆Tbxs=1-α12Kbx
∆Tbys=1-α22Kby
Given: 

∆Tbxs=3∆Tbys
1-α12Kbx=3×1-α12×kby
21-α12=31-α22
α2=0.7
So, α=0.05

Hence, the correct answer is 0.05.

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