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JEE Advanced 2018Paper 1
Exam
JEE Advanced
Year
2018
Paper
Paper 1
Subject
Chemistry
Chapter
Solutions

JEE Advanced 2018 · Paper 1 · Chemistry · Solutions

The plot given below shows P - T curves (where, P is the pressure...

The plot given below shows P−TP - T curves (where, PP is the pressure and TT is the temperature) for two solvents XX and YY and isomolal solutions of NaClNaCl in these solvents. NaClNaCl is completely dissociates in both the solvents.
The plot given below shows P - T curves (where, P is the pressure and T is the temperature) for two solvents X and Y
On the addition of equal number of moles of a non-volatile solute SS in equal amount (in kgkg) of these solvents, the elevation of boiling point of solvent XX is three times that of solvent YY. The solute SS is known to undergo dimerization in these solvents. If the degree of dimerization is 0.70 . 7 in the solvent YY, the degree of dimerization in the solvent XX is _______.

Correct answer

0

Step-by-step solution

From the graph:
For the solvent XX, 

∆Tbx=2∆ {\text{T}}_{bx} = 2
∆Tbx=mNaCl×Kb(x)...(i)∆ {\text{T}}_{bx} = {m}_{NaCl} \times {K}_{b\left(x\right)} . . . \left(i\right)
For the solvent YY,   

∆Tby=1∆ {\text{T}}_{by} = 1
∆Tb(y)=mNaCl×Kb(y)...(ii)∆ {\text{T}}_{b\left(y\right)} = {m}_{NaCl} \times {K}_{b\left(y\right)} . . . \left(ii\right)
From the equations (ii) and (iiii),
⇒Kb(x)Kb(y)=2⇒ \dfrac{{K}_{b\left(x\right)}}{{K}_{b\left(y\right)}} = 2
For the solute SS,
The plot given below shows P - T curves (where, P is the pressure and T is the temperature) for two solvents X and Y
i=(1−\alpha2)i = \left(1 - \dfrac{\text{\alpha}}{2}\right)
∆Tb(x)(s)=(1−\alpha12)Kb(x)∆ {\text{T}}_{b\left(x\right)\left(s\right)} = \left(1 - \dfrac{{\text{\alpha}}_{1}}{2}\right){K}_{b\left(x\right)}
∆Tb(y)(s)=(1−\alpha22)Kb(y)∆ {\text{T}}_{b\left(y\right)\left(s\right)} = \left(1 - \dfrac{{\text{\alpha}}_{2}}{2}\right){K}_{b\left(y\right)}
Given: 

∆Tb(x)(s)=3∆Tb(y)(s)∆ {\text{T}}_{b\left(x\right)\left(s\right)} = 3 ∆ {\text{T}}_{b\left(y\right)\left(s\right)}
\left(1 - \dfrac{{\text{\alpha}}_{1}}{2}\right){K}_{b\left(x\right)} = 3 \times \left(1 - \dfrac{{\text{\alpha}}_{1}}{2}\right) \times {k}_{b\left(y\right)}<br><br >2\left(1 - \dfrac{{\text{\alpha}}_{1}}{2}\right) = 3\left(1 - \dfrac{{\text{\alpha}}_{2}}{2}\right)<br><br >{\text{\alpha}}_{2} = 0 .7<br>So,<br >So,\text{\alpha} = 0 .05

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