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 completely dissociates in both the solvents.

On 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. Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in solvent Y, the degree of dimerization in solvent X is ____.

Explanation

Case I. Solution of NaCl
For solvent X : `Delta T_(X) = iK_(BX)xxn_(NaCl)`….(i)
For solvent T : `Delta T_(Y)=iK_(B Y)xx m_(NaCl)`….(ii)
Dividing (i) and (ii)
`(DeltaT_(X))/(DeltaT_(Y))=(K_(BX))/(K_(BY))`
`(K_(bX))/(K_(bY))=(2)/(1)` Since, `DeltaT_(X)=2,DeltaT_(Y)=1`
Dimerisation of solute S may be given as
`{:(,2S,hArr,S_(2),:,"Total particles"),(t_(0),1,,0,:,1),(t_(eq),1-alpha,,(alpha)/(2),:,1-(alpha)/(2)):}`
`i=(1-alpha//2)/(1)`
Case II. Solution of solute S
`DeltaT_(X)=(1-(alpha_(1))/(2))K_(bX)xxm`
`DeltaT_(Y)=(1-(alpha_(2))/(2))K_(bY)xxm`
Given : `DeltaT_(X) = 3 Delta T_(Y)`
`(1-(alpha_(1))/(2))K_(bX)xxm=3(1-(alpha_(2))/(2))K_(bY)xxm`
`2(1-(alpha_(1))/(2))=3(1-(alpha_(2))/(2))`
Here `K_(bX)=2K_(bY)`
Given `alpha =0.7`
`:. 2(1-(alpha_(1))/(2))=3(1-(0.7)/(2))`
`alpha_(1)=0.05`.