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 $$iso-molal$$ 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 .

Question

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 $$iso-molal$$ 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        .

Infinity Learn · Accepted Answer

From the  graph we can observe thatFor solvent X’      Δ$$Tbx=2$$Δ$$Tbx=mNaCl$$×$$Kb(x)$$  ……….(1)            For solvent ‘Y’          Δ$$Tby=1$$ Δ$$Tby=mNaCl$$×Kby ……….(2)         Equation (1) $$/(2)$$⇒$$KbxKby=2$$             For solute $$S2(S)$$→$$S21$$−αα$$/2i=(1$$−α$$/2)$$Δ$$Tb(x)(s)=1$$−α$$12Kb(x)$$ Δ$$Tb(x)(s)=1$$−α$$22Kb(y)$$ Given Δ$$Tb(x)(s)=3$$Δ$$Tb(y)(s)1$$−α$$12Kb(x)=3$$×$$1$$−α$$22$$×$$Kb(y)$$    $$21$$−α$$12=31$$−α$$22$$α$$2=0.7$$    So α$$1=0.05$$

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