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The vapour pressure of a solvent decreased by $20 mm$ of $Hg$ when a non-volatile solute was added to the solvent. The mole-fraction of the solute in the solution is $0.5$ . What should be the mole-fraction of the solvent for the decrease in the vapour pressure needs to be $10 mm$ of $Hg$ ?

A $\frac{3}{4}$
B $\frac{2}{3}$
C $\frac{1}{4}$
D $\frac{3}{2}$

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{3}{4}$

Step-by-step Solution

Detailed explanation

The vapour pressure of the solute = Po-Ps==20 mm of Hg Now, PA=PA0XA Partial pressure of solute PA=PA0XA=PA0×mole fraction of solutePA0=200.5=40 Pressure of pure solute is equal to the 40 mm of Hg If it is decreases by…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The vapour pressure of a solvent decreased by 20 mm of Hg when a non-volatile solute was added to the solvent. The mole-fraction of the solute in the solution is 0.5. What should be the mole-fraction of the solvent for the decrease in the vapour pressure needs to be 10 mm of Hg ?

Step-by-step Solution

The vapour pressure of a solvent decreased by $20 mm$ of $Hg$ when a non-volatile solute was added to the solvent. The mole-fraction of the solute in the solution is $0.5$ . What should be the mole-fraction of the solvent for the decrease in the vapour pressure needs to be $10 mm$ of $Hg$ ?