Consider a binary solution of two volatile liquid components 1 and 2 . x₁ and y₁ are the mole fractions of component 1 in liquid and vapour phase, respectively. The slope and intercept of the linear plot of 1/x₁ vs 1/y₁ are given respectively as :

Solution

Chemistry ma’am · 4 steps

Get 1/y₁ from Dalton and Raoult, then rearrange so 1/x₁ is on the y-axis.

1. Two laws together. Raoult's law gives the total pressure P = P₂⁰ + (P₁⁰ - P₂⁰)x₁. Dalton's law gives the vapour mole fraction y₁ = (x₁ P₁⁰)/P.
2. Take the reciprocal. 1/y₁ = P/(x₁ P₁⁰) = P₂⁰/P₁⁰·1/x₁ + (P₁⁰ - P₂⁰)/P₁⁰. This line gives 1/y₁ in terms of 1/x₁, which is the wrong way round for this plot.
3. Make 1/x1 the subject. In a plot of 1/x₁ vs 1/y₁, the y-axis is 1/x₁. Move the constant term to the left, then multiply both sides by P₁⁰/P₂⁰.

   1/x₁ = P₁⁰/P₂⁰·1/y₁ + (P₂⁰ - P₁⁰)/P₂⁰

4. So. The slope is P₁⁰/P₂⁰ and the intercept is (P₂⁰ - P₁⁰)/P₂⁰. That is option (d).

The idea to keep. In vapour-liquid plots, first write 1/y₁ as a line in 1/x₁. Then check which quantity sits on the y-axis before you read off the slope and intercept.

Answer from the NTA final answer key. Solution by PrepWiser.