Fun With Fluids!

Chemistry Level 5

Let us have fun with four ideal liquid samples A, B, C, D.
The original pressure of each of these liquid samples when placed alone in a beaker is as follows:

A: \( {P^\circ}_{A} = 100\text{ mm}\) of \(\ce{Hg}\)
B: \( {P^\circ}_{B} = 200\text{ mm}\) of \(\ce{Hg}\)
C: \( {P^\circ}_{C} = 300\text{ mm}\) of \(\ce{Hg}\)
D: \( {P^\circ}_{D} = 400\text{ mm}\) of \(\ce{Hg}\).

We first take 2 moles of A and 8 moles of B in beaker \(\mathbb I \). When equilibrium is reached, we condense the vapors above the liquid sample and pour it in beaker \( \mathbb {II} \).

In beaker \(\mathbb{ II} \) we add liquid C until the mole fraction of A and C becomes equal in the solution. When equilibrium is reached, we condense the vapors over this liquid sample and pour it in beaker \(\mathbb{ III} \).

In beaker \( \mathbb{III} \) we add liquid D until the mole fraction of liquid B and D becomes equal in the solution. When equilibrium is reached, we condense the vapors above this sample and pour it in beaker \(\mathbb{ IV }\).

Let the total pressure (in \(\text{mm}\) of \(\ce{Hg}\)) over the liquid sample in beaker \( \mathbb{IV} \) when equilibrium is reached be denoted by \(P \).

If \(P \) can be expressed as \(\dfrac MN\), where \(M\) and \(N\) are coprime positive integers, submit your answer as \(M\times N\).

Note: Raoult's law is needed to solve this question and all the liquid samples taken follow this law.

Assume that when the liquid is evaporated, there is no considerable change in the composition of the solution. (Following ideal gas principles for low pressure and high temperature).


Original

This is a part of my set Aniket's Chemistry Challenges.
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