Question

Two liquids A and B form an ideal solution. What will be the total pressure at $27{}^\circ C$ of a solution having 1.5 mol of A and 4.5 mol of B? The vapor pressure of A and B at $27{}^\circ C$is 0.116 atm and 0.140 atm respectively.

Answer 1

Hint: The partial pressure of any substance is directly proportional to mole fraction of the solute. The mole fraction is the number of moles of one component upon total number of moles of all components. The sum of all components is 1. Total pressure will be calculated by the sum of partial pressures.

Formula used:
Partial pressure = vapor pressure $\times $ mole fraction = ${{P}_{A}}={{P}^{o}}_{A}.{{\chi }_{A}}$
Total pressure = ${{P}_{A}}+{{P}_{B}}$

Complete answer:
We have been given two liquids A and B to find the vapor pressure when they are having 1.5 mol of A and 4.5 mol of B and the vapor pressure of A and B at $27{}^\circ C$is 0.116 atm and 0.140 atm respectively.
For this first take out the mole fraction from the given number of moles of A and B,
Mole fraction of A, ${{\chi }_{A}}=\dfrac{{{n}_{A}}}{{{n}_{A}}+{{n}_{B}}}$
${{\chi }_{A}}=\dfrac{1.5}{1.5+4.5}=\dfrac{1.5}{6.0}=\dfrac{1}{4}$
Now, we know the mole fraction of both the components A and B is unity so,
Mole fraction of B = ${{\chi }_{B}}=1-\dfrac{1}{4}=\dfrac{3}{4}$
Now, calculating the total pressure by the formula Total pressure = ${{P}_{A}}+{{P}_{B}}$ , where P is the product of vapor pressure and mole fractions of respective components, we have,
${{P}_{total}}={{P}^{o}}_{A}{{\chi }_{A}}+{{P}^{o}}_{B}{{\chi }_{B}}$
${{P}_{total}}=0.116\times \dfrac{1}{4}+0.14\times \dfrac{3}{4}$
P = 0.029 + 0.105
Total pressure = 0.134
Hence, the pressure was calculated as 0.134 atm.

Note:
As the sum of mole fraction of all components is unity, we can only take out one component then subtract that component from 1 to get the other component mole fraction. As mole fraction is a ratio, so it has no units. Total pressure is based on Dalton’s law of partial pressure that total pressure is the sum of partial pressure of all components.