Question

A mixture of ethyl alcohol and propyl alcohol has a vapor pressure of $290{\text{ }}mm$ at $300{\text{ }}K$. The vapor pressure of propyl alcohol is $200{\text{ }}mm$ . If the mole fraction of ethyl alcohol is $0.6$ its vapor pressure (in mm) at the same temperature will be:
A) 350
B) 300
C) 700
D) 360

Answer 1

In the question a mixture of two type of alcohol at $290{\text{ }}mm$vapor pressure at a temperature of $300{\text{ }}K$are given and also the vapor pressure of one alcohol is given along with its vapor pressure. So we have to find the temperature of the ethyl alcohol at $0.6$ vapor pressure.
Formula used: ${P_T} = P{^\circ _A} \times {X_A} + P{^\circ _B} \times {X_B}$
Where, ${P_T}$ = total pressure
$P{^\circ _A}$ = vapor pressure of component A
${X_A}$ = mole fraction of component A in solution
$P{^\circ _B}$ = vapor pressure of component B
${X_B}$ = mole fraction of component B in solution

Complete step-by-step solution:
By using Raoult's law we will find the temperature of the alcohol. We know that when substances were mixed together in a solution, the vapor pressure of the solution decreased simultaneously.
Meanwhile, we know that, according to Raoult’s law
The total vapor pressure of binary mixture of miscible liquids be having ideally is given by
${P_T} = P{^\circ _A} \times {X_A} + P{^\circ _B} \times {X_B}$
Where ${X_A}$ and ${X_B}$ are mole fraction of A and B in the liquid phase
Whereas $P{^\circ _A}$and $P{^\circ _B}$ are vapor pressures of pure liquids.
By putting the values in the formula, we get:
$\Rightarrow P = P{^\circ _A} \times {X_A} + P{^\circ _B} \times {X_B}$
$\Rightarrow 290 = P{^\circ _A} \times 0.6{\text{ }} + {\text{ }}200 \times \;\left( {{\text{ }}1-0.6{\text{ }}} \right)$
$\Rightarrow 290 = 0.6\; \times P{^\circ _A} + 80$
$\therefore P{^\circ _A} = 350$

Hence, the correct answer is option ‘A’.

Note: We can define Rault’s laws that when a solvent’s partial vapour pressure in a solution (or mixture) is equal or identical to the vapors pressure of the pure solvent multiplied by its mole fraction in the solution.