Question

At 25$^{ 0 }$C, the vapour pressure of pure benzene is 100 torr, while that of pure ethyl alcohol is 44 torr. Assuming ideal behaviour, calculate the vapour pressure at 25$^{ 0 }$C of a solution which contains 10g of each substance.
(A.) 33.775 torr
(B.) 54.775 torr
(C.) 64.775 torr
(D.) 60.775 torr

Answer 1

Try to recall the formula for the vapour pressure of a solution. It is the sum of the vapour pressure of pure solute multiplied by their mole fraction and the vapour pressure of pure solvent multiplied by their mole fraction.

_Complete step by step solution: _
We should know that vapour pressure is defined as the pressure exerted by a vapour in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system.
As we know total vapour pressure,
$P_{ t }=P_{ A }^{ 0 }X_{ A }+P_{ B }^{ 0 }X_{ B }$
Where,
$P_{ t }$ = total vapour pressure
$P_{ A }^{ 0 }$ = vapour pressure pure benzene
$X_{ A }$ = mole fraction of benzene
$P_{ B }^{ 0 }$ = vapour pressure of pure ethyl alcohol
$X_{ B }$ = mole fraction of ethyl alcohol

Here in this question, we have 10g of each ethyl alcohol and benzene.
First, we need to calculate their moles:

Moles of benzene = $\dfrac { weight\quad of\quad benzene }{ Molar\quad mass\quad of\quad benzene } =\dfrac { 10 }{ 78 }$
Moles of benzene = 0.128 moles
Moles of ethyl alcohol = $\dfrac { weight\quad of\quad ethyl alcohol }{ Molar\quad mass\quad of\quad ethyl alcohol } =\dfrac { 10 }{ 46 }$
Moles of ethyl alcohol = 0.217

Now, from these values, we need to calculate mole fraction,
Mole fraction of benzene ($X_{ A }$) = $\dfrac { moles\quad of\quad A\quad }{ Total\quad moles } =\dfrac { 0.128 }{ 0.345 }$ = 0.371
Mole fraction of ethyl alcohol ($X_{ B }$) = 1-$X_{ A }$ = 0.629

Now, put these values in the formula
$P_{ t }=P_{ A }^{ 0 }X_{ A }+P_{ B }^{ 0 }X_{ B }$
$P_{ t }$ = 100x0.371 + 44x0.629
$P_{ t }$ = 37.1 + 27.675
$P_{ t }$ ​= 64.775 torr

Therefore, we can conclude that the correct answer to this question is option C.

Note: We should know that the equilibrium vapour pressure or vapour pressure is an indication of a liquid's evaporation rate.