Question

Two compounds A and B in when mixed form nearly ideal solutions. At room temperature, $P_A^0=40mmHg$ and $P_B^0=120mmHg$.
A liquid mixture is composed of $1mol$ of A and $3mol$ of B.
When the last trace of liquid disappears, choose the correct option(s) regarding composition of A and B in liquid phase :
Here,
$x_A=\text{Composition of A in liquid phase when fthe last trace of liquid disappears}$
$x_B=\text{Composition of B in liquid phase when the last trace of liquid disappears}$

• A. $x_A=0.75$
• B. $x_A=0.5$
• C. $x_B=0.25$
• D. $x_B=0.5$

Answer 1

Answer: (B), (D)

$x_B=0.5$

The pressure at which last trace of liquid disappears is the dew point pressure.
Initially
$x_A^{\prime }=\frac{1}{1+3}=0.25x_B^{\prime }=1-0.25=0.75$
But when all the liquid converts to vapour then vapour phase composition is :
$y_A=0.25y_B=0.75$

$\frac{1}{P_T}=\frac{y_A}{p_A^{\circ }}+\frac{y_B}{p_B^{\circ }}$
Putting the values :
$\frac{1}{P}=\frac{0.25}{40}+\frac{0.75}{120}\frac{1}{P}=\frac{1}{80}P=80mmHg$
So, the dew point pressure i.e. the pressure at which all the liquid disappears is $80mmHg$
Now the composition in liquid phase $(x_A,x_B)$ at dew point is to be found out.
This can be calculated by :
$x_A=\frac{y_A\times P}{p_A^{\circ }}=\frac{0.25\times 80}{40}=0.5$

$x_B=1-x_A=1-0.5=0.5$
So, the composition of both A and B when last trace of liquid disappears (i.e. at dew point ) is 0.5