Answer:
x1= 4.5 × 10^-3, y1= 0.9
Explanation:
A binary solution having two species is in equilibrium in a vapor phase comprising of species 1 and 2
Take the basis as the pressure of the 2 phase system is 1 bar. The assumption are as follows:
1. The vapor phase is ideal at pressure of 1 bar
2. Henry's law apply to dilute solution only.
3. Raoult's law apply to concentrated solution only.
Where,
Henry's constant for species 1 H= 200bar
Saturation vapor pressure of species 2, P2sat= 0.10bar
Temperature = 25°C= 298.15k
Apply Henry's law for species 1
y1P= H1x1...... equation 1
y1= mole fraction of species 1 in vapor phase.
P= Total pressure of the system
x1= mole fraction of species 1 in liquid phase.
Apply Raoult's law for species 2
y2P= P2satx2...... equation 2
From the 2 equations above
P=H1x1 + P2satx2
200bar= H1
0.10= P2sat
1 bar= P
Hence,
P=H1x1 + (1 - x1) P2sat
1bar= 200bar × x1 + (1 - x1) 0.10bar
x1= 4.5 × 10^-3
The mole fraction of species 1 in liquid phase is 4.5 × 10^-3
To get y, substitute x1=4.5 × 10^-3 in equation 1
y × 1 bar = 200bar × 4.5 × 10^-3
y1= 0.9
The mole fraction of species 1 in vapor phase is 0.9
