Answer:
Answer:The activities of A and B are and 0.44 and 0.76 the activity coefficients are 2 and 0.97 respectively.
Explanation:
Given that at equilibrium
Xa = 0.220
Ya = 0.314
Vapour pressure of a =Pa* = 73kPa
Vapour pressure of b = Pb*= 92.1kPa
Total pressure Pt = 1atm= 101.325kPa
From Partial Pressure Law
Pt = Pa+Pb. ..... Eqn(1)
Where Pa and Pb are partial pressures of a and b.
Pa= Ya * Pt
=0.314 * 101.328
Pa = 31.82kPa
From Eqn(1)
Pb = Pt -Pa
= 101.325- 31.82
=69.51kPa
From Raoult's Law
Aa = Pa/Pa*
Where Aa is the activity of component a
= 31.82/73
Aa=0.44
Also Ab is the activity of component b
Ab=69.51/92.1
=0.76
The activity coefficients of each component is given by :
Yi = Ai/Xi
For component a
Ya = Aa/Xa
= 0.44/0.220
=2
For component b
Yb = Ab/Xb
Xb is unknown.
But at equilibrium Xa+Xb =1
Therefore, Xb= 1-0.22 =0.78
Yb= 0.755/0.78
= 0.97
