Question

By measuring the equilibrium between liquid and vapor phases of an acetone (A) / methanol (M) solution at 57.2oC at 1.00 atm, it was found that xA = 0.400 when yA = 0.516. Calculate the activities and activity coefficient of both components in this solution on the Raoult’s law basis. The vapor pressures of the pure components at this temperature are: pA* = 105 kPa and pM* = 73.5 kPa. (xA ia the mole fraction in the liquid and yA is the mole fraction in the vapor)

Answer 1

From Raoult's law, γ_i = p_i /(x_i p_i^*)

where, γ_i = activity coefficient

p_i = y_i p_total = partial pressure [p_total = total pressure]

x_i = mole fraction in the liquid

p_i^* = The vapor pressures of the pure component

For acetone:

γ_i = p_i /(x_i p_i^*) = y_i p_total /(x_i p_i^*)

= 0.516 × 1 atm / (0.4 × 105 kPa)

= (0.516 × 101.325 kPa) / (0.4 ×105 kPa)

= 1.24

Activity, a = γ_i × x_i = 1.24 ×0.4 = 0.498

For methanol:

γ_k = p_k /(x_k p_k^*) = y_k p_total /(x_k p_k^*)

= [(1-0.516) × 101.325 kPa] / [(1- 0.4) × 73.5 kPa)]

= 1.112

a = γ_k × x_k = 1.112 × (1-0.4) = 0.667