Question

THERMODYNAMICS

Create a Pxy (T = 343 K) diagram for a binary mixture of cyclohexane and n-hexane. Assume that the liquid forms an ideal solution. Show iterations, if applicable.

Answer 1

Antoine constants : Cyclohexane , log psat(mm Hg)= 6.85146-1206.46/(t+223.136), t in deg.c

n- hexane log psat(mm Hg)= 7.01051- 1246.33/(t+232.988), t in deg.c

at 343K, for cyclohexane , log psat(mm Hg)= 6.85146- 1206.46/(343-273+223.136) , Psat= 544.2 mm Hg

at 343 K= 343-373= 70 deg.c, for n-hexane : log psat(mm Hg)= 7.01051- 1246.33/(70+232.988), Psat= 785.252 mm Hg

hence n- hexane is more volatile than cyclohexane. Hence its vapor pressure is designated as P1sat.   vapor pressure of cyclohexane is designated as P2sat.

since Raoult's law is obeyed, y1P= x1P1sat and y2P= x2P2sat.

where y1, y2 are mole fractions of n-hexane and cyclohexane in the vapor phase, P is total pressure, x1, x2 are mole fraction of n-hexane and cyclohexane in the liquid phase.

addition of the above equations gives P= x1P1sat+ x2P2sat, x1= (1-x2)

assume some x1 ( lies between 0 and 1). Calculate P for each x from above equation. Once P is calculated, y1= x1P1sat/P can be calculated. The calculations are tabulated below.

the P,x, y data generated is plotted and shown below.