Tutorial 1 – Part II: Vapour liquid Equilibrium QUESTION 1 (Using the DePriester Chart - Figure 1 below) Consider the problem of estimating the bubble-point temperature of a liquid at 500 kPa having the following composition: • n-butane (B) = 30 % (on a mole basis) • n-pentane (P) = 30 % • n-hexane (H) = 40% QUESTION 2 Experimental values for the vapour pressure p* (in kPa) of n-hexane (H) and n-octane (O) are given below as a function of temperature.

T (oC) p*(H) p*(O) 68.7 101 16 79.4 137 23 93.3 197 37 107.2 284 58 121.1 400 87 125.7 456 101

(a) Assuming that Raoult’s and Dalton’s laws apply, develop expressions that allow

the vapour (ie yH and yO) and liquid phase compositions (ie xH and xO) to be calculated directly from the vapour pressure data.

(b) Use these expressions to construct x-y and T-x-y plots for this system at

atmospheric pressure. (c) When a liquid containing 30 mole % H is heated at atmospheric pressure, what is

the composition of the initial vapour formed ? (d) What is the temperature when it first begins to boil? (e) What is the composition of the saturated vapour in equilibrium with the saturated

liquid at this point? (f) Calculate α as a function of temperature. Would it be reasonable to use a

constant value for the relative volatility of this system ?

(g) Calculate the K values for n-hexane and n-octane as functions of temperature Note: This assumes that negligible amounts of vapour are formed; otherwise the composition of the liquid will change. QUESTION 3 Assuming Raoult’s Law to be valid for the system of acetonitrile(1)/nitromethane(2), Prepare a T-x-y diagram for a pressure of 101.33 kPa Vapour pressures of the pure species are given by the following Antoine equation below. (Pisat in kPa and T in oC)

ln Pisat =14.2724− 2945.47

T + 224 acetonitrile

ln Pisat =14.2043− 2972.64

T + 209 nitromethane

QUESTION 4

Derive yx

x=

+ −αα1 1( )

and then analyse the x-y equilibrium curves using of this

relation for:

(a) the limits (b) under increasing values of α

Figure 1: K-values for light hydrocarbons1.

1 Taken from Equilibrium Stage Separation Operations in Chemical Engineering, E.J. Henley and J.D. Seader, John Wiley and Sons, 1981