Question

Rayleigh distillation

An aqueous solution of acetic acid is to be enriched by simple (differential) distillation.

The flask is initially charged with 0.025 kmol of solution of composition 0.600 mol

fraction water.

a)

Distillation is continued until the composition of the liquid in the flask has fallen

to 0.300 mol fraction water. Assuming that the vapour is completely condensed

and collected in a cooled receiver, calculate the quantity and composition of the

distillate.

b)

Repeat the calculation for the case in which distillation is stopped when the

composition of the liquid in the still has reached 0.500 mol fraction water.

c)

Explain why separation is so poor, particularly in case (a).

Equilibrium data

x y

0.300 0.420

0.350 0.483

0.400 0.537

0.450 0.592

0.500 0.638

0.550 0.685

0.600 0.728

Answer 1

Solution

a)

Calculate 1/(y-x)

As per Rayleigh Equation

where L1 is feed

L2 is liquid residue

x1 = composition of feed

x2 = composition of bottom

L₁=0.025 kmol

L₂=?

x₁=0.600

x₂=0.300

To solve the above equation plot x Vs 1/(y-x)

x	0.3	0.35	0.4	0.45	0.5	0.55	0.6
y	0.42	0.483	0.537	0.592	0.638	0.685	0.728
1/(y-x)	8.333	7.518	7.299	7.042	7.246	7.407	7.812

plot

area of above curve from x 0.3 to 0.6 =no. of boxes * x axis scal * y axis scale +7*(0.6-0.3)=12.2*0.05*0.2+7*0.3=2.222

so

=2.222

ln(0.025/L2)=2.222

L₂=2.709*10^-3 kmol

therefore

D=L1-L2 = 0.025-2.709*10^-3=0.02229 kmol

compsition of distillate

=(0.6*0.025-0.3*2.709*10^-3)/0.02229

=0.6364

b)

for this case all other conditions are same only x₂=0.5

area under curve between x = 0.5 to 0.6 =7*(0.6-0.5)+no. of boxes from fig * x axis scale *y axis scale =0.7+4.5*0.05*0.2 = 0.745 units

ln L1/L2 = 0.745

ln(0.025/L2) = 0.745

L2 =0.0118 kmol

so

D= L1-L2 = 0.025-0.0118=0.0132 kmol

=(0.025*0.6-0.0118*0.5)/0.0132

=0.6893

c)

to explain why separation is poor specially in case of (a)

from equilibrium data we can see that the liquid phase thats in equilibrium with vapour phase is of nearly same composition or we can say that equilibrium curve is narrow

you can see this by plotting X vs Y data & x=y line

& we know that separation becomes defficult at relative volatility becomes unity

from this same plot we can see that separation is quite easy in range x= 0.5 to 0.6 as curve is far from x=y line .