Question

A liquid containing 55.0 wt% methanol (M), 5.00 wt% polyacrylate (P), and 40.0 wt% water (W) is distilled at steady-state into a top steam and a bottom stream. The total mass flow rates of the top and bottom streams are the same. The top stream has 85.0 wt% M and 0% P. a. Can you set a basis of calculation in this problem? Why or why not? b. Calculate the composition (mass fractions) in the bottom stream.

Answer 1

a) YES ( Basis : F=100kg/h)

b) composition mass fraction in the bottom stream

(Xm)B = 0.25

(Xp)B = 0.1

(Xw)B = 0.65

Step-by-step explanation:

a)

Can you set a basis of calculation in this problem? Why or why not?

Yes we can set a basis if calculation in this problem.

A good basis makes the calculation more easier. the problem are given in weight basis so we can choose basis of feed rate of 100kg/h

BASIS : 100kg/h

b)

given that;

mass flow rate of M in the feeds Mf = 0.55*F = 0.55*100 = 55kg/h

mass flow rate of p in the feeds Pf = 0.05*F = 0.05*100 = 5kg/h

mass flow rate of W in the feeds Pf = 0.40*F = 0.40*100 = 40kg/h

Now Balance

F = T + B

( but T=B)

so F = T + T = 2T

B = T = 50kg/h

TOP

mass flow rate of M in the top Mt = 0.85*T = 0.85*50 = 42.5 KG/H

mass flow rate of P in the top Pt = 0kg/h

mass flow rate of W in the top Wt = 0.15*T = 0.15*50 = 7.5kg/h

balance on M

Mf = Mt + Mb

Mb = Mf - Mt = 55kg/h - 42.5kg/h = 12.5kg/h

Balance on P

Pf = Pb + Pt

Pb = Pf - Pt = 5kg/h - 0kg/h = 5kg/h

Balance on W

Wf = Wt + Wb

Wb = Wf - Wt = 40kg/h - 7.5kg/h = 32.5kg/h

So bottom composition

mass fraction of M in Bottom XmB = Mb/B = (12.5kg/g) / (50kg/h) = 0.25

mass fraction of P in Bottom XpB = Pb/B = (5kg/g) / (50kg/h) = 0.1

mass fraction of W in Bottom XwB = Wb/B = (32.5kg/g) / (50kg/h) = 0.65