Question

2. A mixture containing benzene and toluene with 40% benzene and 60% toluene is to be separated in a fractionating column to give a product containing 96% benzene, bottom product containing 95% toluene. Feed is mixture of two third vapor and one third liquid. Find out the number of theoretical stages required if the reflux ratio of 15 times the minimum is used. Relative volatility is 2.5(McCabe Thiele Method), explain step by step with lengthy process?

Answer 1

From the provided data, we can deduce the following

We can assume $x_w = 0.5$ by mole

The minimum reflux ratio, $q= \frac{1}{3}$

The slope of feed time $\frac{-q}{1-q}=-0.5$

y-intercept of feed line $\frac{x}{1-q}=\frac{0.4}{1-\frac{1}{3}}=0.6$

The equilibrium curve

$\frac{R_{min}}{R_{min}+1}=\frac{x_D-y'}{x_D-x'}=\frac{0.96-0.47}{0.96-0.26}=0.9\\ R_{min}=2.333$

Actual reflux ratio $=1.5 R_{min}= 1.5*2.333=3.5$

The actual slope

$\frac{R}{R+1}=\frac{3.5}{1+3.5}=0.777\\$

y intercept

$\frac{x_D}{R+1}=\frac{3.5}{1+3.5}=0.2133$