$P_2-{14}_A$ What is wrong with this solution? An adiabatic liquid phase exothermic

reaction is to be carried out in a $25d{m}^{3}CSTR.$ The entering molar flow rate

of A times the reciprocal of the rate of reaction is shown below in Figure

$P2-{14}_A(a)$ as a function of conversion.

What is the conversion exiting the CSTR$?$

$($a$)$

$($b$)$

Figure P$2-14$ Levenspiel plots

Solution

We are given $\frac{F_{A0}}{-r_A}$ vs$.x$ and that the volume is $25d{m}^3.$ We need to find the

$x$ such that area of the CSTR rectangle $(x*\frac{F_{A0}}{-r_A})=25d{m}^3.$ This is the trial

and error procedure.

Let's calculate the area in the rectangle with the conversion at the min$-$

imum and see if it matches the volume of $25d{m}^3$ given in the problem state$-$

ment at the minimum.

For $x=0\mathrm{.}5$ the area of the shaded rectangle $[$Figure $P2-{14}_A(b)]$ is

$V=(\frac{F_{Al}}{-r_A})x=(50d{m}^3)(0\mathrm{.}5)=V=25d{m}^3$

It matches!! Therefore $x=0\mathrm{.}5,$