Problem $1$

Consider the isomerization transformation of cis$-2-$butene to trans$-2-$butene.

The reaction can be symbolically written as

$AB$

The first order reaction $(-r_A=k{C}_A)$ is carried out in a plug flow reactor. The volumetric flow rate,

$v$ is constant $(v=v_0).$ Also note that $F_A=v_A.$

a$)$ Start with the design equation for plug flow reactor, $\frac{d{F}_A}{dV}=r_A$

Show that $V=(\frac{v_0}{k})ln(\frac{C_{A0}}{C_A})$

b$)$ Determine the reactor volume necessary to reduce the exiting concentration of $A$ to $10\%$ of entering

concentration, when the volumetric flow rate is $10d\frac{m^3}{m}in$ and $k=0\mathrm{.}23mi{n}^{-1}.$

c$)$ Calculate the volume of a CSTR for the conditions of part $($b$)$ above.

d$)$ Calculate the time necessary to reduce the number of moles of $A$ to $1\%$ of its initial value in a

constant volume batch reactor for the data and reaction of above problem.