$4\mathrm{.}3.$ A liquid$-$phase chemical reaction $AB$ takes place in a well$-$stirred tank. The concentration of $A$ in the feed is $C_{A0}(\frac{\text{m}\text{o}\text{l}}{m^3}),$ and that in the tank and outlet stream is $C_A(mo\frac{l}{m^3}).$ Neither concentration varies with time. The volume of the tank contents is $V(m^3)$ and the volumetric flow rate of the inlet and outlet streams is $V^{}(\frac{m^3}{s}).$ The reaction rate $($the rate at which $A$ is consumed by reaction in the tank$)$ is given by the expression

$r(molA$ consume$\frac{d}{s})=kV{C}_A$

where $k$ is a constant.

$($a$)$ Is this process continuous, batch, or semibatch? Is it transient or steady$-$state?

$($b$)$ What would you expect the reactant concentration $C_A$ to equal if $k=0($no reaction$)?$ What should it approach if $k($infinitely rapid reaction$)?$

$($c$)$ Write a differential balance on A$,$ stating which terms in the general balance equation $($accumulation $=$ input $+$ generation $-$ output $-$ consumption