Species $B$ is to be formed by a reversible reaction from a raw material $A$ in a chemical reactor of volume $V$

equipped with a perfect stirrer. Unfortunately, $B$ undergoes an irreversible first$-$order decomposition to a

third species $C.$ All reactions may be considered to be first order. We use the notation

$k_{1B},k_{1C}$

$ABC$

$k_{1A}$

At time $t=0,$ a solution of $A$ at mass density ${}_{(A)0}$ that is free of species $B$ is introduced into the initially

empty reactor at a constant volume rate of flow $Q.$

Determine that during the filling period the mass of species $B$ in the reactor is the following function of

time

$M_B=\frac{{}_{(A)0}Q}{k_{1C}}[1+\frac{s_{-}}{(s_{+}-s_{-})}{e}^{s_{+}t}-\frac{s_{+}}{(s_{+}-s_{-})}{e}^{s_{-}t}]$

where

$2s_{+-}-=-(k_{1A}+k_{1B}+k_{1C})+-\sqrt[\phantom{2}]{(k_{1A}+k_{1B}+k_{1C}{)}^2-4k_{1B}{k}_{1C}}$