Consider the process flowsheet shown in Figure Q$\mathrm{.}1.$ The reactor receives stream $1,$ containing the raw materials, A and $B,$ that react to produce the products, $C$ and $D,$ as per the reaction: $A+BC+D.$ The output $($stream $2)$ from the reactor is fed to a separator which produces a product stream $($stream $3)$ and a recycle stream $($stream $4).$ Stream $4$ is fed back to the reactor. The specifications for the separator are: $($i$)$ recycle $65\%$ of $D$ and $85\%$ of $C,($ii$)$ the flow of B is equally split between streams $3$ and $4,$ and $($iii$)10\%$ of A goes to stream $3.$

a$)$ Write the mass balance equations for the process flowsheet and carry out a degree of freedom analysis.

$[10]$

b$)$ If degree of freedom is not zero, specify some of the variables so that degree of freedom becomes zero. Re$-$write the mass balance equations in the $Ax=b$ format, where $A$ is a constant and square matrix, $b$ is constant vector and $x$ is vector of unknown variables. Do not solve the mass balance equations.

$15$