A mixture containing $45\mathrm{.}0\%$ benzene $($B$)$ and $55\%$ toluene $(T)$ by mass is fed at a rate of $2000k\frac{g}{h}$ into a distillation column. An overhead stream of $95wt\%B$ is produced and $8\%$ of the benzene fed to the column leaves in the bottom stream.

$1\mathrm{.}1\mathrm{.}1.$ Draw and completely label the process.$(5$ marks$)$

$1\mathrm{.}1\mathrm{.}2.$ Determine the type of process.$(2$ marks$)$

$1\mathrm{.}1\mathrm{.}3.$ Calculate the degree of freedom.$(3$ marks$))$

$1\mathrm{.}1\mathrm{.}4.$ Determine the overhead flow rate and the mass flow rates of benzene and toluene in the bottom stream.$(10$ marks$)$

$1\mathrm{.}2.$Study the process flowsheet given below and calculate the following:

$1\mathrm{.}2\mathrm{.}1.$ Perform the degree of freedom $($DOF$)$ analysis and de duce if the material balance can be solved.$(5$ marks$)$

$1\mathrm{.}2\mathrm{.}2.$ Solve the material balance if $m_3^{}$ is half of the flow rate of $m_1^{}$ and $90\%$ of $C$ in $m_1^{}$ exists in marks$)$