Azeotropes are mixtures of two or more liquid components that cannot be separated by regular distillation; a well$-$known azeotrope exists between ethanol and water. One way to break an azeotrope is to add an additional component to mixture and perform additional processing to achieve a higher purity product. An example flowchart of this process using ethanol, water, and acetone is shown below: The following information is known about each stream:

Stream $1$: Pure acetone fed at a rate of $20\mathrm{.}5$ L$/$min$.$

Stream $2$: A mixture of acetone, ethanol, and water. The component flowrate of water is $679$ mol water$/$min Stream $3$: No information given.

Stream $4$: Total flowrate of $826$ mol$/$min with $60$ mass$\%$ acetone and $40$ mass$\%$ethanol. It is known that $85\%$ of the ethanol fed to the system exits in this stream.

Stream $5$: A mixture of acetone, ethanol, and water. The stream is $70$ mole$\%$water. a$)$ Perform a degree of freedom analysis for the mixer, the distillation column, and the overall system. Specify an order in which the problem could be solved to

determine all unknowns. $($b$)$ Calculate the rate at which ethanol is fed to the mixer $($mol ethanol$/$min$)($c$)$ Calculate the total molar flow rates in stream $1$ and stream $5($mol$/$min$).($d$)$ Calculate the composition of acetone and ethanol in stream $5($mol fractions$).($e$)$Calculate the total flowrate of the stream entering the distillation column

$($mol$/$min$).$