Question $1$

A gas stream containing acetone in air flows from a solvent recovery unit at a rate of $142\frac{L}{s}$ at $150C$ and $1\mathrm{.}3$atm. The stream flows into a condenser which liquefies most of the acetone, and the liquid and gas outlet streams are in equilibrium at $-18C$ and $5\mathrm{.}0$atm. Shaft work is delivered to the system at a rate of $25\mathrm{.}2kW$ to achieve the compression from $1\mathrm{.}3$atm to $5\mathrm{.}0$atm. To determine the condenser feed stream composition, a $3\mathrm{.}00-$liter sample of the gas is taken and cooled to a temperature at which essentially all the acetone in the sample is recovered as a liquid. The liquid is poured into an empty flask with a mass of $4\mathrm{.}017g.$ The flask containing the liquid acetone is weighed and found to have a mass of $4\mathrm{.}973g.$

s$-$iter sampie

Condense and weigh acetone

$($a$)$ Carry out a degree$-$of$-$freedom analysis to show that enough information is available to determine the compositions of all streams and the required heat transfer rate.

$($b$)$ Write out a complete set of equations for the molar flow rates of all streams $($mass and energy balances$),$ mole fractions of acetone in the feed and product gas streams, and the rate $(kW)$ at which heat must be removed in the condenser. Do not calculation.

$($c$)$ Solve the equations of part $($b$)$ by hand.