A gas stream containing acetone in air flows from a solvent recovery unit at a rate of 142 L/s at 150C and 1.3 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 5.0 atm. Shaft work is delivered to the system at a rate of 25.2 kW to achieve the compression from 1.3 atm to 5.0 atm. To determine the condenser feed stream composition, a 3.00-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 4.017 g. The flask containing the liquid acetone is weighed and found to have a mass of 4.973 g. Q(~W) Ws =-25.2 kW 1 j Gas at -18C, 5 atm 142 Us, 150C, 1.3 atm r--'-----l..~a~ce:.::to~n~e~(v~).~a~ir--- ... acetone(v), air ---r-----~CONDENSER I I t 3-liter sample Condense and weigh acetone Acetone(l) at 18C, 5 atm Encyclopedia Equipment evaoorator (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, the 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 no calculations. (c) Solve the equations of part (b) by hand. *(d) Solve the equations of part (b) using an equation-solving program

Problem 8.49A gas stream containing acetone in air flows from a solvent recovery unit at a rate of 142 L/s at150°C and 1.3 atm. The stream flows into a condenser which liquefies most of the acetone, andthe liquid and gas outlet streams are in equilibrium at -18°C and 5.0 atm. Shaft work is deliveredto the system at a rate of 25.2 kW to achieve the compression from 1.3 atm to 5.0 atm. Todetermine the condenser feed stream composition, a 3.00-liter sample of the gas is taken andcooled to a temperature at which essentially all the acetone in the sample is recovered as aliquid. The liquid is poured into an empty flask with a mass of 4.017 g. The flask containing theliquid acetone is weighed and found to have a mass of 4.973 g.(a) Carry out a degree-of-freedom analysis to show that enough information is available todetermine 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, the molefractions of acetone in the feed and product gas streams, and the rate (kW) at which heat mustbe removed in the condenser. Do no calculations.(c) Solve the equations of part (b) by hand.(d) Solve the equations of part (b) using an equation-solving program Step-by-step solution Step 1 of 11 ^Draw a flowchart for the system.(a)Perform a degree of freedom analysis n the system.Recall the equation for a degree of freedom analysis. n = n -n df unknownsindependent equationsThere are 6 unknowns shown on the flowchart: and .\nTwo material balances: an acetone balance and an air balance, and one energy balance can bewritten. There are three additional specifications: an ideal gas law relationship for the feed gas,saturation conditions at the outlet and a sample taken of the feed gas.Thus, 6 independent equations can be written.Perform a degree of freedom analysis. n = 6 - 6 df = 0There are . The system is fully specified and the problem can be solved.