Question

A gas stream contains 18.0 mole% hexane and the remainder nitrogen. The stream flows to a condenser, where its temperature is reduced and some of the hexane is liquefied. The hexane mole fraction in the gas stream leaving the condenser is 0.0500. Liquid hexane condensate is recovered at a rate of 1.50 L/min. (a) What is the flow rate of the gas stream leaving the condenser in mol/min? (Hint : First calculate the molar flow rate of the condensate and note that the rates at which C6H14 and N2 enter the unit must equal the total rates at which they leave in the two exit streams.) (b) What percentage of the hexane entering the condenser is recovered as a liquid?

Answer 1

(a) The first thing to do is to put all of the information given on a common basis.Right now the compositions are in mole% but the flow rate of the hexanecondensate is a volumetric flow rate.

The easiest thing is to convert the hexanecondensate flow rate to a molar flow rate. From Appendix B.1 at the back of thetext we can find the density and molecular weight of hexane. Then

g 1000 cm3 1 mol nhex.cond-1.50-0.659-ー mol min min

Adding values for the unknowns into the process flow diagram and noting thatwhatever is not hexane must be nitrogen in the two gaseous streams we get

2 0.82 icH 0.18 уг.v2 0.95 Y2c6H1 0.05 Condenser mol min Уз.v2 0.0 3c6H14 1.00 A balance on all components gives mol min A balance on just the hexane gives з Уз.c6H14 mol min h0.18)2(0.05)11.5(1.00) Note that there are only two unknowns in this set of two equations. So substitute the first equation into the second equation to get

mot i2 + 1 1.5 min) (0.18)- mol #2(0.05) + 1 1.5 min( 1.00) Solve this for ni to get n 72.4the flow rate in moUmin of the gas stream leaving the condenser (b) From the balance on all of the components we can get the flow rate of the stream entering the condenser as mol mol min mol min mol min min Thus the amount of hexane entering the condenser is ňLC6H14-k6H14n1 # 0.18 (83.8 min)-15.1 min mol mol

The amount of hexane leaving the condenser as a liquid as determined to be 11.5 molmin. Thus the percentage condensed is mol -11.5 min 100% 76.0% in % condensed m 15.1 min