Calculating Gas Stream Flow Rate from Condenser

[Mangoes]

Homework Statement

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 0.05. Liquid hexane condensate is recovered at a rate of 1.50 L/min.

What is the flow rate of the gas stream leaving the condenser in mol/min?

The Attempt at a Solution

I looked up the specific gravity for hexane in the textbook this problem is assigned and found it to have a value of 0.659 at 20 degrees Celsius. Since hexane has a molecular weight of 86 g/mol,

1.5L hexane, by the specific gravity, is equal to 0.99 kg of hexane. By the molecular weight, this came out to be 11.47 moles of liquid hexane leaving the condenser.

I don't know where I'd go next with this though. Using conservation of mass, if I make up some initial amount of moles of hexane input into the condenser, I can subtract the liquid hexane output. The remaining would be the gaseous hexane output and then I'd use the mole fraction conversion to find the moles of gas, but the concentration of the output would be dependent on the initial input since there's a fixed liquid output only. A 100 mol input of hexane gives a different flow rate than a 1000 mol input.

I've been stumped on this question for a while now and I don't see where else I can go with this. Would anyone please guide me in the right direction?

 

[Chestermiller]

You are very close to having this solved, and your methodology looks pretty good. Assume a basis of 100 moles coming in. Then 82 of these moles are N2, and 18 moles are hexane. The number of moles of nitrogen in the gas doesn't change. So the number of moles of nitrogen leaving in the gas is 82. The rest of the gas is hexane. If the mole fraction of hexane in the exit is 0.05, x/(82+x)=0.05, where x is the number of moles of hexane in the exit gas. How many moles does that leave of liquid hexane exiting the condenser per 100 moles of gas entering? So the ratio of moles liquid hexane exiting per mole of gas entering is? If you know the actual mass flow rate of liquid hexane exiting the condenser, you can use this ratio to calculate the molar flow rate of gas to the condenser.

Chet

 

[Mangoes]

Okay, so per 100 mol of input, there's about 4.3 mol of gaseous hexane output by the definition of molar fraction.

Since there's an input of 18 mol of hexane, the remaining output (liquid) must be 13.7 mol. So 13.7 liquid mol of hexane per 100 moles of input, or 0.137 moles of liquid hexane per mol of input.

Since there are 11.47 mol/min of liquid hexane leaving, and there's a mol of input for 0.137 mol of liquid hexane, that's 83 mol of input.

If input = output,

83 = 11.47 + y, y = 72.2 mol of gas leaving the container per minute.

Wasn't expecting so much trouble with this problem. Thanks for the help! I hadn't thought about using the mole fraction in that way and it was throwing me off.