Calculating feed rates and recycle stream flow rate

[kari82]

The demand for a particular hydrogenated compound, S, is 5.00k mol/h. This chemical is synthesized in the gas-phase reaction A + H2 = S.

The reaction equilibrium constant at the reactor operating temperature is

kp=ps/(pa x ph2)=0.1 atm^-1

the fresh feed to the process is a mixture of A and hydrogen that is mixed with a recycle stream consisting of the same two species. The resulting mixture, which contains 3 k mol A/k mol H2, is fed to the reactor, which operates at an absolute pressure of 10.0 atm. The reaction products are in equilibrium. The effluent from the reactor is sent to a separation unit that recovers all of the S in essentially pure form. The A and hydrogen leaving the separation unit form the recycle that is mixed with fresh feed to the process. Calculate the feed rates of hydrogen and A to the process in k mol/h and the recycle stream flow rate in SCMH (standard cubic meters per hour).

I have been working on this problem for a while now, and I'm not able to figure out how to solve it. My first question will be, can I assume that kp=0.1=ys x (10 atm)/ 0.25(10atm) x 0.75(10atm) because the products and reactants are at equilibrium? Then, what the 5 kmol/h means? is it the product stream? Should I assume a feed stream of (for example) 100 kmol/h...

Thank you very much!

 

[Valkarie]

Yes, you can assume that kp=0.1=ys x (10 atm)/ 0.25(10atm) x 0.75(10atm), since the products and reactants are in equilibrium. The 5 kmol/h is the rate of production of S, so it is the product stream. You could assume any feed stream, but it should be consistent with the given information (i.e. the feed must contain 3 kmol A/k mol H2). Once you have assumed a feed rate, you can calculate the feed rates of hydrogen and A to the process in kmol/h, and then convert them to SCMH using the molar volume of the respective gases.