This is chemical engineering question I got everything right except for the last

Question

This is chemical engineering question

I got everything right except for the last quesion.

What is the ratio of the recylcle flow to purge flow? I can't find n7 and n2. Which the andswer is n7/n6

n6 is 11.08mo/hr.

Methanol is being produced according to the reaction Map CO+2H2 CH3OH A synthesis gas stream consisting of 67.10% H2, 32.50% CO, and 0.400% CH4 (by mole) is fed into the process described below at a rate of 100 mol/hour. The effluent stream from the reactor is fed into a separator where the methanol is completely removed, and the unconverted reactants are recycled to the reactor. To avoid the buildup of methane, a portion of the recycled stream is purged. At present operating conditions, the CO conversion over the entire process is 91.20%, and the methane mole fraction at the reactor inlet (Stream 2) is 2.870%. 4 Reactor Separator methanol 7 6 purge What is the production rate of methanol? Number 29.64 mol CH,OH/ hr

Explanation / Answer

n1 = 100

(xCH4)1 = 0.004

(xCH4)6 = 0.036

(xCH4)2 = 0.0287

n2 = n1 + n7    ................(1)

also,

n1(xCH4)1 + n7(xCH4)6 = n2(xCH4)2

100*0.004 + n7*0.036 = n2*0.0287

Substituting n2 from equation 1

100*0.004 + n7*0.036 = (n1 + n7)*0.0287

0.4 + n7*0.036 = (100 + n7)*0.0287

0.4 + n7*0.036 = 2.87 + n7*0.0287

n7*0.036 - n7*0.0287 = 2.87 - 0.40

0.0073*n7 = 2.47

n7 = 338.35 mol/hr

Ratio of the recylcle flow to purge flow:

n7 / n6 = 338.35 / 11.08

= 30.53

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