Cyclohexane can be produced by reacting benzene with hydrogen: ??6??6 + 3 ??2 ? ??6??12 A...

Cyclohexane can be produced by reacting benzene with hydrogen: ??6??6 + 3 ??2 ? ??6??12 A fresh feed of benzene combined with 20% excess hydrogen is blended with a recycle stream and fed to a reactor. The recycle stream is 22.74% benzene and the rest hydrogen, on a molar basis. The reactor achieves a single-pass conversion of benzene of 20%. The reactor effluent is sent to a separator, where one stream is the recycle and the other is the product. It is desired to attain a 95% overall conversion of benzene. (a) To make that happen, what must be the ratio of the flow rate of the recycle stream to the fresh feed stream, in units of moles recycle per moles fresh feed? (b) What is the molar flow rate of the product stream? What are the mole fractions of chemicals in this stream?

Solutions

Expert Solution

Single pass conversion = 0.2

Overall conversion required = 0.95

Let F be the feed, R be the recycle and E be the stream entering the reactor. Then the product balance can be given as,

Benzene in feed = Benzene/Total feed = Fb/(4.2*Fb + Fb) = 0.1923

Overall conversion = 95% , so product formed = 0.95*0.1923F

Benzene entering the reactor =Benzene from feed +Benzene from recycle = 0.1923F + 0.2274R

Single pass conversion = 0.20

Product formed in single pass = 0.2* 0.1923F + 0.2274R

Equating the products formed equations,

0.95*0.1923F = 0.2* (0.1923F) + 0.2274R

R/F = 3.17 moles recycle/mole feed

b) Molar flow rate of product stream :

Basis : 5.2 mol/hr of feed ; 1 mol/hr of benzene and 4.2 mol/hr of H₂

Benzene in feed = 1 mol/fr

Given 95% of Benzene conversion is attained.

So cyclohexane formed = 0.95*1 = 0.95 mol/hr

Benzene leaving with the product = Benzene in feed - Benzene consumed in the reaction = 1 - 0.95 = 0.05 mol/hr (Overall balance)

H₂ leaving with the product = H₂ in feed - H₂ consumed in the reaction = 4.2 - (3*0.95) = 1.35 mol/hr ( Overall balance)

For a feed flow rate of 5.2 mol/hr , molar flow rate of product stream = 0.95 + 0.05 + 1.35= 2.35 mol/hr

c) Mole fraction of cyclohexane = Molar rate of cycloheaxane/Molar rate of product stream= 0.95/2.35 = 0.404

Mole fraction of benzene = Molar rate of benzene/Molar rate of product stream= 0.05/2.35 = 0.0212

Mole fraction of H₂ = Molar rate of H₂ /Molar rate of product stream= 1.35/2.35 = 0.574

Amanda K answered 1 year ago

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