A process is carried out in which a mixture containing 25.0 wt% methanol, 42.5%

Question

A process is carried out in which a mixture containing 25.0 wt% methanol, 42.5% ethanol, and the balance water is seperated into two fractions. A technician draws and analyzes samples of both product streams and reports that one stream contains 39.8% methanol and 31.5% ethanol and the other contains 19.7% methanol and 41.2% ethanol. You examine the reported figures and tell the technician that they must be wrong and that stream analyses should be carried out again.

(a) Prove your statement.

(b) How many streams do you ask the technician to analyze? Explain.

Explanation / Answer

let the Feed =100 gm . It contains 25 wt% methanol =25 gm methanol , 42.5% ethanol= 42.5 gm ethanol and balance =100-(25+42.5)= 32.5 gm water

Let D= methanol rich stream and W= methanol lean stream

F= D+W (1) 100 = D+W and W= 100-D

25 ( methanol )= D*0.398+W*0.197 =D*0.398+(100-D)*0.197

25= D*(0.398-0.197)+19.7

25-19,7= D*(0.201)

D =26.4 kg W= 100-26.4= 73.6 kg

Water in the feed = 32.5 gms

Percentage of water in D = 100-(39.8+31.5)= 28.7% and that in W = 100-(19.7+41.2)= 39,1%

Under steady state

Total water entering = 32.5 gms

water leaving from W+ water leaving from D =73.6*0.391+0.287*26.4=36.3 gms

This is not correct.

b) Four stream are enough. One is the composition of   methanol and ethanol in D which enables one to calculate water percentage and the compsition of methanol and ethanol in W which composition of ethanol and methanol need to be specified. The flow rate of mixture helps one to Calculate D and W.

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