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 separated 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.

Please draw the stream and lable everything

Explanation / Answer

Let the feed flow rate be 100 kg/hr, It contains 25 kg/hr methanol, 42.5 kg/hr ethanol and 100-(25+42.5)=32.5 kg/hr water.

Let D1. D2 are the products with drawn.

Writing methanol balance, 25= D1*0.398+D2*0.197 , 127= D1*2.02+D2 (1)

Ethanol balance gives 42.5 = D1*0.315+D2*0.412, 103.2 = D1* 0.76+D2 (2)

Eq.1-Eq.2 gives 23.8= D1*(2.02-0.76), D1= 18.8, D2= 100-18.8= 82.2 kg/hr

Water balance should give 32.5 kg/hr, % of water in D1= 100-(39.8+31.5)= 28.7%, water in D1= 18.8*0.287= 5.4, water % in D2= 100-(19.7+41.2)= 39.1, water in D2= 82.2*0.391= 32.4 kg/hr

Total water= 32.4+5.4= 37.8 kg/hr . This is not the water that is sent to the process. Hence the analysis is incorrect. Since there are three variables ( out of which two compositions are specified, third one can be calculated. Hence analysis of ethanol in both the streams, methanol composition in one stream is adequate).

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