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. Prove your statement. How many streams do you ask the technician to analyze? Explain.

Explanation / Answer

In order to solve this problem we need to imagine a process where m1kg mixture containing 25.0 wt% methanol(xA1=0.25), 42.5 wt% ethanol(xB1=0.425) is fed. And the technician found 39.8 wt% methanol(xA2=0.398) in one stream and 19.7 wt% methanol(xA3=0.197), 41.2 wt% ethanol(xB3=0.412) in the other stream.

Let us assume 100kg of mixture is fed to the process & each stream has 50kg of mixture.

Methanol balance:

m1xA1=m2xA2+m3xA3

Ethanol Balance:

m1xB1=m2xB2+m3xB3

Here xB2 is unknown & if we solve for it then we find xB2=0.013

Now here the top product should be ethanol enriched & the bottom product should be methanol enriched. But here we can cleary see the top product is methanol enriched & bottom product is ethanol enriched. So the analysis done by the technician is incorrect.

The answer of part (b) depends upon the physical situation of the process.

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