In a process for the catalytic hydration of ethylene (C_2H_4) to ethyl alcohol (
ID: 523154 • Letter: I
Question
In a process for the catalytic hydration of ethylene (C_2H_4) to ethyl alcohol (C_2H_5OH), only a fraction of the ethylene is converted. The reaction stoichiometry is given by C_2H_4 + H_2O rightarrow C_2 H_5OH The conversion of ethylene in the converter is 4.5% per pass. The condenser converts all of the ethanol to a liquid as well as some of the water. The gas phase leaving the condenser contains both water and ethylene. The mole fraction of water vapor in the recycle stream is 0.065. The molar ratio of water to ethylene in the feed to the converter (the stream leaving the mixer) is 0.55. Based on 100 moles in the feed stream to the converter (not the fresh feed), determine the number of moles of the remaining streams in the system.Explanation / Answer
Feed to the converter= 100 moles , moles of water/moles of ethylene = 0.55, moles of water= 0.55* moles of ethylene , moles of water + moles of ethylene = 100, 1.55*moles of ethylene =100
Moles of ethyleen =100/1.55 =64.51, moles of water = 100-64.51= 35.49
Moles of ethylene converted =4.5%per pass
Moles of ethylene converted= 64.51*4.5/100=2.9 moles, moles of water reacted also =2.9 moles
Moles of ethyl alcohol formed= 2.9 moles. let x= moles of water got condensed. Then moles of water remaining and returned with ethylene gas= 35.49-2.9-x, moles of ethylene recycle= 64.51-2.9= 61.61 moles
Total moles recycled = 61.61+35.49-x=97.1-x
Mole fraction of water= (35.49-2.9-x)/ (97.1-x)=0.065
(32.59-x) =0.065*(97.1-x), 32.59-x = 0.065*97.1-0.065x=6.31-0.065x
Hence x*(1-0.065)= 32.59-6.31, x= 28.11, mole of water condensed= 28.11 mole
Produdct contains 28.11 moles water and 2.9 moles of C2H5OH.
Moles of water remaining = 35.49-2.9-28.11= 4.48 moles
4.48 moles of water along with 61.61 moles of ethylene gas is returned as recycle.
Moles of water in fresh feed= moles of water used for reaction+ moles of water condensed = 2.9+28.11= 31.01 moles
Moles of ethylene gas in fresh feed =2.9.
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