Sunflower oil contains 0.070 mol palmitic acid (C16H32O2)/mol, 0.060 mol stearic

Question

Sunflower oil contains 0.070 mol palmitic acid (C16H32O2)/mol, 0.060 mol stearic acid (C18H36O2)/mol, 0.29 mol oleic acid (C18H34O2)/mol, and 0.58 mol linoleic acid (C18H32O2)/mol. To create margarine from sunflower oil, the liquid oleic and linoleic acids are hydrogenated in the presence of a metal catalyst to form solid stearic acid.

C18H34O2+H2 -> C18H36O2

C18H32O2+3H2 -> C18H36O2

At a margarine production facility, a stream of 380.0 mol sunflower oil/hr is fed into a reactor. The fresh hydrogen source available is a mixture containing 0.95 mol H2/mol and 0.050 mol N2/mol. (N2 is inert in this process.) To insure complete hydrogenation, the hydrogen gas mixture is introduced into the reactor in 60.0% excess. All reaction products leave the reactor and proceed to a separator where palmitic and stearic acids are separated from the hydrogen gas mixture. The hydrogen gas mixture is recycled to the fresh feed stream, and 150.0 mol gas/hr of this recycle stream is purged to prevent the buildup of nitrogen gas.

1.

Explanation / Answer

consider 1 hour of operation
mol of sunflower oil introduced in the reactor = 455

as per the composition,

mol of palmitic acid = 0.07*455 = 31.85
mol of stearic acid = 0.06*455 = 27.3
mol of oleic acid = 0.29*455 = 131.95
mol of linoleic acid = 0.58*455 = 263.9

now, 1 mol oleic acid needs 1 mol hydrogen for complete hydrogenation
and
1 mol linoeic acid needs 3 mol hydrogen

so theoretical amount of hydrogen needed = (1*131.95)+(3*263.9) = 923.65 mol

but hydrogen is introduced in 65% excess

so mol of H2 actually fed = 1.65*923.65 = 1524 mol

so molar flow rate of H2 in the reactor = 1524 mol/hr

assuming complete hydrogenation, out of 1524 mol H2 fed per hour, 923.65 mol H2 reacts and is consumed

so,

mol H2 left = 1524-923.65 = 600.35

and as N2 is inert, it passes out unreacted

mol N2 in gaseous stream leaving the reactor per hour = 80.2

so the gaseous stream has 600.35 mol H2 and 80.2 mol N2

as the gaseous stream is purged from the gases leaving the reactor, the composition of purge stream is same as composition of gaseous stream leving the separator.

hence the composition of purge stram in terms of mole fractions is given as

mol fraction H2 = 600.35/(600.35+80.2) = 0.8822 mol H2/mol gas

mol fraction N2 = 80.2/(600.35+80.2) = 0.1178 mol N2/mol gas ....... (answer 2)

also a total of 600.35 mol H2 and 80.2 mol N2 leave from separator

so molar flow rate of gaseous stream leaving the separator = 600.35+80.2 = 680.55 mol/hr.........(answer 3)

now out of 680.55 mol of gases leaving the separator, 100 moles are purged and rest are recycled

so the molar flow rate of recycle line = 680.55-100 = 780.55 mol/hr ......(answer 4)

we have already seen that 1524 mol of H2 is to be fed to reactor

out of the 1524, (780.55*0.8822) = 688.6 mol H2 comes from recycle line

the rest 1524-688.6 = 835.4 moles come from fresh feed

hence as per composition of fresh feed, moles of N2 that come in with 835.4 mol H2 = (5/95)*835.4 = 43.97 mol

so,

molar flow rate of H2 in fresh feed = 835.4 mol/hr

molar flow rate of N2 in fresh feed = 43.97 mol/hr .... (answer 1)

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