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While ethanol (CH, CH,OH) is produced naturally by fermentation, e.g. in beer- a

ID: 701410 • Letter: W

Question

While ethanol (CH, CH,OH) is produced naturally by fermentation, e.g. in beer- and wine-making, industrially it is synthesized by reacting ethylene (CH,CH,) with water vapor at elevated temperatures. A chemical engineer studying this reaction fills a 2.0 L flask at 7.2 °C with 1.6 atm of ethylene gas and 2.8 atm of water vapor. He then raises the temperature considerably, and when the mixture has come to equilibrium determines that it contains 0.60 atm of ethylene gas and 1.8 atm of water vapor. The engineer then adds another 0.93 atm of water, and allows the mixture to come to equilibrium again. Calculate the pressure of ethanol after equilibrium is reached the second time. Round your answer to 2 significant digits. | atm 0x10 *n?

Explanation / Answer

7.2 oC = 7.2 + 273 = 280.2 K

moles of ethylene = n = PV/RT = 1.6 atm x 2L / 0.08206 atm.L/mol.K x 280.2K = 0.13917 mol

moles of water vapour = 2.8 atm x 2L / 0.08206 atm.L/mol.K x 280.2K = 0.24355 mol

CH2=CH2 + H2O -------> CH3CH2OH

1.6 atm 2.8 atm 0 initially

X Y 0 initially at raised temperature T

X-a Y-a a at equilibrium

X-a = 0.6 atm

Y-a = 1.8 atm

ratio of pressures at higher temperature should be same = 1.6 atm / 2.8 atm = X/Y

Y = 1.75 X

putting in above equation

X-a = 0.6 atm --(1)

1.75X - a = 1.8 atm --------(2)

(2) - (1)

0.75 X = 1.2 atm

X = 1.6 atm

Y = 1.75 x 1.6 = 2.8 atm

We have got the same pressure as equal to initial temperature it mean the equlibrium is brought back to initial temperature after reaction

a can be calculated as a = X - 0.6 = 1.0 atm

Kp = 1.0 atm/ 0.6 atmx 1.8 atm = 0.9259 atm-1

Kp should remain same at any fixed temperature

CH2=CH2 + H2O -------> CH3CH2OH

0.6 atm 1.8 atm + 0.93 atm = 2.73atm 1.0 atm initially

0.6 atm -x 2.73 -x 1.0 + x

Kp =   0.9259 atm-1 = ( 1+ x) / (0.6 -x)(2.73-x)

we get a quadratic equation after simplifying this

0.9259x2 - 4.08x + 0.52 = 0

two roots of this equation can be calculated in calculator easily

x1 = 4.2752

x2 = 0.1314

x1 is invalid as it will make pressure negative

valid value is x2 = 0.1314 atm

pressure of ethanol = 1 atm + 0.1314 atm =1.1 atm = 1.1 x 100 atm upto two significan digits