tutorial sheet 03 2014

8/12/2019 Tutorial Sheet 03 2014

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Tutorial Sheet No. 3 (2014)

Engineering Design of Chemical Reactors Using Chemical Reaction

Equilibrium Calculations

Please complete and hand-in Question 3 by 3pm Monday 24thMarch 2014.

1) Ethanol decomposes in the vapour phase over a catalyst according to the gas phase

reaction:

(g)O H(g)HC(g)OHHC 24252

a)Using the following data calculate the heat, Gibbs Free energy and entropy of the reactionat 298 K. Is this reaction spontaneous at 298 K?

Compound o298f

H

kJ / kmol

o

298fG

kJ / kmol

C2H5OH (g) -235000 -168400

C2H4(g) +52340 +68160

H2O (g) -242000 -228800

[5 marks]

b)Using the following data calculate the heat, Gibbs Free Energy and entropy of the reactionat 650 K. Is this reaction spontaneous now?

3

i

2

iiiP TdTcTbaC i (units kJ kmol-1K-1)

Compound ai bi ci di

C2H5OH (g) 9.014 0.2141 -8.39 10-5 1.373 10-9

C2H4(g) 3.806 0.1566 -8.348 10-5 17.55 10

-9

H2O (g) 32.24 0.001924 1.055 10-5 -3.596 10-9

[5 marks]

c)What is the equilibrium constant,KP, for this reaction at 650 K?[5 marks]

d)Assuming that the gas phase system is ideal, calculate the equilibrium conversion of pureethanol feed at 2 atm pressure and 650K?

[5 marks]

e)Repeat the above calculation but now we are at 200 atm and 650 K (so the system is notideal).

[5 marks]

Supplied Data: Universal Gas ConstantR= 8.314 kJ kmol-1K-1

Data Sheet No. 1 Table of Critical Constants of Gases.

Data Sheet No. 2 Dimensionless Plot of the Fugacity Coefficient (fi/ PT)

versus Reduced Pressure (Pr) and Reduced Temperature (Tr).1 atm = 1.013 105Pa


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2) Sulphur trioxide, SO3(g), decomposes when heated, by undergoing the reversible reaction:

2SO3(g) 2SO2(g) + O2(g)

Using the following data:

Compound f298

H

kJ kmol-1

0

298S

kJ kmol-1

K-1

PC

kJ kmol-1

K-1

SO3(g) -395700 256.7 68.76

SO2(g) -296800 248.1 50.15

O2(g) 0 205.0 32.96

(i) For a closed system, operating at constant temperature and pressure, state theconditions in terms of Gwhich give rise to an equilibrium/no change system,and spontaneous change system.

(ii) Calculate the standard enthalpy change (heat of reaction, HR) for thedecomposition of sulphur trioxide at 298 K.(iii) Calculate the standard entropy change (S) for the decomposition of sulphur

trioxide at 298 K.

(iv) Calculate the free energy change (G) of the reaction at 298 K.(v) Is this reaction spontaneous at 298 K? If it isnt and assuming the enthalpy and

entropy changes do not vary with temperature, estimate the temperature at which

the reaction becomes spontaneous.

(vi) Allowing for changes in enthalpy and entropy with temperature, calculate thetemperature at which the reaction becomes spontaneous.

[25 marks]


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3) Carbon black is produced by the decomposition of methane at 650 C and 1 atm by

undergoing the reaction:

CH4(g) C (s) + 2H2(g)

For equilibrium at 650 C and 1 atm, the Gibbs Free Energy Change (G) for the reaction is1.109 104kJ kmol-1.

a) What factors affect the equilibrium yield of a chemical reaction?[5 marks]

b) What is the gas phase composition of gases exiting the reactor if pure methane only

enters the reactor, and what fraction of methane decomposes? State any assumptions

you make.

[10 marks]

c) Repeat the same calculation as for part (b) when the feed to the reactor is now an

equimolar mixture of methane and nitrogen.

[10 marks]


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4) The gas phase hydration of ethylene for the production of ethanol is described by the

stoichiometric balance equation of:

(g)OHHC1(g)OH1(g)HC1 52242

This gas phase catalysed reaction takes place in a reactor vessel operated at a system pressureof 70.0 atm and a system temperature of 600 K over a phosphoric acid catalyst. The feedstock

gas contains an equimolar concentration of steam and ethylene. The reacting gas phase can be

assumed to be ideal.

a) Starting with the Vant Hoff Isochore equation, namely:

constant1-lno

TR

HKp

and using appropriate thermodynamic relationships show that the constant is equal to:

R

So

constant

[5 marks]

b) Using the Vant Hoff Isochore calculate the magnitude of the equilibrium constant (KPin

m2N-1) for the gas phase reaction at 600 K.

[5 marks]

c) Report the value of the Gibbs Free Energy at 600 K ( -1o600 (kmol)kJ,G )[5 marks]

d) Using the calculated value of KPat 600 K, determine the magnitude of the molar yield of

ethanol on ethylene at the system pressure of 70.0 atm ab.

[5 marks]

e) With reference to the results of the analysis of this reaction system, comment on how

product yield is affected by the operational temperature and pressure of the reactor vessel.

[5 marks]

Supplied Data: Enthalpy and Entropy of Formation Data at 600 K:

Components ofH

kJ / kmol

o

fS

kJ / (kmol K)

C2H4(g) + 52 280 219.5

H2O (g) -242 200 188.7

C2H5OH (g) -235 300 282.0


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Data Sheet No. 1: Table of Critical Constants of Gases.

Substance Formula Molar Mass

kg/kmol

TC

K

PC

MPaAir - 28.97 132.5 3.77

Ammonia NH3 17.03 405.5 11.28Argon Ar 39.948 151 4.86

Benzene C6H6 78.115 562 4.92

Bromine Br2 159.808 584 10.34

n-Butane C4H10 58.124 425.2 3.80

Carbon dioxide CO2 44.01 304.2 7.39

Carbon monoxide CO 28.011 133 3.50

Carbon tetrachloride CCl4 153.82 556.4 4.56

Chlorine Cl2 70.906 417 7.71

Chloroform CHCl3 119.38 536.6 5.47

Dichlorodifluoromethane (R-12) CCl2F2 120.91 384.7 4.01

Dichlorofluoromethane (R-21) CHCl2F 102.92 451.7 5.17Ethane C2H6 30.070 305.5 4.48

Ethanol C2H5OH 46.07 516 6.38

Ethylene C2H4 28.054 282.4 5.12

Helium He 4.003 5.3 0.23

n-Hexane C6H14 86.179 507.9 3.03

Hydrogen (normal) H2 2.016 33.3 1.30

Krypton Kr 83.80 209.4 5.50

Methane CH4 16.043 191.1 4.64

Methyl alcohol CH3OH 32.042 513.2 7.95

Methyl chloride CH3Cl 50.488 416.3 6.68

Neon Ne 20.183 44.5 2.73

Nitrogen N2 28.013 126.2 3.39

Nitrous oxide N2O 44.013 309.7 7.27

Oxygen O2 31.999 154.8 5.08

Propane C3H8 44.097 370 4.26

Propylene C3H6 42.081 365 4.62

Sulfur dioxide SO2 64.063 430.7 7.88

Tetrafluoroethane (R-34a) CF3CH2F 102.03 374.2 4.059

Trichlorofluoromethane (R-11) CCl3F 137.37 471.2 4.38

Water H2O 18.015 647.1 22.06

Xenon Xe 131.30 289.8 5.88


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Data Sheet No. 2: Dimensionless Plot of the Fugacity Coefficient (fi/ PT) versus Reduced

Pressure (Pr) and Reduced Temperature (Tr).

tutorial sheet 03 2014

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