Question 3 [25 marks in total]

3. The oxidative coupling of methane is a promising chemical reaction to

convert underused methane (CH) from natural gas into ethylene (CH),

valuable chemical feedstock. This reversible reaction accurs via the following

route:

2CHOCH+ 2H₂O

Table 3.1. Thermodynamic properties of selected molecules

298.15 K, 1 bar SH/kJ mol SJK mol C/JK mol

CHA

0₂

C₂H₂

H₂O

-75

0

52

-242

210

205

219

151

64

34

84

39

a. Using values from Table 3.1 above, calculate the standard Gibbs

energy of this reversible reaction

[6 marks]

b. This reversible reaction is usually conducted at a pressure of 1, bar

and at a temperature of 800 °C. Using Table 3.1 above, calculate

1. The change in molar enthalpy associated with this reaction.

(T), at 800 °C and 1 bar, noting that the molar heat

capacities at constant pressure can be assumed as

independent of temperature.

(4 marks]

ii. The change in molar entropy associated with this reaction,

AS(7), at 800 °C and 1 bar, noting that the molar heat

capacities at constant pressure can be assumed as

independent of temperature

[3 marks]

c. Assume this reversible reaction occurs during the burning of natural

gas at 3000 K and 1 bar, where the equilibrium constant. K-6.5.

L. Determine the molar Gibbs energy for the reversible reaction at

this temperature.

[2 marks]

il. Assuming all gases can be considered ideal, derive an

expression for the equilibrium constant, K, for the reversible

reaction in terms of the mole fractions of the gases.

[4 marks]

Starting from 2 moles of methane (CH) and 1 mole of oxygen

(Ozi), use the expression derived in Question 3c i to show

that the molar quantity of ethylene (CH) at equilibrium-0.651

moles

[4 marks]

iv. What would be the effect on the final number of moles of

ethylene (CaH) at equilibrium f an inert gas was introduced to

the reaction modure? Briefly explain your answer.

[1 mark]

v. What would be the effect on the final number of moles of

ethylene (CH) at equilibrium of the pressure of the reaction

mixture was increased? Briefly explain your answer.

M1 mark]

End of Question 3