Question 1 [25 marks in total]

1. Dimethyl ether gas is stored in a vessel at 40 bar and 350 K. Under these

conditions its behaviour can be described by the Clausius Equation of State

(EOS):

RT

P = -

v-b

2 RTC

with b= 25 Pc

Assume the reference state of dimethyl ether to be the ideal gas state at To

= 298 K and Po = 1 bar at which hG(To) = 0 and s/G(To, Po) = 0. The ideal gas

heat capacity of dimethyl ether averaged between 298 K and 350 K is cp =

68.9 J mol-¹ K-¹. Critical properties of dimethyl ether are the following: Pc =

54.3 bar; Tc = 401.2 K.

a. Calculate the compressibility factor.

[4 marks]

b. Derive an expression for the fugacity coefficient and calculate the gas

fugacity (bar).

[6 marks]

c. Derive expressions for the residual enthalpy and residual entropy and

calculate the gas enthalpy (J mol-¹) and entropy (J mol-¹ K-¹).

[12 marks]

d. Discuss briefly whether the Clausius EoS is suitable to predict vapour-

liquid equilibrium.

[3 marks]