CL 253 Tutorial 6 2009 1

CL 253- Tutorial – 6, Oct 2009 1. Show that the fugacity coefficient for a gas obeying the Redlich-Kwong equation of state

is given by

( )ln ln ln ln

( )b a a V b V b V a

V b RT V b bRT V V V b RT V bφ

⎡ ⎤+ −⎛ ⎞ ⎛ ⎞= − − − − −⎢ ⎥⎜ ⎟ ⎜ ⎟− + − +⎝ ⎠ ⎝ ⎠ ⎣ ⎦;

where, V =molar volume 2. Estimate the fugacity of ammonia vapor at 1.95 MPa and 321.55 K assuming that it

obeys the RK equation of state. (Note: that the expressions for pure component fugacity and of individual species in a mixture are the same as that of SRK EOS, except that the the parameter ‘a’ in RK is dependent only on T, while for SRK ‘a’ is a function of both ω and T). [1.7316MPa]

3. Show that the fugacity coefficient of a gas which obeys the Berthelot equation of state is given by:

2 22ln ln lnb a V b V a

V b V V bRT V RT Vφ −⎛ ⎞ ⎡ ⎤= − − − −⎜ ⎟ ⎢ ⎥− −⎝ ⎠ ⎣ ⎦

; v =molar vol.

4. Estimate the fugacity of methane at 32C and 9.28 bar. Use the generalized compressibility factor correlation. [9.15bar]

5. Estimate the fugacity of ethane at 122.2 K and 2 bar using the virial coefficient correlation. [1.54bar]

6. Estimate the second virial coefficient for a mixture of 40 mole% propane and 60 mole% n-pentane at 500K. [B11 = – 1.1833x10-4 m3/mol; B22 = – 3.4407x10-4 m3/mol; B12 = – 2.0091x10-4 m3/mol; Bmix = – 2.3923x10-4 m3/mol]

7. It is desired to store 100 kmol mixture of 30 mole percent propane and 70 mole percent n-pentane at 500K and 50 bar. Determine the size of the tank using the pseudocritical properties. [ ~ 50m3]

8. A storage tank of 50 m3 capacity is filled with a mixture of 70 mole percent ethylene and 30 mole percent propylene at 600 K and 60 bar. Assuming that the mixture follows the van der Waals equation of state, determine the mass of mixture in the tank. [ 2043.6kg]

9. Calculate the changes in enthalpy and entropy per mole when a mixture of 70 mole % ethylene and 30 mole% propylene at 323K and 10 bar is taken to 60 bar and 600 K using the generalized compressibility factor approach. [4.785kJ/mol; – 3.64J/mol K]

3 6 2 9 31 4.196 154.565 10 81.076 10 16.813 10ig

pC x T x T x T− − −= + − + ;

3 6 2 9 32 3.305 235.821 10 117.58 10 22.673 10ig

pC x T x T x T− − −= + − + 10. Calculate the fugacities of ethylene and propylene in a mixture of 70 mole percent

ethylene and 30 mole percent propylene at 600 K and 60 bar. Assume that the mixture follows the Redlich-Kwong equation of state. [41bar; 16.6bar]

11. For the system in problem ‘6’ compute the species fugacity coefficients for an equimolar mixture at 20 bar and 500K. [0.9626; 0.9082]

12. For methane at 298K and 2 MPa compute the fugacity using SRK equation. [1.9342MPa]

13. For ethane at 400K and 1MPa compute the fugacity using PR equation. [0.9662MPa]