Text 8.7 Using the virial equation of state for hydrogen at 298 K given in problem 7 (text 8.6), calculate a. The fugacity of hydrogen at 500 atm and 298 K b. The pressure at which they fugacity is twice the pressure c. The change in Gibbs free energy caused by a compression of 1 mole of hydrogen from 1 to 500 atm. What is the magnitude of the contribution to (c) caused by the non ideality of hydrogen

a). P = 688 atm

b). P = 1083.04 atm

c).Δ G = 16.188 J/mol    

Explanation:

a). Fugacity 'f' can be calculated from the following equations :

where, P = pressure ,  Z = compressibility

Now, the virial equation is :

 ........(1)

Also, PV=ZRT for real gases .......(2)

∴

So from the fugacity equation ,

Putting the value of P = 500 atm in the above equation, we get,

f = 688 atm

b). Given f = 2P

  ∴  P = 1083.04 atm

c). dG = Vdp -S dt  at constant temperature, dT = 0

Therefore, dG = V dp

Δ G = 16.188 J/mol  

c. is the answer

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