Chemical Forums
Chemistry Forums for Students => Physical Chemistry Forum => Topic started by: ptcek on August 21, 2008, 02:55:14 PM
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Hi folks,
I'm learning physical chemistry and found a problem. I don't know how to derive fugacity as a function of temperature ... f = f(T).
It should look like this at the final stage:
ln f(T,p) = ln f(T0,p) - INTT0T {Hm - Hmid}/{RT2} dT
where f = fugacity
T = thermodynamic temperature
p = pressure
Hm = molar enthalpy
Hmid = molar enthalpy of ideal gas
R = gas constant
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Hello ptcek ,
You can use the gibbs-helmholtz equation for a system undergoing a change in temperature from To to T. Consider a real system versus an ideal system. Then you can write :
d [ ( G - Gid ) / T ] / dT = - ( H - Hid ) / T2
Then the classical relation G = Go + RT Ln f ( f = P for an ideal system ) is substituted to yield :
d Ln ( f / p ) = - 1 / R [ ( H - Hid ) / T2 ] dT
We can now integrate setting T between To and T on the right. On the left the Ln(f/p) changes as a function of T from To to T. However P is the same for both states. Thus , Ln( 1/p ) cancels and you get :
Ln f ( T,p ) - Ln f ( To , p ) = - 1 / R Integral ( H - Hid ) / T2 dT with the integral limits already set. This is the relation required.