Page 93 - Modeling of Chemical Kinetics and Reactor Design

Thermodynamics of Chemical Reactions 63

where

 ∂U   ∂U   ∂H   ∂A 
µ =  =   =   =  
i 
 ∂n   ∂n   ∂n   ∂n  (2-24)
i
,,
, ,
,,
, ,
SV n j i TPn j i SP n j i TVn j
CRITERIA FOR EQUILIBRIUM
For a reversible change, dS = q/T. If we consider a closed system
undergoing a reversible change at dT = 0, dP = 0, then the only form
of work is pdV. From the first law:

dU = q – pdV (2-1)

From the second law of thermodynamics:

dS = q , is a reversible change
T
q = TdS (2-2)

Combining the first and second laws gives:
dU = TdS – pdV (2-3)

That is
dU – TdS + pdV = 0 (2-25)

Defining
G = U + PV – TS (2-9)

Differentiating gives

dG = du + pdV + Vdp – TdS – SdT (2-11)

Restricting this to the case of isothermal and isobaric, dP = 0,
dT = 0, then

dG = dU + pdV – TdS (2-26)