Page 92 - Modeling of Chemical Kinetics and Reactor Design

62 Modeling of Chemical Kinetics and Reactor Design

 ∂ G  ∂ G k  ∂ G 
dG = dT + dP + ∑   dn (2-14)
 ∂ T   ∂ P   ∂ n  i
,
,
,,
Pn i Tn i i=1 i TPn j
If the compositions are held constant, then
 ∂G =−  ∂G =
 ∂T  S,  ∂P  V (2-15)
,
,
Pn i Tn i
And again, µ is defined as
i
 ∂G 
µ ≡
 ∂n 
i   (2-16)
i
,,
TPn j
Substituting Equations 2-15 and 2-16 into Equation 2-14 gives
=
ik
dG =− SdT + VdP + ∑ µ i dn i (2-17)
i =1

Other state functions are the enthalpy function:

H = U + pV (2-18)

and the Helmholtz function:

A = U – TS (2-19)

The chemical potential µ can also be expressed in terms of H and
A. The complete set of equations are:

dU = TdS pdV+ ∑ µ i dn i (2-20)
−

=
dG Vdp − SdT + ∑ µ i dn i (2-21)

dH = TdS Vdp+ ∑ µ i dn i (2-22)
+

−
dA =− SdT pdV+ ∑ µ i dn i (2-23)