Page 103 - Modeling of Chemical Kinetics and Reactor Design

Thermodynamics of Chemical Reactions 73

This is identical with the definition of µ in terms of G , but this is
i
i
only true for G because only the pressure P and temperature T hold
constant for G. Therefore, in general
 ∂ K 
µ ≡ /  
i
 n ∂  (2-72)
i
,,
TPn j
This can be expressed as
H = U + PV i (2-73)
i
i
and

µ = G ≡ H − TS i (2-74)
i
i
i
From Equation 2-21
dG =− SdT + PdV + ∑ µ i dn i (2-21)
i=1

Also

∂ 
 G
  = V
∂ 
 p (2-75)
,
,
Tn in j
Differentiating Equation 2-75 with respect to n gives
2
∂ G = ∂V
∂∂np ∂n (2-76)

∂G
But = µ i (2-77)
∂n i

Differentiating Equation 2-77 with respect to P yields

2
∂ G ∂µ
= i
∂∂Pn i ∂P (2-78)