Page 102 - Modeling of Chemical Kinetics and Reactor Design

72 Modeling of Chemical Kinetics and Reactor Design

PARTIAL MOLAR QUANTITIES

Considering any extensive property K, the partial molar quantity is
defined by

 ∂ K 
K =   (2-66)
 n ∂ 
i
i
,,
TPn ji j≠,
where T, P, n are held constant, then
j

K = K(T, P, n , n , . . . n . . . n ) (2-67)
1
2
k
i
Differentiating Equation 2-67 gives

dK =  ∂ K dT +  ∂ K dP + ∑  ∂ K   dn (2-68)

 ∂ T   ∂ P   n ∂  i
,
,
,,
Pn i Tn i i=1 i TPn j
Once again, integrating as in the Gibbs-Duhem equation, yields

K = ∑ n K i (2-69)
i
i=1

Similarly,

U = ∑ n U , H = ∑ n H and G = ∑ n G i (2-70)
i
i
i
i
i
i=1 i=1 i=1
For a pure component
U = u , H = h and G = g i (2-71)
i
i
i
i
The partial molar Gibbs function is given by
∂ 
 G
 
∂ 
 n i
,,
TPn j