Page 104 - Modeling of Chemical Kinetics and Reactor Design

74 Modeling of Chemical Kinetics and Reactor Design

Since the order of differentiating is indifferent, then

∂ 
 ∂µ   V
 i  =   = V i (2-79)
∂ 
∂ 
 P  n
,
i ,
,,
Tn n j i TPn j
and similarly
 ∂µ i   −∂  S
  = =− S i (2-80)
∂ 
∂ 
 T  n ,,
i ,
,
Pn n j TPn j
Substituting Equation 2-80 into Equation 2-74 gives
 ∂ µ 
µ = H + T i  (2-81)
i i  ∂ T 
i ,
,
Pn n j
Rearranging Equation 2-81 yields

 ∂  µ i  
  T   −H i (2-82)
  = 2
 ∂T  T
 
,
i ,
Pn n j
EFFECT OF TEMPERATURE ON
THE EQUILIBRIUM CONSTANT

Generally,

 ∑ υµ o 

−

K = exp  i  (2-83)
 RT 


or

ln K = −1 ∑ υµ o (2-84)
i
R T