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3.3 T Reactors w o-Phase Agitated 89

In the general case, the concentration of a gas reactant A is

x )
N A N A,i (1 A
C
A
x )(
V V (1 R A P P T T )( ) i
i
i
1  x   P   T 
C A,i   1 RA A x   i   i   (3.93)
   P
  T
where N A are the moles of the reactant and V the total v for con- Then, olume of gas phase.
stant P and T (isobaric and isothermal operation, respecti v ely),
N A 1 x A
C C (3.94)
A A,i
V (1 R A 1 RA x
x )
i
and the concentration of B is
N C B,i b  Cx A,i A 
C B (3.95)
B  
V (1 R A x ) 1 RA x a 1  RA x 
i
In the case of 0 and constant P and T ,
R
C C x (1 ) (3.96)
A A,i A
b
C C Cx (3.97)
B B,i A,i
a
where C A,i is the initial (feed) concentration of A.
Note that the volume change in a system involving a g as component could be a result of

• a change in the total number of moles due to the reaction ( ≠ 0),
R
• a change in temperature ( T ≠ T ), i
• a change in pressure ( P ≠ P ), or
i
• a combination of the abo v e cases.
In reactions involving only liquid components without phase change, the pressure and tem-
perature variation do not have any significant effect on the volume of the reaction mixture, and
at the same time, the eactor is al xpansion f ays zero. Thus, w V V i in batch or Q Q i in
continuous-flow systems and eqs. (3.96) and (3.97) are applicable.
Example 1
enspiel’
If P and T are constant, use the following Les relationship for the fractional
v
change in the volume of the system between no conversion and complete conversion of the
reactant, where x is the con v ersion of reactant:
V ( x 1) V ( x 0)

R
V
( x 0)