Page 296 - Modeling of Chemical Kinetics and Reactor Design
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266 Modeling of Chemical Kinetics and Reactor Design
The average rate of reaction during δt is
− ( r A ) + 1 − ( dr A ) + t δ ...... (5-3)
2 dt
During δt, OUTPUT = ACCUMULATION
( t +δ t) − t
1 − ( dr ) dN
−− ( r A ) + A δ tV R • t δ = N A + A t δ − N A (5-4)
2 dt dt
1 − ( dr ) dN
−− ( r A ) + A δ tV R = A (5-5)
2 dt dt
As δt → 0, the term 1/2[d(–r )/dt] δt → 0, and Equation 5-5 becomes
A
−− ( r )V = dN A (5-6)
A R
dt
Rearranging Equation 5-6 gives
− ( r A )=− 1 dN A (5-7)
V R dt
In terms of the fractional conversion X
A
X = N AO − N A
A (5-8)
N AO
Rearranging Equation 5-8 gives
N = N (1 − X ) (5-9)
A
A
AO
Differentiating Equation 5-9 gives
dN =− N AO dX A (5-10)
A
