10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 2: The Reaction Rate & Reaction Mechanisms
The lecture covers: Definitions in terms of reacting compounds and reaction extent,
rate laws, Arrhenius equation, elementary, reversible, non-elementary, catalytic
reactions.
From previous lecture:
dN A
= FAo − FA + GA , GA = ∫ rA dV
dt
Example:
A + B → 2C
*Reactions are reversible (often will neglect reverse)
XA =
N Ao − N A
N Ao
XA =
A,B
FAo − FA
FAo
XC =
FC
2 FAo
C,A,B
FAo
FBo
Figure 1. A reactor with reactants A and B constantly flowing in and product C and
unused reactants A and B flowing out.
FAo =
moles A flowing in
= [ A]input vin = [ A]o vo
sec
liters
sec
moles A flowing out
FA =
= [ A]output vout
sec
[ A]output vout
X = 1−
[ A]in vin
Closed reactor, const. V
Detailed balance- all steps in equilibrium, total system
d [ A]
dt
= rA = − k [ A][ B ]
[C ]
K eq =
[ A][ B ]
2
when
[ A][ B ]
[C ]
=
2
K eq
the rxn. stops -> rA=0
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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2
⎛
C]
[
⎜
rA = − k [ A][ B ] −
⎜
K eq
⎝
⎞
k
⎟ , krev = for , forward-reverse in one expression
⎟
K eq
⎠
same!
Catalysis
rA, forward = kcat [ catalyst ][ A] f
( [ B ])
may be included
i.e. when B is
very small
Rate limiting step determines the kinetics (slow step). The kinetics are insensitive to
[B] because B is not part of this slow step.
[C ]
K eq [ A][ B ]
2
rA,reverse = rA, forward
rA,net
2
⎛
⎞
C]
[
⎟
= − kcat [ catalyst ] ⎜ [ A] −
⎜
K eq [ A][ B ] ⎟
⎝
⎠
K eq = e − ΔG RT
ΔG = ΔG of , products − ΔG of ,reactants
Standard state
A→ B+C
[ B ][C ] = moles
K eq =
[ ]
liter
[ A]
KC
Partial Pressures
pB pC
pA Po
= K eq =
[ B ][C ]
Po
[ A] RT
Ideal Gas: pV = nRT ⇒
n
P
=
V RT
Po is the standard state pressure (1 atm), this makes the units cancel. Using partial
pressures is accurate within 10%, more error with liquids.
Stoichiometric coefficient
N A = N A,initial + ∑ν A,iξi
Extent of rxn.
N rxn
N C = N C ,initial + ∑ν C ,iξi
i =1
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 2
Page 2 of 3
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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column
vector
column
vector
matrix vector
N = No + ν i ξ
Do columns span space? Often no, limits on what is achievable.
NC
Reaction trajectoryPlot state of system
ξ=ΝΑο
t=10
ξ
t=0.01
NB
d
(N ) = F (N)
dt
ξ1=0
NA
Figure 2. A plot of the reaction trajectory. ξ is the extent of reaction.
Conservation Laws
Conserve atoms
2CH 4 + O 2 → C2 H 4 + 2H 2 O
C A N A + CB N B + CC N C = const.
constant moles
C :1× NCH 4 + 2 × NC2 H 4 = N C ,initial
H : 4 × NCH 4 + 4 × NC2 H 4 + 2 N H 2O = N H ,initial
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 2
Page 3 of 3
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].