Contour Plots for Reaction Rates
Contour Plots for Reaction Rates
Consider a reversible reaction with the reaction rate and the equilibrium constant given by:
A⇋B
r
K
eq
r=-=exp--(1-X)-exp--X
r
f
r
b
E
af
R
1
T
1
T
0
C
A0
E
ab
R
1
T
1
T
0
C
A0
K
eq
E
af
E
ab
R
1
T
1
T
0
where is the conversion fraction, is the inlet concentration (taken to be 10 moles/liter), is the universal gas constant (1.987 cal/mol K), and is the temperature (in kelvin).
X
C
A0
R
T
Use the sliders to vary the activation energies for the forward () and reverse () reactions. Both of these activation energies are expressed in cal/mol.
E
af
E
ab
This Demonstration plots the contour lines for the reaction rate either for exothermic reactions or for endothermic reactions . The equilibrium conversion = is plotted versus the temperature (see the black curve, for which we have ). It can be easily shown that =(-). Thus, for endothermic reactions, > and >, so >0 and will increase monotonically with if you move along a horizontal line (i.e. at a constant conversion fraction). On the other hand, for exothermic reactions we have <, thus we have along a horizontal line (i.e. at a constant value of ): (1) at low temperature > and >0; and (2) at higher temperature < and <0. In conclusion, for an exothermic reaction, the reaction rate initially increases with increasing , reaches a maximum value when =0, then starts to decrease until it reaches the equilibrium conversion curve where . The loci of the points where are indicated by the gray dots and curve.
r
ΔH=-<0
E
af
E
ab
ΔH=->0
E
af
E
ab
X
eq
K
eq
1+
K
eq
r=0
∂r
∂T
X
1
R
2
T
E
af
r
f
E
ab
r
b
E
af
E
ab
r
f
r
b
∂r
∂T
X
r
T
E
af
E
ab
X
E
af
r
f
E
ab
r
b
∂r
∂T
X
E
af
r
f
E
ab
r
b
∂r
∂T
X
r
T
r
max
∂r
∂T
X
r=0
r=
r
max