1. 3-d plot
Contour
Plot
2 of 3
coordinates
Symmetric
Stretch
r
Energy
Simplest possible “reaction”
D + H2 →
→
→
→ HD + H
rHH
Energy
V(rHH) →
→
→
→ H2 as H - D
distance increases.
Potential Energy Surfaces Potential Energy Curves
Energy
Q
Energy
Q
Reac. Prod.
Endothermic
Energy
Q
Reac. Prod.
Exothermic
Ea
∆
∆
∆
∆E or
∆
∆
∆
∆H
∆
∆
∆
∆E or ∆
∆
∆
∆H
Ea
Activation Energy, Ea
Activation Energy, Ea
Reaction Coordinate
Reaction Coordinate
Reac. Prod.
2. Temperature Dependence of a Reaction Rate Constant:
Temperature Dependence of a Reaction Rate Constant:
Velocity distribution in gas phase at temperature T
Nv
|v|
Critical velocity for reaction, vc
|v| < vo No
Reaction
|v| > vo
Reaction
T = 300 K
T = 500 K
T = 1000 K
T = 5000 K
The minimum energy that must be supplied
by a collision is the Activation Energy.
KE = ½mv2 ≥
≥
≥
≥ Ea
k = A∞
∞
∞
∞ e-Ea/kBT
|v|
Nv
Rate constant
Boltzmann
Constant
Pre-exponential
factor
Population with
KE sufficient
to drive the
reaction.
3. k = A∞
∞
∞
∞ e-Ea/kBT
Temperature
k
k = 0.9 A∞
∞
∞
∞
k
B
T
=
10
E
a
k
B
T
=
E
a
k = 0.36 A∞
∞
∞
∞
Ea = Joules/molecule
for Ea = Joules/mole
k = A∞
∞
∞
∞ e-Ea/RT
RT
=
10
E
a
RT
=
E
a
k = A∞
∞
∞
∞
A∞
∞
∞
∞ = maximum possible rate at
infinite temperature
ln k = -Ea 1 + ln A∞
∞
∞
∞
R T
A plot of ln k vs 1/T will be
linear.
ln
k 1/T
Intercept = ln A∞
∞
∞
∞
Slope = -Ea/R
Arrhenius Equation
Arrhenius Equation
Arrhenius Plot
Arrhenius Plot
Activation barriers are determined
experimentally by measuring the rate
over as large a range of T as possible.
4. But What About Entropy?
But What About Entropy?
An exothermic reaction will occur
rapidly if Ea < RT and only very
slowly if Ea >> RT.
Potential
Energy
∆
∆
∆
∆E
Ea
∆
∆
∆
∆H
Reaction Coordinate
An endothermic reaction
will have a large activation
energy, Ea.
Reaction Coordinate
∆
∆
∆
∆H Ea
Potential
Energy Entropy accounts for the
number of different
states that contribute all
along the reaction path.
5. We plot Gibbs energy
along reaction coordinate
to account for entropy.
Gibbs
Energy
∆
∆
∆
∆Gŧ
∆
∆
∆
∆rG
Reaction Coordinate
∆
∆
∆
∆Gŧ
is the free energy or
Gibbs energy of activation.
= kBTe∆
∆
∆
∆Sŧ/R e-∆
∆
∆
∆Hŧ/RT
h
= kBT e-(∆
∆
∆
∆Hŧ-T∆
∆
∆
∆Sŧ)/RT
h
k = kBT e-∆
∆
∆
∆Gŧ/RT
h
Pre-exponential
factor A∞
∞
∞
∞
k
h = Planck’s Constant
∆
∆
∆
∆Sŧ = Entropy of Activation
∆
∆
∆
∆Hŧ = Enthalpy of Activation ⇒
⇒
⇒
⇒ microscopic Ea
6. Sample Problem:
Sample Problem:
Sample Problem:
If a reaction doubles its rate when the temperature is increased
from 305 K to 315 K, what is the activation energy?
k = A∞
∞
∞
∞ e-Ea/RT
k(315 K) = A∞
∞
∞
∞ e-Ea/R(315 K) = 2
k(305 K) A∞
∞
∞
∞ e-Ea/R(305 K)
2 = e-Ea(1/305 – 1/315)/R
A∞
∞
∞
∞ is approximately T independent
ln2 = -Ea(1/305 – 1/315)/R
Ea = ln2 (8.3145 J mol-1 K-1) 10-3 kJ
0.0001041 K-1 J
= 55.4 kJ/mol
7. Catalysis:
Catalysis:
Catalysis:
Consider: 2 H2O2(l) →
→
→
→ 2 H2O (l) + O2(g)
∆
∆
∆
∆rG
∅
∅
∅
∅
= 2(-237.13) + 0 - 2(-120.35) = -233.56 kJ
∆
∆
∆
∆rH
∅
∅
∅
∅
= 2(-285.83) + 0 - 2(-187.78) = -196.10 kJ
In fact the equilibrium constant is huge.
K = e-∆
∆
∆
∆rG /RT
∅
∅
∅
∅
K = exp = 1.15 ×
×
×
× 1041
233.56 ×
×
×
× 103 J
8.31451 J K-1 298
Energy Q
Reac. Prod.
H
O – O
H
→
→
→
→
H
O – H + O •
•
•
•
∆
∆
∆
∆rH
∅
∅
∅
∅
Very high
activation
energy
This reaction is exothermic and spontaneous!
8. 2 H2O2(l) 2 H2O (l) + O2(g)
MnO2
Add MnO2
MnO2 acts as a catalyst – that is, it provides a mechanism
with a much smaller activation energy.
Old Path
Energy Along
the Catalyzed
Path
Energy
Q
H2O + O2
H2O2
Initial and final states are unaffected by catalyst. The
nature of the reaction coordinate is changed.
“Q”
Energy
QCAT
“Q”
Energy
QCAT
9. Catalyst is in a different phase than reactants.
Heterogeneous Catalysis:
Heterogeneous Catalysis:
Usually a solid surface catalyzing gas or liquid
phase reactions.
Homogeneous Catalysis:
Homogeneous Catalysis:
Catalyst is in the same phase as the reactants.
Usually in liquid solution.
Rhodium, Platinum, Zeolites, Metal Oxides, …
Complexes of Rhodium and Platinum, Enzymes,
Strong Acids, …
Examples:
Examples:
2 H2O2(l) 2 H2O (l) + O2(g)
Catalase
In the presence of Catalase
Manganese Catalase in certain Lactobacillus type bacteria.
