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07.pdf-Chemistry 5.12 Spri ng 2003, Week
07.pdf-Chemistry 5.12 Spri ng 2003, Week
07.pdf-Chemistry 5.12 Spri ng 2003,...
07.pdf-Chemistry 5.12 Spri ng 2003, Week
Page 4
4
B.
Thermodynamics:
energy changes that accompany chemical and physical
transformations
•
Thermodynamics
are used to describe systems that are in their
equilibrium
state
A
B
Equilibrium Constant:
K
eq
=
[B]
[A]
[products]
[reactants]
=
Gibbs Free Energy:
G =
H – T
S = –RT(ln
K
eq
)
R = 1.987 cal/K·mol
T = temperature (K)
Gibbs Free Energy:
G =
H – T
S = –RT(ln
K
eq
)
entropy (
S):
disorder or freedom of motion; an increase in entropy (
∆
S > 0) is
favorable
enthalpy (
H):
the amount of heat evolved or consumed in a reaction (bonds
broken/formed)
endothermic:
∆
H > 0; need to put energy into the reaction (uphill)
exothermic:
∆
H < 0; energy given off by the reaction (downhill)
•
In the Gibbs Free Energy equation, the enthalpy term (
∆
H) is generally much larger
than the entropy term (T
∆
S).
In other words, the change in enthalpy (bond
breaking/bond formation) usually governs the favorability of a reaction.
Page 5
5
The 1.4 Rule:
At 25 °C (298 K), every
1.4 kcal/mol change in
G°
results in a
factor of 10 difference in
K
eq
(useful for estimating conversion of a reaction).
∆
G°
–4.2
–1.4
+1.4
+4.2
+2.8
0
–2.8
K
eq
10
3
10
10
–1
10
–3
10
–2
1
10
2
ratio
[B] : [A]
1000 : 1
10 : 1
1 : 10
1 : 1000
1 : 100
1 : 1
100 : 1
conversion
[B]/([B] + [A])
> 99.9%
91%
9%
< 0.1%
< 1%
50%
99%
Standard Gibbs Free Energy:
∆
G° =
∆
G at 298K and 1 atm
conversion:
percentage of starting material that is converted to products at equilibrium
[A]
[B]
Note:
Similar rules apply at different
temperatures:
100 °C (1.7), 50 °C (1.5), 0 °C
(1.3), –78 °C (0.9), etc.
C.
Kinetics:
Reaction Rates
reaction rate:
how fast products appear and reactants disappear (measured
experimentally)
rate equation:
relationship between concentration of reactants and observed reaction
rate (determined experimentally and used to deduce reaction mechanisms)
observed rate = –d[A]/dt = d[C]/dt
=
k
r
[A]
a
[B]
b
(
k
r
= rate constant)
[A]
[B]
[C]
[D]
a:
order of the reaction with respect to A
b:
order of the reaction with respect to B
a + b:
overall order of the reaction
These all depend on the
reaction
mechanism.
Page 6
6
Arrhenius Equation:
k
r
=
A
e
–
Ea/RT
A
= Arrhenius prefactor
E
a
= activation energy (minimum energy the reactants must
have for the reaction to occur)
•
The rate constant is dependent on the activation energy and the temperature.
•
In this class, we'll also refer to the activation energy of a reaction in terms of
∆
G
‡
(
free energy of activation
).
Enough equations!
Now let's look at pictures!
D.
Reaction-Energy Diagrams
•
A
reaction-energy diagram
is a plot of the potential energy as reactants are
converted to products (also called a
reaction-coordinate diagram
);
very useful
for understanding thermodynamics and kinetics!
reaction coordinate
potential energy
•
X-axis is the progress
of the reaction.
•
Y-axis can be either
G or
H.
•
The
transition state
is state of highest
energy between
reactants and products.
•
Transition states are
transient (written in
brackets).
•
Transition states are
unstable, do not have a
finite lifetime, and
cannot be isolated
.
reactants
products
H°
(or
G°)
E
a
(or
G
‡
)
transition
state
‡
reactants
transition
state
products
‡
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