Lecture Recap, CHEM 162

9/22-9/23
Hº compares product stability to reactant stability.
Hº compares product bond strengths to reactant bond strengths.
At constant temperature (T = 0), a chemical system that absorbs or releases energy, gains or
loses chemical potential energy, respectively.
Source of chemical potential energy: electrostatic attraction of bonding electrons to mutual
nuclei.
Temperature is a measure of the average kinetic energy of a system of particles.
Rate of Rxn typically increases with:
Increasing concentration
Increasing temperature
A Catalyst
Decreasing complexity of particle geometry
Atomic Theory necessarily predicts a Collision Theory of Kinetics:
Increasing concentration
Increasing temperature
A Catalyst
Decreasing complexity
of particle geometry

Increasing Frequency of Collisions
Increasing Energy of Collisions
Increasing Frequency of Collisions
Majority of productive collisions are
less dependent on trajectory
9/24-9/26
A mechanism is one or more elementary steps indicating how collisions between reactants and
intermediates lead to product formation. Any mechanism whose elementary steps do not sum to
the overall balanced equation can be eliminated. Multiple mechanisms can and should be
proposed for a chemical reaction. Experiment is used to eliminate some or all. Mechanisms can
not be proved.
For the balanced equation, aA + bB  cC + dD:
rate of reaction =
1
a
 A

t
1
b
 B

t
1
c
C 

t
1
d
D 
t
= 1/a * the rate of disappearance of A
= 1/b * the rate of disappearance of B
= 1/c * the rate of formation of C
= 1/d * the rate of formation of D
Method of Initial Rates
More typically the concentration of a reactant, rather than that of a product, is monitored over
time. The tangent line slope at t = 0 in a concentration vs. time curve yields the instantaneous
initial rate. An equilibrium condition is typically not allowed to occur.
Experimental Rate Law and Order of Reactant Concentration
Using the method of initial rates, a reactant’s concentration is varied, all other things being equal,
to see how the initial rate is affected.
If no rate change is observed when concentration is changed then the reaction is zeroth (0th)
order in the reactant concentration.
If the rate is directly proportional to the concentration the reaction is first (1st) order in the
reactant concentration.
If the rate is directly proportional to the square of the concentration the reaction is second (2nd)
order in the reactant concentration.
Once all reactant concentration orders are experimentally determined an experimental rate law
can be written: rate = k[A]x[B]y for the reaction A + B  products, where k is the average rate
constant calculated from all trials, i.e. k = rate/[A]x[B]y.
A rate law simply shows how rate varies with concentration. From collision theory it is known
that rate  concentration, from experiment, rate  (concentration)x, where x = 0, 1, 2.

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Method of Integrated Rate Laws
Two equivalent expressions of rate can be manipulated to derive a differential equation that can
be integrated over concentration and time ranges.
  A
Rate =
= k[ A] x
t
  A
=  kt
[ A] x
[ A]
=
x

[ A ]0 [ A]
[ A ]t
t
  kt
t0
The integration yields linear equations whose slope  k. These equations allow one to find the
concentration of a reactant at any time.
0th
[ A]t  kt  [ A]0
1st
ln[ A]t  kt  ln[ A]0
2nd
1
1
 kt 
[ A]t
[ A]0
Both the initial rate and integrated rate methods produce a rate law. The latter can generate
additional information, i.e. concentration at any time.
Half-life
Half-life is the time for ½ of the starting material to disappear. It can be calculated for each
order by solving the integrated rate law for time when [A]t = [A]0/2
0th
t½ =
[ A]0
2k
1st
t½ =
ln 2
k
2nd
t½ =
1
k [ A]0
half-life is constant
Methods for Determining Reactant Concentration Order
Graphical: Plot [A] vs. time. A linear plot with negative slope suggests 0th order. A curved plot
is either 1st or 2nd order. Plot ln[A] vs. time. A linear plot with negative slope suggests 1st order.
Plot 1/[A] vs. time if needed a linear plot with positive slope suggests 2nd order. Experimental
data could suggest all orders are possible. In this case the “best line” wins, i.e. the linear plot
with R2 closest to 1.
100
2
R = 0.9874
-4.2
Raw Data
Linear (Raw Data)
-4.3
-4.4
Raw Data
-4.5
Linear (Raw Data)
-4.6
-4.8
50
time (min)
100
2
R = 0.9996
120
100
80
Raw Data
60
Linear (Raw Data)
40
20
-4.7
0
y = 0.8756x + 59.146
140
y = -0.0101x - 4.1131
50
1/[C 4H6], M-1
-4
-4.1 0
2
R = 0.9551
ln[C4H6]
[C 4H6] (M)
y = -0.0001x + 0.0161
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
Kinetic Profile for the Dimerization of
1,3-butadiene
Kinetic Profile for the Dimerization of
1,3-butadiene
Kinetic Profile for the Dimerization of
1,3-butadiene
0
0
-4.9
time (min)
50
100
time (min)
Half-Life: This method allows for a quick assessment of order by inspecting the concentration
and time data. Compare successive half-lives. Each successive half-life will be ½ that of the
previous one, the same as the previous one, and double the previous one for 0th, 1st, and 2nd order,
respectively. Often times perfect half way points are not available so use this method with care.
Constant k: Calculate three values of k using an integrated rate law. Typically it’s best to pick
data from the beginning, middle, and end of a kinetic run. A particular order is supported if the k
values are the same within experimental error (significant figures)