# Monday, November 29 - Chemistry at Winthrop University ```Chemical Kinetics
• Kinetics: The Study of the rate of chemical
reactions
• Thermodynamics: The study of the energy
associated with chemical reactions
• Remember: Thermodynamics is concerned
with state functions (where we started and
where we finished) but Kinetics is concerned
with how we get to where we finish.
The Rate of a Chemical Reaction
What is a rate?
A rate is a change in a property per unit time.
For example, how do we define the speed of a
ski boat?
There are 2 types of speed:
1. Average speed: The total distance traveled
divided by the total time
2. Instantaneous speed: Looking at the
speedometer on the boat tells you the rate
you are traveling RIGHT THEN
The Reaction Rate
The reaction rate is the change in the rate of formation of
products OR consumption of reactants per unit time
[R] 2  [R]1 
-[Reactants]
Rate =
= - 
 Note : The minus sign
t
 t 2  t1 
[Products] 
[P]2  [P]1
Rate = 
 =


t
t


Reaction Rate and Stoichiometry
• In the example:
2NH3 (g) --&gt; N2 (g) + 3H2 (g)
The rate of formation of N2 is one half the
rate of disappearance of NH3. Prove
this.
Use the previous answer (0.017mM NH3 per sec)
You can use use stoichiometries to convert rates
Unique Average Rate
• Because it can be confusing to express
rates of different products or reactants,
we use the Unique Average Rate in
many instances
aA + bB --&gt; cC + dD
The Unique Average Rate =
1 [A]  1 [B]  1 [C] 1 [D] 
 
  
  
  

a  t  b  t  c  t  d  t 
Instantaneous Rate of Reaction
When you measure the rate of
a reaction, the rate is
constantly changing as the
composition of the reaction
mixture changes
•You want to choose 2 points
that are close together so that
you have a straight line
The instantaneous reaction rate is the
slope of a tangent line drawn to the
graph of concentration versus time
For most reactions, the rate decreases as
the reaction proceeds (when we are
plotting the concentration of reactants)
Rate Laws and Reaction Order
Let’s look at an
experiment on the
decomposition of
dinitrogen pentoxide
N2O5 --&gt; 4NO2 + O2
5 different initial concentrations of
N2O5, and 5 different rates
Rate Laws
• We could describe the rate
of dinitrogen pentoxide
decomposition as:
Rate = k [N2O5]
• We can see this
experimentally.
– As the [N2O5] increases,
the rate increases
• k is the rate constant for
the reaction and if we
plotted rate versus [N2O5], it
is equal to the slope.
Rate Laws
Rate of N2O5 decomposition = k [N2O5]
This is a rate law
•
An expression for the instantaneous
reaction rate as a function of concentration
Every chemical reaction has its own rate law
and unique rate constant, k
The rate constant is independent of reactant
concentration but dependent on temperature
Order of Reaction
If we look at another reaction, we’ll find that there may be a
different dependence on reactant concentration:
2NO2 (g) --&gt; 2NO (g) + O2 (g)
Rate vs.
[NO2]
Note
shape of
plot!
Rate vs.
[NO2]2
Note
shape of
plot!
Order of Reaction
2NO2 (g) --&gt; 2NO (g) + O2 (g)
This observation of concentration dependence on rate is telling
us something that the balanced chemical equation was and we
may have missed…
O=N=O
O=N +
+
O=N=O
O=N +
O=O
In order for the reaction to proceed, we need 2 molecules of
O=N=O
The rate law is: Rate of Consumption of NO2 = k [NO2]2
The reaction is a second order reaction
Rate Laws and Reaction Order
aA + bB --&gt; cC + dD
Rate = Rate constant [concentration of reactant A]a
Or
Rate = Rate constant [concentration of reactant B]b
Examples:
Rate = k [N2O5]
(First Order)
Rate = k [NO2]2
(Second Order)
Doubling the [reactant] of a first order reaction doubles the
reaction rate
Doubling the [reactant] of a second order reaction quadruples
the reaction rate
Zero Order Reactions
Some reactions just happen
and continue at a constant rate
until the reactant is completely
consumed
2NH3 --&gt; N2 + 3H2
The decomposition of ammonia
is an example of a zero order
reaction
Experimental data tells us the
order of the reaction
Rate Laws and Order
The rate law for a reaction is experimentally determined and
cannot be known simply by looking at the balanced chemical
equation for the reaction.
Overall Reaction Order
•We have discussed reaction order with respect
to a single reactant, but we must also be able
to describe the rate law for reactions that
depend on more than one reactant
•Anabolic reactions or synthetic reactions
•To describe a reaction like this, we have to
include the concentration of both reactants in
the rate law
Example: Overall Reaction Order
• Let’s look at the reaction between:
Ca(OH)2 (aq) + 2HCl (aq) 
CaCl2 (s) + 2H2O (l)
• Because we are making solid CaCl2, the rate
depends on the concentration of Ca2+ and Cl-.
Rate of Consumption of Ca(OH)2 = k[Ca(OH)2][HCl]2
And the overall reaction order is the sum of the exponents = 1+2
= 3.
Odd Rate Laws
•
•
Experiments have provided data for reactions that have nonstandard reaction orders.
These non-standard orders tell us specific things about the
reaction
1)
2O3 (g) --&gt; 3O2 (g)
The presence of O2 slows the reaction down significantly
2)
3SO2 (g) + O2 (g) --&gt; 3SO3 (g)
[O 3 ]2
Rate = k
= k [O 3 ]2 [O 2 ]1
3
[O 2 ]

Rate = k
[SO 2 ]
[SO 3 ]
1
2

= k [SO 2 ] [SO 3 ]
1
2

Integrated Rate Laws
• A rate law by itself is interesting , but
not terribly informative
• To make the laws useful, we need them
to tell us the concentration of reactants
or products at any time after the
reaction begins
• An Integrated Rate Law does this
(I guess)
Integrated Rate Law for a Zero Order
Reaction
• We want to find the difference in the concentration of
reactant A from its initial value, [A]0
• We know that this difference will be proportional to
the time elapsed since the reaction started.
– Why?
– The rate constant is the proportionality constant
[A]0 - [A]t = kt
or
[A]t = [A]0 - kt
Integrated Rate Laws for First Order
Reactions
[A] t 
ln 
 = - kt
[A] 0 
(for when you want k)
[A] t = [A] 0 e -kt
(for when you are given [A]
0
and want [A] t )

Exponential decay plot
The rate decreases as more and more
reactant is used up

Confirming that a Reaction is First
Order
In order to confirm that a reaction is truly first order, we
need to plot ln[A]t as a function of t
(does everyone understand what I mean by that?)
[A] t = [A] 0 e -kt
ln[A] t = ln[A] 0 - kt
y
= b + mx
We should see a straight
line!
Half Lives of First Order Reactions
• The half life, t1/2, of a substance is the time
needed for its concentration to decrease by
one half.
• We use half lives in:
–
–
–
–
Environmental Chemistry
Nuclear Science
Biochemistry
Pharmacology
Half Lives of First Order Reactions
• The higher the value of k, the higher the rate.
– The amount of time necessary to decrease the
reactant concentration by 1/2 is inversely
proportional to k
ln2
t1/2 
k

The half life for first
order reactions is
constant
Second Order Integrated Rate Laws
Remember:
The rate law for a second order reaction is
Rate of consumption of A = k[A]2
The Integrated Rate Law is:
1
1

 kt
[A] t [A] 0
When we know [A]t and [A]0
or
[A] 0
[A] t 
1 kt[A] 0
When we know [A]0 and want [A]t


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