AP Chemistry - Chemical Kinetics
Rates of Reaction
Introduction: The rate of a reaction has a special meaning for chemists.

Definition: The rate of a reaction is usually expressed in terms of a change in concentration of one of the participants per unit time.

rate = [ ]

The rate of a reaction is the speed at which reactants are converted into products. Experiments show that for most reactions, the []'s of all participants change the most rapidly at the beginning of the reaction. That is, the [products] shows the greatest rate of increase and the [reactants] shows the greatest rate of decrease at the beginning. This means that the rate of a reaction changes with time. Therefore a rate must be specified with a specific time unit.
A + B ---> AB
Methods of Measuring Reaction Rates
Techniques used to measure concentration vary with the reaction and available apparatus. Titrations can be done on reactions in solution. Changes in colour can be indications of concentration change and can be measured in a spectrometer. Density and electrical conductivity may vary with concentration. For gases a pressure change may tend to indicate a concentration change. The rate of a reaction is usually measured as a function of the concentration of a reactant or product over time. This does not have to true in all cases. The main feature of a rate is that it must be able to be measured physically. i.e. pressure, temperature, concentration, colour. 
Factors That Affect Reaction Rates
The following are the factors that will affect the rate of a reaction:
1. Nature of the Ions Being Used
MnO4- added dropwise to                    MnO4- added dropwise to
acidified Fe2+ ions                                acidified C2O42- ions

Results:                                                Results:


The only difference is the nature of the reactants. The ferrous ion is simple and monatomic while the oxalate ion is polyatomic covalent in nature. In general reactions between simple ions such as Ag+ and Cl- which combine in a 1-1 mole ratio, are almost instantaneous. Experimental measurements show that most of these reactions occur in about 1/1,000,000th of a second. The nature of the reactants affects the rate of a reaction. Generally, a more complicated species will react more slowly than a simple ion.
2. Concentration of Reactants [reactants]
The concentration of reactants affects the rate of a chemical reaction but exactly how will be dealt with in the Iodine-Clock experiment.
3. Temperature Increases and Decreases
The temperature at which an reaction is carried out affects the rate of a chemical reaction but exactly how will be dealt with in the Iodine-Clock experiment.
4. Catalysts
Demo: MnO4- and Fe2+       MnO4- + C2O42-          MnO4- + C2O42- + Mn2+ ions


Substances which affect the reaction rate without being consumed by the overall reaction are called catalysts. Catalysts may be consumed during some intermediate step in the reaction and then are regenerated in a subsequent step.
Starch, Water & Iodine                                     Starch, Water, Iodine and Ptyalin

Sugar Cube                                                       Sugar Cube with Cigarette ash


5. Surface Area
This becomes important in heterogeneous reactions:   Heterogenous reactions are ones that have mixed phases.

eg. Zn(s) + 2 HCl(aq) ----> ZnCl2(aq) + H2(g)

4 Fe(s) + 3 O2(g) ----> 2 Fe2O3(s)

Starch pile                                                   Starch powder

As the surface area increases the rate of reaction should also increase. Dust and grain silo explosions are good examples of surface area reactions.

Activation Energy and the Activated Complex
This is the energy that must be reached by 2 colliding molecules before a reaction can take place.
If enough energy is supplied to the boulder to push it over the hill (activation energy barrier), it will spontaneously roll down the mountain, releasing energy as it moves to a lower state of potential energy. The rate of boulders being pushed over the cliff will depend on the height of the activation energy barrier.
Collision Theory
The rate of a reaction depends on two factors.
1) The number of collision per unit time between the reacting species.
2) The fraction of these collisions that are successful in producing a mew molecule.
Collision Geometry
If two or more molecules collide but are not orientated correctly then no reaction will take place.

For a reaction to occur, molecules must collide not only with sufficient energy but with the proper orientation.
Why is there an Activation Energy Barrier?
During the course of a reaction considerable redistribution of electrons may occur. Consider, for example, the reaction of CH3Br with Cl- in water at 298K.
As the bimolecular reaction occurs (i) there is angle bending: the initially pyramidal CH3 grouping become planar; (ii) there is bond-making and breaking: a partial CBr bond is weakened. The energy released by the formation of the partial CCl bond will not fully compensate for the other two (endothermic) changes and yet there is no lower energy pathway from reactants to products. The reactants can get to the point of highest potential energy (the "activated complex" or "transition state" - in curly braces above) only if they initially have sufficient kinetic energy to turn into the potential energy of the activated complex. The activated complex can not be isolated; it is that arrangement of reactants which can proceed to products without further input of energy.
It is often useful to make a schematic plot of the total energy (enthalpy) of the combined reactant molecules during the various stages of the chemical reaction. The points on the plot which we can pinpoint are:
(i) the difference between the average energy of the products and the average energy of the reactants, Hreaction (~ + 25 kJ mol- for CH3Br + Cl- ) and
(ii) the activation energy (obtained experimentally; 103 kJ mol- for CH3Br + Cl-).
If we assume the total energy varies smoothly with the course of the reaction we obtain the following "energy profile":
It is important to note that there will be more than one way for the reactants to interact and so pass to the products. However, there can only be one minimum energy pathway and essentially all of the reaction will occur via this pathway.
Effect of Catalysts on the Activation Energy
Catalysts provide a new reaction pathway in which a lower A.E. is offered.
A catalyst increases the rate of a reaction by lowering the activation energy so that more reactant molecules collide with enough energy to surmount the smaller energy barrier.
Reaction Rate Law
Law of Mass Action: The rate of a chemical reaction is proportional to the product of the concentrations of the reactants.
For any general reaction
aA + bB ------->
the rate law expression is: r [A]m[B]n
where A and B represent the molar concentrations of A and B. m and n are the powers to which the concentrations must be raised. k is a constant of proportionality known as the rate constant. Data show that the rate constant is not affected by [] (concentration) changes but does vary with temperature changes. The values of 'm' and 'n' are not the stoichiometric numbers obtained from the balanced equation; unless; the equation is deemed to be a one-step reaction, but more on this latter. The only valid way to obtain the values of m and n is to use experimental data.
The exponents, m and n may be zero, fractions or integers.
The sum of the exponents is called the reaction order.
eg. H2(g) + I2(g) -----> 2 HI(g)
r = k[H2][I2]
This is a second order reaction. The sum of the components is 2.
In this case the values of 'm' and 'n' just happen to be the same as the stoichiometric numbers in the balanced equation. Therefore it must be a one-step reaction. i.e., there is only the one reaction step needed to convert reactants into products.
This is not always the case and a simple reaction may proceed through a number of intermediate steps. 
Experimental Determination of Reaction Order
The rate is usually given in terms of moles/Litre seconds but this is not always the case. You will have to be very careful about the units of each participant reactant in order to get the proper units for the rate constant itself.
Before we can determine the value of the rate constant 'k', we need to find the exponential value for each participant. To find the relationship of one reactant it is necessary to keep the other reactant(s) constant so look at the following reaction and data table:
NO + H2 -----> HNO2
(balance it if you'd like, but the balanced equation will not give you the exponential values unless the equation is a one-step reaction).
Rates of reaction between NO and H2 at 800oC
Experiment      NO            H2         Initial Rate of Reaction
Number        moles/L     moles/L        moles/L sec
   1                 0.001      0.004               0.002
   2                 0.002      0.004               0.008
   3                 0.003      0.004               0.018
   4                 0.004      0.001               0.008
   5                 0.004      0.002               0.016
   6                 0.004      0.003               0.024
From the equation we can write a partial rate law as

rate = k[NO]m[H2]n

You have 6 experiments to choose from. Using these 6 experiments you must determine the values of 'm', 'n' and 'k'. There are only two reactants, so choose one to start to work with. We'll start with NO. Choose any two experiments where the concentration of NO changes but the concentration of H2 stays the same. We want to determine how the NO changes the rate! We will choose experiments 1 and 2.
Using experiments 1 and 2 you can see that the concentration jumps from 0.001 to 0.002 moles/L. IT DOUBLES!! Take a look at the rates for these same experiments. The rate jumps from 0.002 to 0.008 moles/L seconds. IT QUADRUPLED!!.
The exponential constant 'm' for the [NO] is the mathematical relationship between these two values. i.e.
2m = 4 therefore m = 2 because 22 = 4
To confirm this, compare experiments 1 and 3. The concentration of the NO gas TRIPLES. The rate jumps by a factor of nine. Therefore
3m = 9 so m = 2 because 32 = 9
The rate law expression can now be updated to: rate = k[NO]2[H2]n
We will now use experiments where the [NO] concentration is kept constant and the [H2] changes.
Look at experiments 4 and 5. The H2 concentration DOUBLES and the rate DOUBLES.
2n = 2 therefore n = 1 since 21 = 2
To confirm this number look at experiments 4 and 6. The H2 concentration TREBLES from 0.001 to 0.003 The rate also TREBLES from 0.008 to 0.024
3n = 3 therefore n = 1 since 31 = 3
So the rate law expression can be rewritten as
rate = k [NO]2 [H2]1
From the sum of the exponents this is a third order reaction.
Now to determine the value of 'k'. 'k' is a constant. It's value should not change (except under temperature changes). Choose any one of the experiments. It should not matter which one.
We will use experiment 1. Using the rate law, above fill in the values from the data table.
0.002 mol/L sec = k (0.001 mol/L)2 * (0.004 mol/L)
0.002 mol/L sec = k * (0.000001 mol2 /L2) * (0.004 mol/L)
0.002 mol/L sec = k * 0.000 000 009 mol3/L3

k =       0.002 mol/L sec
      0.000 000 004 mol3/L3

= 500,000 sec/mol2 L2 or sec mol-2 L-2

Therefore the rate law equation for this reaction is

rate = 500,000 sec mol-2 L-2 [NO mole/L]2 [H2 mol/L] 

Enzymes, Biological Catalysts
enzyme inhibitor               enzyme-inhibitor                 enzyme blocked
molecule + molecules             complex                            from joining
                                                                                               A & B
An inhibitor molecule with a shape simlar to the enzyme's can block the ability of the enyzme to catalyze the reaction of other molecules.
Why Do Catalysts Work?
Solid catalysts have large surface areas and are capable of adsorbing the reactants onto their surfaces. One of the reactants molecules may readily react with the atoms of the catalyst and form an intermediate species. This new intermediate species then reacts readily with the second reactant. The desired product is formed leaving behind the catalyst.
Relationship Between The Activation Energies of Opposing Reactions
Slow reactions have high activation energies. Fast reactions have relatively low activation energies. An endothermic reaction always has a greater activation energy and a slower rate than the opposing exothermic reaction. An increase in the temperature affects the rate of the endothermic reaction more than that of the exothermic reaction.
Reaction Mechanisms
An elementary process is a one-step process in which the product particles are in most cases the direct result of collisions of only 2 reactant particles. There are three particles collisions but they are rare. The chances of 4 or more particles forming a one-step reaction reach infinity. The reaction mechanism for
H2(g) + Cl2(g) ---> 2 HCl(g) is made up of 4 elementary steps.
Rate Determining Step
When a reaction is the result of a series of elementary processes, the rate of the overall reaction is determined by the slowest reaction in the sequence.
eg. Ag+(aq) + Cl-(aq) ---> AgCl(s) 
a simple reaction involving only a single 1 step mechanism therefore very fast.
eg. 2 NO(g) + 2 H2(g) ----> N2(g) + 2 H2O(g) 
This appears to be a 4 particle reaction as written. Impossible!!
The reaction mechanism for the above reaction has been determined to be:
step #1 2 NO + H2 ----> N2 + H2O2 slow since it invovles a rare three particle collision. This is the slowest and therefore is the step that determines the rate of all the other steps.
step #2 H2 + H2O2 ------> 2 H2O fast reaction
Deduction of Rate Laws from Mechanisms
The mechanism of a reaction is the series of elementary steps by which the reaction takes place. We have already seen that in a series of steps there will usually be one (the slowest or rate-determining step) which is slower than the others and which therefore controls the rate of reaction.
If the rate-determining step is the first or the only in a sequence, then the rate law can be written down directly from the stoichiometry of the first step; e.g. the overall reaction
N2O5(g) + NO(g) -----> 3 NO2(g)
There are only two reactants and it is a one-step reaction. Therefore the rate law can be determined to be
rate = k [N2O5][NO]
In an reaction that is not a one-step reaction then you must first determine what the slowest step in the mechanism will be. Then once you've decided on the slowest step, the rate law can be written directly from the slowest step.

Go to the Molecular Rate Law Worksheet