Chapter 12 Chemical Kinetics. The study of reactions rates Thermodynamics – does a reaction take place? Kinetics – how fast does a reaction proceed?. Chemical Kinetics. The study of reaction rates
The study of reactions rates
Thermodynamics – does a reaction take place?
Kinetics – how fast does a reaction proceed?
The study of reaction rates
Spontaneous reactions---is the tendency for the reaction to occur but it does not imply how fast.
Ex. Diamond will spontaneously turn into graphite --- eventually
A goal of chemical kinetics is to understand the steps by which a reaction takes place.
The series of steps is called the reaction mechanism.
If we understand the mechanism, we can find ways to facilitate the reaction
Particles have to collide to react
They have to hit hard enough
Things that increase this increase rate
High temps – faster reaction
High concentration – faster reaction
Small particles = greater surface area – faster reaction
The brackets mean concentration (Molarity)
rate = -
N2 + 3H2 2NH3
N2 + 3H2→ 2NH3
N2 + 3H2→ 2NH3
N2 + 3H2→ 2NH3
[Br2]final – [Br2]initial
average rate = -
tfinal - tinitial
instantaneous rate = rate for specific instance in time
Rate of NO2 = 2.4 x 10-5 mol/L•s
Rate of NO = 8.6 x 10-6 mol/L•s
Rate of O2 = 4.3 x 10-6 mol/L•s
Notice the rate of NO is twice that of O2. This makes sense since twice as much NO is produced according to the reaction.
We looked at the reaction
2NO2 (g) 2NO(g) + O2 (g)
But we need to understand that the reverse happens too.
2NO(g) + O2 (g) 2NO2 (g)
Chemical reactions ARE reversible
When forward and reverse reaction rates are equal, it is called chemical equilibrium. When this occurs, there will be NO changes in the concentrations of reactants and products.
in the reaction depends on the difference in the rates of the forward and reverse reactions.
If you choose conditions where the reverse reaction can be neglected. Then the reaction rate will depend only on the concentrations of the reactants. The rate for the decomprxn is
This shows that the rate depends on the concentration of the reactants…this is the rate law expression.
k = the rate constant
n = order of the reactant
both must be determined by experiment
(although n can be an integer or a fraction, we will typically look at positive integer orders in this book.)
The question is which reactant or product do we choose for defining the “rate” in the rate equation:
The value of the rate constant, k, depends on how the rate is defined.
Differential rate laws – once you know the value of n – the rate law expresses how the rate depends on concentration. Often just called “the rate law” – rate as a function of concentration.
Integrated rate law – expresses how concentration depends on time
Once you find one experimentally, you know the other. The one you find experimentally is based on which is easier to collect data.
aA + bBcC + dD
Rate = k [A]x[B]y
Reaction is xth order in A
Reaction is yth order in B
Reaction is (x +y)th order overall
The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some power.
2N2O5 4NO2 + O2
Rate = k [N2O5]n
Here’s some data
Notice that the concentration of N2O5 is halved, the rate is also halved. This means that the rate is completely dependent on concentration of N2O5 to the FIRST power.
Notice: It is NOT based on the coefficient from the reaction.
The initial rate is the instantaneous rate found immediately after the reaction has begun.
The experiment must be run several times with various initial concentrations
The initial rate is found for EACH “run”
Then compare rates to determine the form of the rate law.
The general form of the rate law
We need experimental data to determine the values of n and m
Compare: [NO2-] doubles as the rate doubles there fore m = 1
Here’s the math as a ratio to find m
This means that “m” must be 1
Do this again for “n” with rates 2 & 3
Again, when the [NH4+] doubles so does the rate n = 1
Which mean “n” must be 1 and the rate law is
The rate law is first order for both reactants with an overall reaction order of 2
The reaction order is the sum of the orders for the various reactants
With all this info you can now calculate the rate constant for this reaction.
Pick ANY one of the experiments and substitute and solve for k.
We’ll do the same one as the book. But you could choose either!
The orders of each reactant, the overall reaction order, and the value of the rate constant.
So far we’ve looked at rate as a function of reactant concentrations.
Integrated rate laws relate concentration to reaction time.
Let’s look at reactions with a single reactant.
What is the basic rate law?
First Order - double the concentration… double the rate
rate law integrated if n=1
Shows how concentration of A depends on time. If [A]o &k are known [A] at any time can be calculated.
If plotting ln[A] vs. time gives a straight line where k is the slope, then it proves the reaction is first order.
Often shown as a ratio.
Half life is the time required for a reactant to reach half its original concentration.
For a first order reaction
Starting with the basic rate law
Double the concentration…quadruple the rat OR triple the concentration …nine times the rate.
Integrated law when n=2
If you plot versus t and get a straight line with a slope of k…the reaction is proven to be second order.
The equation for 2nd order half life
For second order reactions, t1/2 is dependent on [A]0. For first order reactions t1/2 is independent on [A]0.
For a 2nd order reaction each successive ½ life is double the preceding one.(ex. The 1st ½ life of C4H6 reacting to form a dimer is 1630 sec, but the 2nd ½ life takes 3570 seconds.)
The reaction has a constant rate.
When n=0 Rate=k
Integrated rate law when n=0
Most zero order reactions are when a substance such as a metal or an enzyme is required for the reaction to occur.
Most often the kinetics of a complicated reaction can be studied by opbserving the behavior of one reactant at a time.
If one reactant has a concentration that is much smaller than the others, then it is used to determine the order of the reaction in that component.
The type of rate law depends on the type of data that is most conveniently collected. Once we have one type of rate law we can determine the other.
The most common method for differential rate law is the method of initial rates.
For integrated rate laws concentrations are measured at various values of t.
Most chemical reactions occur by a series of steps called reaction mechanisms.
The whole purpose of kinetics is to learn about the steps.
Termolecular are rare. The probability of 3 molecules colliding at the same time is extremely small.
First requirement is met. Overall reaction is obtained from adding the elementary steps.
The rate determining step must be found.
Multistep reactions always have one step that is much slower.
The rate determining step is the slowest step in the sequence of the steps leading to product formation.
The RDS should predict the same rate law that is determined experimentally.
if you assume the first step is the rate determining step the rate law would be:
This is the experimentally determined rate therefore, we can say this mechanism satisfies both requirements.
The experimentally determined rate law is
Is the mechanism below acceptable?
Based on the idea that molecules must collide to react
Concentration and temperature affect collisions.
Collisions must be hard enough to cause a reaction.
The minimum energy required to initiate a chemical reaction.
Rate is NOT determined by E but rather by the size of Ea
The higher the activation energy, the slower the reaction at a given temperature.
The observed reaction rate is considerably smaller than the rate of collisions with enough energy to overcome the barrier.
This is because even though the collision has enough energy it still does not produce a reaction.
Arrhenius said that the number of collisions with the necessary energy increases exponentially with temperature.
p= steric factor (the fraction of collisions with efffective orientations)
= the fraction of collisions with sufficient energy to produce a reaction.
A, the frequency factor, replaces zp
And taking the natural log of each side gives:
Ln(k) versus 1/T yields a straight line.
The slope is Ea/R and y-intercept is ln(A)
The fact that most rate constants obey the Arrhenius equation indicates that the collision model is physically reasonable.
Given the reaction and data below, calculate the value of Ea for the reaction.
Plot the ln(k) versus 1/T & find slope
If you find the rate constant at only two temperatures and subtract the first from the second equation, you’d get the formula:
Sometimes raising the temperature to speed up a reaction is not feasible.
Catalysts are often used. Catalysts speed up a reaction without being used up by the reaction.
Catalysts lower the reaction energy, but do not affect the E.
Reaction of the adsorbed substances. New C-H
bonds are formed.
Escape or desorption of the products. New
Catalysts will speed up a reaction, but only to a certain point.
Past a certain point, adding more reactants won’t change the rate. Rate increases until the active sites of catalyst are filled.
Then rate is independent of concentration.