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 time2. 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

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Rate = -Δ[Reactants]

Δt = -

[R]2 −[R]1

t 2 − t1

⎛

⎝ ⎜

⎞

⎠ ⎟ Note : The minus sign

Rate = Δ[Products]

Δt

⎛

⎝ ⎜

⎞

⎠ ⎟ =

[P]2 − [P]1

Δt

Reaction Rate and Stoichiometry

• In the example:

2NH3 (g) --> 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 --> cC + dD

The Unique Average Rate =

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−1

a

⎛

⎝ ⎜

⎞

⎠ ⎟Δ[A]

Δt

⎛

⎝ ⎜

⎞

⎠ ⎟= −

1

b

⎛

⎝ ⎜

⎞

⎠ ⎟Δ[B]

Δt

⎛

⎝ ⎜

⎞

⎠ ⎟=

1

c

⎛

⎝ ⎜

⎞

⎠ ⎟Δ[C]

Δt

⎛

⎝ ⎜

⎞

⎠ ⎟=

1

d

⎛

⎝ ⎜

⎞

⎠ ⎟Δ[D]

Δt

⎛

⎝ ⎜

⎞

⎠ ⎟

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 --> 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 concentrationEvery 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 ReactionIf we look at another reaction, we’ll find that there may be a different dependence on reactant concentration:

2NO2 (g) --> 2NO (g) + O2 (g)

Rate vs. [NO2]

Note shape of plot!

Rate vs. [NO2]2

Note shape of plot!

Order of Reaction2NO2 (g) --> 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

O=N + 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

Rate = Rate constant [concentration of reactant A]a

Or

Rate = Rate constant [concentration of reactant B]b

aA + bB --> cC + dD

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 --> 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 non-

standard reaction orders.• These non-standard orders tell us specific things about the

reaction

1) 2O3 (g) --> 3O2 (g)

The presence of O2 slows the reaction down significantly

1) 3SO2 (g) + O2 (g) --> 3SO3 (g)

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Rate = k [O3]2

[O2]3 = k [O3]2[O2]−1

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Rate = k [SO2]

[SO3]1

2

= k [SO2] [SO3]−

1

2

Integrated Rate Laws

• A rate law by itself is interesting (I guess), 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

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

€

ln[A]t

[A]0

⎛

⎝ ⎜

⎞

⎠ ⎟ = - kt (for when you want k)

[A]t = [A]0e-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?)

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[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

€

t1/2 =ln2

k

The half life for first order reactions is constant

Second Order Integrated Rate Laws

€

1

[A]t

−1

[A]0

= kt or [A]t =[A]0

1+ kt[A]0

When we know [A]t and [A]0 When we know [A]0 and want [A]t

Remember:

The rate law for a second order reaction is

Rate of consumption of A = k[A]2

The Integrated Rate Law is: