In chemistry, we care not only about what reacts, but also how fast. Black powder explodes in a flash, while the sugar in your coffee never seems to dissolve fast enough. We try to speed up environmental cleanup and retard rust and aging. In other words, rates matter!

A B

rate = -D[A]Dt

rate = D[B]Dt

time

Definition of Reaction Rate• The reaction rate is the increase in molar

concentration of a product of a reaction per unit time.

• It can also be expressed as the decrease in molar concentration of a reactant per unit time.

Outline: Kinetics

Reaction Rates How we measure rates.

Rate Laws How the rate depends on amounts of reactants.

Integrated Rate Laws How to calc amount left or time to reach a given amount.

Half-life How long it takes to react 50% of reactants.

Arrhenius Equation How rate constant changes with T.

Mechanisms Link between rate and molecular scale processes.

Calculating reaction rates

• Average reaction rate = Δ quantity/ Δ time

• Δ quantity = final amount - initial amount

• Δ time = final time - initial time

Sample question

• In a reaction between butyl chloride (C4H9Cl) and water the intial concentration of butyl chloride was 0.220M at time 0.00 s and the concentration at time 4.00 s was 0.100M. Calculate the average reaction rate over this time period.

• Known: t1 = 0.00 s C4H9Cl at t1 = 0.220M t2 = 4.00 s C4H9Cl at t2 = 0.100M

• Unknown: average reaction rate = ? M/s

Answer

• Average reaction rate = Δ quantity / Δ time

• = 0.100 M - 0.220 M / 4.00 s - 0.00 s

• = (0.120 M)/4.00 s

• = 0.0300 M/s

Why do reactions occur?

Because molecules collide. When molecules collide with enough energy, they will transfer electrons and create new products.

It is pretty obvious that if you have a situation involving two species they can only react together if they come into contact with each other. They first have to collide, and then they may react.Why "may react"? It isn't enough for the two species to collide - they have to collide the right way around, and they have to collide with enough energy for bonds to break.

(The chances of all this happening if your reaction needed a collision involving more than 2 particles are remote. All three (or more) particles would have to arrive at exactly the same point in space at the same time, with everything lined up exactly right, and having enough energy to react. That's not likely to happen very often!)

Of the collisions shown in the diagram, only collision 1 may possibly lead on to a reaction.

• Rates of chem rxns are related to the properties of atoms, ions, and molecules through a model called collision theory

• According to collision theory, atoms, ions, and molecules can react to form products when they collide– provided that the particles have enough kinetic

energy

Collision Theory

• Amount of energy required to start a reaction. Some require small amounts and others require large amounts of energy.

• Think about getting up in the morning. Have you every felt like not getting up?

• Sugar won’t break down until heat is added.

The energy required to get the products can be seen in the graph below. In most reactions, energy must be added to the system to get the reaction started. Once enough energy is present, the reaction will proceed on its own.

A reaction requiring energy is very much like pushing a rock up a hill, only to have it fall down the other side on its own.

The energy required to start the reaction is called the activation energy (Ea), and is the uphill part of the graph.

Activation EnergyEven if the species are orientated properly, you still won't get a reaction unless the particles collide with a certain minimum energy called the activation energy of the reaction.Activation energy is the minimum energy required before a reaction can occur. You can show this on an energy profile for the reaction. For a simple over-all exothermic reaction, the energy profile looks like this:

If the particles collide with less energy than the activation energy, nothing important happens. They bounce apart. You can think of the activation energy as a barrier to the reaction. Only those collisions which have energies equal to or greater than the activation energy result in a reaction.

Note:  The only difference if the reaction was endothermic would be the relative positions of the reactants and products lines. For an endothermic change, the products would have a higher energy than the reactants, and so the green arrow would be pointing upwards, as seen below (c). It makes no difference to the discussion about the activation energy.

Exothermic reaction and endothermic reactions

Factors Affecting the Rate of a Reaction• Concentration

• Temperature

• Pressure/Surface Area

• Catalysts

For many reactions involving liquids or gases, increasing the concentration of the reactants increases the rate of reaction. In a few cases, increasing the concentration of one of the reactants may have little noticeable effect of the rate.

Don't assume that if you double the concentration of one of the reactants that you will double the rate of the reaction. It may happen like that, but the relationship may well be more complicated.

The higher the concentration, the more molecules in the solution. If there are more molecules, there is a higher chance that they will collide and cause a reaction.

Limiting Reactant

• Sometimes there aren’t enough reactants to use everything up. One of the substances used in the reaction is used up before the other.

• Suppose you have 20 slices of bread and 15 slices of cheese to make sandwiches. Which will run out first?

As you increase the temperature the rate of reaction increases. As a rough approximation, for many reactions happening at around room temperature, the rate of reaction doubles for every 10°C rise in temperature.You have to be careful not to take this too literally. It doesn't apply to all reactions.

Even where it is approximately true, it may be that the rate doubles every 9°C or 11°C or whatever. The number of degrees needed to double the rate will also change gradually as the temperature increases.

The higher the temperature, the faster the molecules will move and the higher energy each molecule will have. The faster the molecules move, the higher chance they will collide and cause a reaction.

The higher the pressure, the faster the molecules will move and the closer they will be together, increasing the chance of a collision and reaction.

The higher the surface area of a solid, the higher the chance of a molecule hitting it and reacting. One solid piece will have less surface area than several pieces and will react less.

Catalysts, typically known as enzymes, provide a way to lower the amount of energy needed to start a reaction without actually becoming a part of the reaction itself.

A catalyst is a substance which speeds up a reaction, but is chemically unchanged at the end of the reaction. When the reaction has finished, you would have exactly the same mass of catalyst as you had at the beginning.

Enzyme action (lock-and-key model).

Collisions only result in a reaction if the particles collide with enough energy to get the reaction started. This minimum energy required is called the activation energy for the reaction.

To increase the rate of a reaction you need to increase the number of successful collisions. One possible way of doing this is to provide an alternative way for the reaction to happen which has a lower activation energy.

Adding a catalyst has exactly this effect on activation energy. A catalyst provides an alternative route for the reaction. That alternative route has a lower activation energy. Showing this on an energy profile:

Catalysts• Catalysts help speed up a reaction. Your body uses

enzymes to help breakdown food. The enzymes help your body breakdown food faster.

• Your body has enzymes to break down proteins, carbohydrates, and fats. They help speed up the reaction. Without these enzymes food would take 24 hours to breakdown in your stomach.

• Can also be heat or energy. They are not involved in the reaction, just help it get started

A word of caution! "A catalyst provides an alternative route for the reaction with a lower activation energy."

It does not "lower the activation energy of the reaction". There is a subtle difference between the two statements that is easily illustrated with a simple analogy.

Suppose you have a mountain between two valleys so that the only way for people to get from one valley to the other is over the mountain. Only the most active people will manage to get from one valley to the other.

Now suppose a tunnel is cut through the mountain. Many more people will now manage to get from one valley to the other by this easier route. You could say that the tunnel route has a lower activation energy than going over the mountain.

But you haven't lowered the mountain! The tunnel has provided an alternative route but hasn't lowered the original one. The original mountain is still there, and some people will still choose to climb it.

In the chemistry case, if particles collide with enough energy they can still react in exactly the same way as if the catalyst wasn't there. It is simply that the majority of particles will react via the easier catalyzed route.

Inhibitors

• Inhibitors slow down a reaction. They don’t stop the reaction completely

• Some foods have chemicals called preservatives to prevent it from spoiling (going bad).

• The brown bottle of peroxide prevents the liquid inside from breaking down.

• The rate of a rxn depends in part on the concentration of the reactants– Concentration is a measure of how much stuff is

available to react• For a rxn in which reactant A reacts to form

product B in 1 step, you can write a simple rxn eqn: A B

• The speed that A forms B is dependent on how the conc of A changes over time– As the conc of A decreases the rate of the rxn

generally decreases

Rate Laws

Rate =DADt

• You can express the rate as the change in A (DA) with respect to the change in time (Dt)

• The rate of disappearance of A is proportional to the concentration or mol-arity (# of moles/Liter) of reactant A

• This proportionality can be expressed as a constant (k) multiplied by the concentration of reactant A

k•[A]

Rate Laws

• This mathematical expression is an example of a rate law

– An expression which relates the rate of a rxn to the conc of reactants

• The magnitude of the rate constant (k) depends on the conditions at which the rxn is conducted

– If reactant A reacts to form product B quickly, the value of k will be large

– If reactant A reacts to form B slowly, the value of k will be small

Rate Laws

• Rxns are classified as either zero-order, first-order, second-order, or mixed order (higher order) rxns.

– The rate of chemical rxns and the size of the rate constant (k) is dependent on the “order” of the rxn

• Zero-Order Rxns– (Order = 0) have a constant rate. This rate is

independent of the conc of the reactants. The rate law is: k, with k having the units of M/sec.

Rate Laws

In general:

rate of reaction = change in concentration time required for change

If 0.048 moles of magnesium (Mg) completely reacts with acid in 20 sec, what would be the rate of reaction in units of mole per second?

0.048 moles = 0.0001 mol/sec 20 sec

Try: It was found that 7.0 g of zinc metal reacted completely with acid in 30 sec. Calculate the average rate of this reaction.

And, of course, when something matters in chemistry, there is some kind of mathematical formula involved.

Rate of Reaction for a single compound decomposing:

A B + C

rA = -k[A] rA = rate

[A] = concentration of A

k = rate constant

k is by nature positive. But since the amount of reactant is decreasing, we make it negative.

• First-Order Reactions– (order = 1) has a rate proportional to the

conc of one of the reactants. A common example of a first-order rxn is the phenomenon of radioactive decay. The rate law is: k[A]1 (or B instead of A), with k having the units of sec-

1

Rate Laws

Now, suppose 2 molecules collide to form a new product. The rate formula changes:

A + B products

r = -k[A][B]

For example:

NO2 + O2 NO + O3

r = -k[NO2][O2]

In reactions of this type, you will be given information to solve for concentration, k, or r.

The Overall Rate of Reaction Formula:

aA + bB products

r = -k[A]a[B]b

Note: When talking about rate of reaction, the products don’t matter unless the reaction is reversible (more on that later).

For example:

The concentration of zinc metal is 3M, the concentration of HCl is 8M. k for this reaction is 1.08. What is the rate of reaction?

Zn + 2HCl ZnCl2 + H2

r = -k[Zn][HCl]2 = (-1.08)(3M)(8M)2 = -207.36 M/sec

• Second-Order Reactions– (order = 2) has a rate proportional to the conc

of the square of a single reactant or the product of the conc of two reactants.

– Rate law =k[A]2 (or substitute B for A or k multiplied by the concentration of A, [A], times the concentration of B, [B]), with the units of the rate constant M-1sec-1

Rate Laws

• Rate laws can only be determined experimentally.– It is not an easy process to determine the order of

the reaction or the rate constant– Unless you determine a class of rate laws called

Integrated Rate Laws.

Determining Rate Laws

o Integrated Rate Laws are determined by graphing a series of rate data and analyzing the graph looking for a specific pattern.

• The Zero order integrated rate law shows that its rate is independent of the [A]– Where [A] vs. t is a straight

line with a slope of - k

Integrated Rate Law: Zero Order

0[A]kt [A]

Zero Order

Rate Law kRate

Constant Slope = - k Integrated Rate Law [A] = -kt + [A]0

Graph [A] versus t ½ Life t ½=[A]0/2k

• The first order integrated rate law can be used to determine the concentration of [A] at any time.– It can be determined graphically

• Where – y = ln[A]– x = time

Integrated Rate Law: First Order

• m = -k• b = ln[A] 0

First Order

Rate Law k[A]Rate

Constant Slope = - k Integrated Rate Law ln[A] = -kt + ln[A]0

Graph ln[A] versus t ½ Life t ½=0.693/k

• The second order integrated rate law can be used to determine the concentration of [A] at any time.– It can be determined graphically

• Where – y = 1/[A]– x = time

Integrated Rate Law: Second Order

• m = k• b = 1/[A] 0

Second Order

Rate Law k[A]2

Rate Constant Slope = k Integrated

Rate Law

Graph 1/[A] versus t ½ Life t ½=1/k[A]0

0[A]1 kt[A]

1

• In some kinds of rxns, such as double replacement, 2 substances react to give products

• The coefficients in the eqn for such a rxn can be represented by lower-case letters: aA + bB cC + dD

• For a 1 step rxn of A+B, the rate of rxn is dependent on the concentrations of reactants A & B

• It’s rate law would follow the eqn:

Rate = k[A]a[B]b

Rate Laws

o When each of the exponents a & b in the rate law equals 1, the rxn is said to be 1st order in A, 1st order in B, & 2nd order overall

o The overall order of a rxn is the sum of the exponents for the individual reactants

o If enough info were available, you could graph all the energy changes that occur as the reactants are converted to products in a chem rxn

Rate Laws

o Such a graph would be called a rxn progress curve

o The simplest would be a one-step, elementary rxn• Reactants form products in a

single step• 1 activated complex• 1 energy peak

Rate Laws

Overall Reaction Order• We can use the method of initial rates to

determine the overall reaction order.• Examine the experimental data below to

determine the reaction order.

Overall Reaction Order• Recall the general rate law is• Rate = k[A]m[B]n • Looking at trial 1 and 2 we see doubling A doubles the

initial rate. Therefore the reaction is 1st order with A concentration (m=1).

• Looking at trials 2 and 3 we see doubling B quadruples the initial rate. Therefore the reaction is 2nd order with B (n=2).

• The overall rate is 3rd order which is the sum of m and n.

Your Turn

• Determine the general rate law formula and overall reaction order based on the experimental data below.

• For a more complex rxn, or a higher order rxn, the rxn progress curve resembles a series of hills & valleys

– The peaks correspond to the energies of the activated complexes

– Each valley represents an intermediate product which becomes a react of the next stage of the rxn

• Intermediates have a significant lifetime compared with an activated complex

– They have real ionic or molecular structures and some stability

Reaction Mechanism

• Intermediates do not appear in the overall eqn for a rxn

• For example in the following overall rxn:

H2(g) + 2ICl(g) <==> I2(g) + 2HCl(g)

Reaction Mechanism

o This reaction is not exactly accurate• There is an intermediate reaction in

between the reactants and products.

1) H2(g) + 2ICl(g) ICl(g) + HCl(g) + HI(g) 2) ICl(g) + HCl(g) + HI(g) I2(g)

+2HCl(g)

Reaction Mechanism

o If a chem rxn proceeds in a sequence of steps, the rate law is determined by the slowest step because it has the lowest rate.

• The slowest-rate step is called the rate-determining step

o Consider this rxn: NO2 + CO NO + CO2

• the rxn is believed to be a 2 step process following this mechanism

Reaction Mechanism

Step 1: NO2 + NO2 NO + NO3Step 2: NO3 + CO NO2 + CO2

SLOWFAST

o In the 1st step • 2 molecules of NO2 collide,

forming the intermediate NO3. • The NO3 species collides with a

molecule of CO and reacts quickly to produce 1 molecules each of NO2 and CO2

o The 1st step is the slower of the 2 steps and is therefore the rate-determining step

Reaction Mechanism

Its rate law: R=k[NO2]2

The rate determining step and the rate law are both determined

experimentally

Reaction Mechanisms

• Many chemical reactions consist of a sequence of two or more reactions

• Such is evident in the earth’s stratosphere where 2O3 3O2

• This is the overall reaction after three steps occur which is started by intense UV radiation from the sun liberates chlorine atoms from certain compounds.

Reaction

• Elementary step: Cl + O3 O2 + ClO

• Elementary Step: O3 O2 + O

• Elementary Step: ClO + O Cl + O2

• Complex reaction: 2O3 3O2

Reaction Mechanisms continued• The destruction of ozone on the previous slide is a

complex reaction

• The complete sequence of elementary steps that make up a complex reaction is known as a reaction mechanism.

• In a reaction mechanism some substances are produce and remain while others known as intermediates are produced by one reaction but consumed in a subsequent reaction.

Rate determining step

• A complex reaction can only proceed as fast as its slowest step

• Meaning the slowest step limits the rate of the overall reaction

• The slowest reaction is known as the rate-determining step.

Outline: Kinetics

First order Second order Second order

Rate Laws

Integrated Rate Laws

complicated

Half-life complicated

k(T)