Chapter 14

Chemical Kinetics (part 2)

The Collision Model• Goal: develop a model that explains why

rates of reactions increase as concentration and temperature increases.

• The collision model: in order for molecules to react they must collide.

• The greater the number of collisions the faster the rate.

• The more molecules present, the greater the probability of collision and the faster the rate.

Temperature and Rate

The Collision Model• The higher the temperature, the more

energy available to the molecules and the faster the rate.

• Complication: not all collisions lead to products. In fact, only a small fraction of collisions lead to product.

The Orientation Factor• In order for reaction to occur the reactant

molecules must collide in the correct orientation and with enough energy to form products.

Temperature and Rate

The Orientation Factor• Consider:

Cl + NOCl NO + Cl2

• There are two possible ways that Cl atoms and NOCl molecules can collide; one is effective and one is not.

Temperature and Rate

The Orientation Factor

Temperature and Rate

Activation Energy• Arrhenius: molecules must posses a

minimum amount of energy to react. Why?– In order to form products, bonds must be broken in the reactants.– Bond breakage requires energy.

• Activation energy, Ea, is the minimum energy required to initiate a chemical reaction.

Temperature and Rate

Activation Energy• Consider the rearrangement of methyl

isonitrile:

– In H3C-NC, the C-NC bond bends until the C-N bond breaks and the NC portion is perpendicular to the H3C portion. This structure is called the activated complex or transition state.

– The energy required for the above twist and break is the activation energy, Ea.

– Once the C-N bond is broken, the NC portion can continue to rotate forming a C-CN bond.

H3C N CC

NH3C H3C C N

Temperature and Rate

Activation Energy• The change in energy for the reaction is the

difference in energy between CH3NC and CH3CN.

• The activation energy is the difference in energy between reactants, CH3NC and transition state.

• The rate depends on Ea.• Notice that if a forward reaction is

exothermic (CH3NC CH3CN), then the reverse reaction is endothermic (CH3CN CH3NC).

Temperature and Rate

Activation Energy• How does a methyl isonitrile molecule gain enough

energy to overcome the activation energy barrier?• From kinetic molecular theory, we know that as

temperature increases, the total kinetic energy increases.

• We can show the fraction of molecules, f, with energy equal to or greater than Ea is

where R is the gas constant (8.314 J/mol·K).

RTEa

ef

Temperature and Rate

Activation Energy

Temperature and Rate

The Arrhenius Equation• Arrhenius discovered most reaction-rate data

obeyed the Arrhenius equation:

– k is the rate constant, Ea is the activation energy, R is the gas constant (8.314 J/K-mol) and T is the temperature in K.

– A is called the frequency factor.– A is a measure of the probability of a favorable collision.– Both A and Ea are specific to a given reaction.

RTEa

Aek

Temperature and Rate

Determining the Activation Energy• If we have a lot of data, we can determine Ea

and A graphically by rearranging the Arrhenius equation:

• From the above equation, a plot of ln k versus 1/T will have slope of –Ea/R and intercept of ln A.

ARTE

k a lnln

Temperature and Rate

Temperature and Rate

Determining the Activation Energy• If we do not have a lot of data, then we

recognize

122

1

2121

22

11

11ln

lnlnlnln

lnln and lnln

TTRE

kk

ARTE

ARTE

kk

ARTE

kARTE

k

a

aa

aa

Temperature and Rate

• The balanced chemical equation provides information about the beginning and end of reaction.

• The reaction mechanism gives the path of the reaction.

• Mechanisms provide a very detailed picture of which bonds are broken and formed during the course of a reaction.

Elementary Steps• Elementary step: any process that occurs in a single

step.

Reaction Mechanisms

Elementary Steps• Molecularity: the number of molecules

present in an elementary step.– Unimolecular: one molecule in the elementary step,– Bimolecular: two molecules in the elementary step, and– Termolecular: three molecules in the elementary step.

• It is not common to see termolecular processes (statistically improbable).

Reaction Mechanisms

Multistep Mechanisms• Some reaction proceed through more than one step:

NO2(g) + NO2(g) NO3(g) + NO(g)

NO3(g) + CO(g) NO2(g) + CO2(g)• Notice that if we add the above steps, we get the

overall reaction:NO2(g) + CO(g) NO(g) + CO2(g)

Reaction Mechanisms

Multistep Mechanisms• If a reaction proceeds via several elementary steps,

then the elementary steps must add to give the balanced chemical equation.

• Intermediate: a species which appears in an elementary step which is not a reactant or product.

Reaction Mechanisms

Rate Laws for Elementary Steps• The rate law of an elementary step is

determined by its molecularity:– Unimolecular processes are first order,– Bimolecular processes are second order, and– Termolecular processes are third order.

Rate Laws for Multistep Mechanisms• Rate-determining step: is the slowest of the

elementary steps.

Reaction Mechanisms

Rate Laws for Elementary Steps

Reaction Mechanisms

Rate Laws for Multistep Mechanisms• Therefore, the rate-determining step governs the

overall rate law for the reaction.Mechanisms with an Initial Fast Step

• It is possible for an intermediate to be a reactant.• Consider

2NO(g) + Br2(g) 2NOBr(g)

Reaction Mechanisms

Mechanisms with an Initial Fast Step

2NO(g) + Br2(g) 2NOBr(g)• The experimentally determined rate law is

Rate = k[NO]2[Br2]• Consider the following mechanism

NO(g) + Br2(g) NOBr2(g)k1

k-1

NOBr2(g) + NO(g) 2NOBr(g)k2

Step 1:

Step 2:

(fast)

(slow)

Reaction Mechanisms

Mechanisms with an Initial Fast Step• The rate law is (based on Step 2):

Rate = k2[NOBr2][NO]• The rate law should not depend on the concentration

of an intermediate (intermediates are usually unstable).

• Assume NOBr2 is unstable, so we express the concentration of NOBr2 in terms of NOBr and Br2 assuming there is an equilibrium in step 1 we have

]NO][Br[]NOBr[ 21

12

kk

Reaction Mechanisms

Mechanisms with an Initial Fast Step• By definition of equilibrium:

• Therefore, the overall rate law becomes

• Note the final rate law is consistent with the experimentally observed rate law.

]NOBr[]NO][Br[ 2121 kk

][BrNO][NO][]NO][Br[Rate 22

1

122

1

12

kk

kkk

k

Reaction Mechanisms

• A catalyst changes the rate of a chemical reaction.

• There are two types of catalyst:– homogeneous, and– heterogeneous.

• Chlorine atoms are catalysts for the destruction of ozone.

Homogeneous Catalysis• The catalyst and reaction is in one phase.

Reaction Mechanisms

Homogeneous Catalysis• Hydrogen peroxide decomposes very slowly:

2H2O2(aq) 2H2O(l) + O2(g)• In the presence of the bromide ion, the

decomposition occurs rapidly:– 2Br-(aq) + H2O2(aq) + 2H+(aq) Br2(aq) + 2H2O(l).

– Br2(aq) is brown.

– Br2(aq) + H2O2(aq) 2Br-(aq) + 2H+(aq) + O2(g).– Br- is a catalyst because it can be recovered at the end of the

reaction.

Catalysis

Homogeneous Catalysis• Generally, catalysts operate by lowering the

activation energy for a reaction.

Catalysis

Catalysis

Homogeneous Catalysis• Catalysts can operate by increasing the number of

effective collisions.• That is, from the Arrhenius equation: catalysts

increase k be increasing A or decreasing Ea.• A catalyst may add intermediates to the reaction.• Example: In the presence of Br-, Br2(aq) is generated

as an intermediate in the decomposition of H2O2.

Catalysis

Homogeneous Catalysis• When a catalyst adds an intermediate, the activation

energies for both steps must be lower than the activation energy for the uncatalyzed reaction. The catalyst is in a different phase than the reactants and products.

Heterogeneous Catalysis• Typical example: solid catalyst, gaseous reactants

and products (catalytic converters in cars).• Most industrial catalysts are heterogeneous.

Catalysis

Heterogeneous Catalysis• First step is adsorption (the binding of reactant

molecules to the catalyst surface).• Adsorbed species (atoms or ions) are very reactive.• Molecules are adsorbed onto active sites on the

catalyst surface.

Catalysis

Catalysis

Heterogeneous Catalysis• Consider the hydrogenation of ethylene:

C2H4(g) + H2(g) C2H6(g), H = -136 kJ/mol.– The reaction is slow in the absence of a catalyst.– In the presence of a metal catalyst (Ni, Pt or Pd) the reaction

occurs quickly at room temperature.– First the ethylene and hydrogen molecules are adsorbed onto

active sites on the metal surface.– The H-H bond breaks and the H atoms migrate about the metal

surface.

Catalysis

Heterogeneous Catalysis– When an H atom collides with an ethylene molecule on the

surface, the C-C bond breaks and a C-H bond forms.– When C2H6 forms it desorbs from the surface.– When ethylene and hydrogen are adsorbed onto a surface, less

energy is required to break the bonds and the activation energy for the reaction is lowered.

Enzymes• Enzymes are biological catalysts.• Most enzymes are protein molecules with

large molecular masses (10,000 to 106 amu).

Catalysis

Enzymes• Enzymes have very specific shapes.• Most enzymes catalyze very specific reactions.• Substrates undergo reaction at the active

site of an enzyme.• A substrate locks into an enzyme and a fast

reaction occurs.• The products then move away from the

enzyme.

Catalysis

Enzymes• Only substrates that fit into the enzyme lock

can be involved in the reaction.• If a molecule binds tightly to an enzyme so

that another substrate cannot displace it, then the active site is blocked and the catalyst is inhibited (enzyme inhibitors).

• The number of events (turnover number) catalyzed is large for enzymes (103 - 107 per second).

Catalysis

Enzymes

Catalysis