k =Ae−(Ea /RT )

Arrhenius equation

lnk =lnA −

Ea

RT

Ea: activation energy

A: frequency factor

Temperature dependence of reaction rates

Typically rates of reactions double for every 10oC rise in temperature,

An Arrhenius plot of ln k against 1/T is used to determine Ea and A

The higher the Ea the stronger the temperature dependence of the rate constant

Collision Theory

Collisions between two (or more) atoms/molecules required for a reaction.

However, every time two reactants collide they may not react

As temperature increases:

atoms/molecules collide more frequently

kinetic energy of atoms/molecules increases

Collision theory: reaction occurs only if the reactants collide with a kinetic energy of at least the activation energy, and they do so in the correct orientation.

Kinetic energy is important

2 NOCl 2 NO + Cl2

Orientation is important

2 AB -> A2 + B2

N

O

Cl

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k =Ae−(Ea /RT )

lnk =lnA −

Ea

RT

The factor e-Ea/RT: fraction of molecules that have at least the minimum energy required for reaction.

For an Ea = 40 kJ/mol

Temperature (K) e-Ea/RT

298 9.7 x 10-8

400 5.9 x 10-6

600 3.3 x 10-4

A: reflects orientation effect or steric effect

Measuring k as a function of T Ea to be determined

ln

k2

k1

=−Ea

R(1T2

−1T1

)

Reaction coordinate diagram

Activated complex or transition state - highest energy along reaction coordinate

Reactants must collide with sufficient energy to reach this point and collide in a preferred orientation to form the activated complex

E = (Ea)forward - (Ea)reverse

Endothermic reaction: Ea(forward) > Ea(reverse)

Exothermic reaction: Ea(forward) < Ea(reverse)

Higher temperatures favor products for an endothermic reaction and reactants for an exothermic reaction

CH3OH(aq) + H+(aq) CH3OH2+(aq)

CH3OH2+(aq) + Br- (aq) CH3Br + H2O(aq)

Catalysis

Catalyst: a compound which speeds up the rate of a reaction, but does not itself undergo a chemical change.

Simple mechanism

A + catalyst intermediates

intermediates B + catalyst

Overall: A B

Concentration of catalyst is included in k; hence k varies with concentration of catalyst

Presence of a catalyst provides an alternate path with a lower Ea

2H2O2(aq) 2H2O(aq) + O2(g)

In the absence of a catalyst, Ea = 76 kJ/mol

In the presence of a catalyst (I-); Ea = 57 kJ/mol;

rate constant increases by a factor of 2000

C C

CH3

HH

H3C

(g) C C

CH3

HH3C

H

(g)

cis-2-butene trans-2-butene

Catalyzed by I2

C2H4(g) + H2(g) C2H6 (g) Pt

Example of heterogenous catalysis

A catalyst does not effect the thermodynamics of the reaction

K = k1/k-1; catalyst speeds up both the forward and reverse reaction

G is not affected by catalyst; neither is K

Equilibrium concentrations are the same with and without catalyst; just the rate at which equilibrium is reached increases in the presence of a catalyst

Enzymes

Practically all living reactions are catalyzed by enzymes; each enzyme specific for a reaction.

Enzymes typically speed up rates by 107 - 1014 times rate of uncatalyzed reactions

Ea for acid hydrolysis of sucrose: 107 kJ/mol

Ea for catalyzed acid hydrolysis of sucrose: 36 kJ/mol

Rate increase of 1012 at body temperature

E + S ES

ES P + E

“Poisoning” a catalyst

Arsenic poisoning: Ingestion of As(V) as AsO43- results in

reduction to As(III) which binds to enzymes, inhibiting their action

Nerve gases - block enzyme-controlled reactions that allow nerve impulses to travel through the nerves.

Catalytic Converters

Incomplete combustion of gasoline produces CO, hydrocarbon fragments (CmHn)

High temperature in the engine causes oxidation of N2 to NO and NO2

Conversion of these pollutants to less harmful compounds is speeded up in the presence of catalysts.

Catalyst: pellets of Pt, Pd, Rh

2 NO(g) N2(g) + O2(g)catalyst

CO, CmHn, O2 CO2, H2Ocatalyst

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