Arrhenius Theory: Understanding Reaction Rates and Temperature Dependence, Slides of Chemistry

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Reaction Rates and Temperature;

Arrhenius Theory

CHEM 102

T. Hughbanks

Arrhenius Theory

k = Ae −Ea RT Both A and E a are specific to a given reaction .! k is the rate constant! E a is the activation energy! R^ is the ideal-gas constant (8.314 J/Kmol)! T is the temperature in K! In addition to carrying the units of the rate constant, “ A” relates to the frequency of collisions and the orientation of a favorable collision probability! Potential Energy

Reaction Progress!

∆HRXN!

Eact! In order for the reaction to proceed, the reactants must posses enough energy to surmount a reaction barrier.!

E

a

, The Activation Energy

 Energy of activation for forward reaction:

Ea = Etransition state - Ereactants

 A reaction can’t proceed unless reactants

possess enough energy to give Ea.

 ∆E, the thermodynamic quantity, tells us

about the net reaction. The activation energy,

Ea , must be available in the surroundings for

the reaction to proceed at a measurable rate.

The temperature for a system of particles is described by a distribution of energies. At higher temps, more particles have enough energy to go over the barrier. E > Ea! E < Ea! Since the probability of a molecule reacting increases, the rate increases.

The orientation of a molecule during collision can have a

profound effect on whether or not a reaction occurs.!

The reaction occurs only when the orientation of the molecules is just right…!

In some cases, the reactants must have proper

orientation for the collision to yield products.!

This reduces the number of collisions that are reactive!!

Temp. and Rate Acceleration

Arrhenius Equation

 Arrhenius noted that reaction rates could be

understood to depend on Ea and T with the

exponential form:

k = A exp(– Ea/RT)

 Or, in logarithmic form:

lnk = lnA – (Ea/RT)

using base 10 logs: [logk = logA - (Ea/2.303RT)]

Arrhenius Eqn., Alternative Form

 Taking two measured values of the rate (at

two different temperatures) one can write:

lnk 1 = lnA – (Ea /RT 1 ) lnk 2 = lnA – (Ea /RT 2 ) lnk 2 – lnk 1 = – (Ea /R)[(1/T 2 ) – (1/T 1 )] ln(k 2 /k 1 ) = – (Ea/R)[(1/T 2 ) – (1/T 1 )]

Arrhenius Eqn., Graphical Form

A “best fit” to many data is better! lnk = -(Ea/R)(1/T) + lnA

Catalysts - lowering Ea. Mechanism may change.

Energy

“Reaction Coordinate”

Ea(uncatalyzed)

∆Erxn

reactants

products

Ea(catalyzed) Catalytic Converters, 2NO → O 2 +N 2 Pt surface

Pt

2H 2 O 2 → 2H 2 O + O 2

MnO 2

Iodine-Catalyzed Isomerization of cis -2-Butene