Kinetics

The Study of Rates of Reaction

Rate of a Reaction

The speed at which the reactants disappear and the products are formed determines the rate of the reaction.

The reaction rate slows as the concentration of the reactants decrease and the concentration of the products increases.- Elephant toothpasteRelated Videos

Factors that Effect the Rate of a Reaction

1. Concentration2. Temperature3. Ability of the reactants to meet:

heterogeneous vs. homogenous and particle size

4. CatalystsYouTube - "Glow in the Dark“YouTube - Brainiac Thermite and Liquid Nitrogen

Measuring the Rate

Rate with respect to x = (concen of X) t

Units of rate = Molarity/ second= mol/L = mol

L-1s-1

s Reaction rate is always given a positive

value: the rate at which the concentration is increasing or decreasing is positive.

Rates and Coefficients The coefficients of the balanced equation

may be used to find the rates with respect to the other species in the equation.

2 N2O5 NO2 + O2

Rate = 8.31 x 10-4 M/s

What is the rates at which the oxygen concentration is increasing?

8.31 x 10-4 N2O5 x 1 mol O2

2 mol N2O5

=4.1 x 10-4 O2 M/s forming

Rates and Coefficients

2 N2O5 NO2 + O2

Rate = 8.31 x 10-4 M/s What is the rate at which N2O5 is

disappearing? 8.31 x 10-4 M/s

Concentration and Rate Law

A + B productsRate Law:

Rate = k [A]m[B]n

K = rate constant[ ] = concentration (M)m,n = the order of the reactantdetermined experimentally

Determining the Order of a Reaction Measure how varying the

concentration of the reactants effects the rate

1st order if the rate increase by the same magnitude as the reactant. A doubles and the rate doubles A triples and the rate triples

2nd order if the rate increases by a factor of 2 compared to the reactant.

A + B products

[A] [B] products

.10 .10 .20

.20 .10 .40

.30 .10 .60

.30 .20 2.4

.30 .30 5.4

2x 4x

2x 2x

3x 9x

Determining the Rate Law

A doubles rate doubles A triples rate triples

n = 1

B doubles rate 4x greater B triples rate 9x greater

m = 2

Rate = k[A]1 [B]2

Order of a Reaction

The overall order of the reaction is the sum of the orders for each reactant m + n = overall order

Zero order - the concentration of the reactant does not effect the rate and is not included in the rate law.

Concentration vs. Time

I) Rate Law wrt Reactant AZero order: rate = k ,

units of k (rate constant) are M/sFirst order: rate = k [A]

units of k are sec-1

Second order: rate = k [A]2

units of k are L mol-1 s-1

Zero Order Plots

First Order Plots

Second Order Plots

Concentration vs. TimeReaction

Order

Differential Rate

Law

Integrated Rate Law

KineticPlot

Slope

Units of RateConstant

Zero[A] = [A]0 - k

t[A] vs

t- k mole L-1 sec-1

First[A] = [A]0 e

- k

t

ln [A] vs t

- k sec-1

Second

1/[A] vs t

k L mole-1 sec-1

d [A]

-d t = k

-d t = k [A]

-d t = k[A]2

[A] = 1 + kt[A]0

Collision Theory The rate of the reaction is proportional

to the number of effective collisions. Not every collision between the

reactants produces a product, or else all reactions would be explosions.

Activation Energy (EA) the minimum energy that must be supplied for an effective collision to occur.

The Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann Distribution

Points to notice: No molecules at zero energy Few molecules at high energy No maximum energy value

For the reaction to occur, the particles involved need a minimum amount of energy - the Activation energy. If a particle is not in the shaded area, then it will not have the required energy so it will not be able to participate in the reaction.

Collision Theory and Reaction Rates

1. Activation Energy:Particles must have the minimum energy (Ea) required for an effective collision.

2. Kinetic Energy:Increasing the temperature of the reaction increases the KE and number of particles with the required Ea for an effective collision.

3. Molecular Orientation:Reactants must be oriented correctly for an effective collision to occur.

Transition State

The activated complex has partially formed and partially broken bonds

H = EA (forward) – E’A

(reverse) Pot

enti

al e

nerg

y

Catalysts increase the reaction rate by lowering the activation energy required to form the products.

Measuring EA

The Arrhenius Equation gives the relationship between the EAand temperature of the reaction

K = rate constant A = frequency factor (combines collision

frequency & orientation factors) T = Kelvin temperature R = gas constant

Notice that a small increase in temperature causes a large increase in the rate constant

App. a factor of 2 to 3 increase in rate for every 10oC increase in temperature

k = A e-Ea/RT

Measuring EA

1. Graphical Method Taking the natural log of both sides of the

Arrhenius Equation gives the equation of a line

Ln k = ln A + ln e –EA/RT

Ln k = ln A – EA/RT Ln k = (-EA/R)(1/T) + ln A

Y = m x + b-so the slop of this graph is the

activation energy divided by the gas constant

Measuring EA

2. Temperature change method Using the Arrhenius equation and

Determining the rate constant at different temperatures gives the activation energy

ln k2 = EA 1 - 1

k1 R T1 T2

Reaction Mechanism and Rate

If several steps are involved in an overall chemical reaction, the slowest step limits the rate of the reaction.

Thus, the slow step is called the rate determining step.

(Slow)

2N2O5 4NO2 + O2

Reverse this equation to get the overall

The high Ea for the slow step limits the reaction rate

The reaction cannot be any faster than the slowest step

Example 1

If the reaction:2 NO2 + F2 = 2 NO2F

follows the mechanism,(i) NO2 + F2 = NO2F + F (slow)(ii) NO2 + F = NO2F (fast)

What is the rate law?Since step (i) is the rate-determining step, the rate law is:

Rate = k [NO2]m [F2]n

The Rate Law

The rate law is not derived from the overall equation, but the rate determining step.

The rate law should not contain any intermediate products that are not in the overall reactions.

The exponents of the reaction is determined experimentally and does not depend on the stoichiometric coefficients.

Derive the rate law that is consistent with the proposed mechanism (i) Cl2 2 Cl- (fast)

(ii) Cl- + CO ClCO (fast) (iii) ClCO + Cl2 Cl2CO + Cl-(slow)

The overall reaction is Cl2 + CO Cl2CO

Example 2

What is the rate law for the overall reaction Cl2 + CO = Cl2CO ?

From the rate-determining (slow) step, the rate appears to be

Rate = k3 [ClCO] [Cl2]

But [ClCO] is an intermediate that is not part of the overall reaction. Put it in terms of Cl2 and CO by substituting for ClCO.

[ClCO] = k-2 [Cl] [CO]

(express [Cl] in terms of [Cl2] using step (i))

What is the rate law for the overall reaction Cl2 + CO = Cl2CO ?

[Cl] = k-1[Cl2](1/2) (Substitute and combine the k’s)

Rate = K [CO] [Cl2](3/2)

where K = k-1 k-2 k3, the observed rate constant.

The overall order of the reaction is 5/2, strange but that is the observed rate law.

Catalysts

Homogenous catalyst occurs in a homogeneous mixture Example: Decomposition of H2O2 with KI

Heterogeneous catalyst adsorbs the reactants onto a solid surface Example: Decomposition of H2O2 with MnO2

Neither catalyst appears in the overall reaction

H2O2 O2 + H2O