Chemical Kinetics

• Factors that Affect Reaction rates

• Reaction Rates

• Concentration and Rate

• The Change of Concentration with Time

• Temperature and Rate

• Reactions Mechanisms

• Catalysis

Chemical Kinetics

Is the study of the rate at which reactions occur and also gives us information on how the reaction occurs (the Reaction Mechanism)

Factors that Affect Reaction Rates

Reaction rates depend on several factors

Physical State of the Reactants and Mixing

The concentration of the Reactants

The Temperature and Pressure at which the

reaction occurs

Catalysts

On a molecular level Reaction rates depend on the frequency with which molecules collide

The greater the frequency of collisions (with enough energy to break bonds), the faster the rate of the reaction

A quantitative definition of the rate of a chemical reaction is defined in terms of product(s) forming and reactant(s) disappearing per unit time

N2(g) + 3H2(g) → 2NH3(g)

Reaction Rates

Rate of ammonia formation can be expressed as

[NH3]t2 - [NH3]t1 = Δ[NH3] = 0.50M - 0Mt2 - t1 Δt 25s - 0s

= 0.50M / 25s = 0.02 M/s

(Rates are expressed as positive quantities, units: M or mol/L per second)

This is the average rate, it doesn’t gives us an actual rate at a given moment in time

Gives information on the rate at a particular moment, for this we plot the concentration of product or reactant with time and determine the slope at our time of interest

Instantaneous Rate

C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)

Reaction Rates and Stoichiometry

2HI(g) → H2(g) + I2(g)

In this case the rate of appearance (formation) of H2 and I2 is equal, but 2 mols of HI are consumed for every 1 mol of H2 and I2 formed, so we can express this as:Rate = - 1 Δ[HI] = Δ[H2] = Δ[I2]

2 Δt Δt Δt

The rate of HI disappearance is twice the rate of H2 and I2 appearance

This leads to the generalization that in a given reaction

aA + bB → cC + dD

Rate = -1 Δ[A] = -1 Δ[B] = 1 Δ[C] = 1 Δ[D]a Δt b Δt c Δt d Δt

In the reaction 2O3(g) → 3O2(g). O2 is formed at 2.0 x 10-5 M/s at a given instant, at what rate is O3 disappearing at this instant

Concentration and Rate Rate = k[A]m[B]n

NH4+(aq) + NO2

−(aq) N2(g) + 2 H2O(l)

The rate is proportional to the concentration of both reactants, doubling either

the concentration of NH4+ or NO2

- doubles the rate of the reaction, so we say

that the reaction order for NH4+ and NO2

- is 1 : we can express the rate law as

Rate = k [NH4+][NO2

-] m and n are both 1

For the Reaction: A + B → C + D

The experimentally data was tabulated as shown, Write the rate law for the reaction

Expt [A] M [B] M Init.Rate M s-1

1 0.1 0.1 0.001

2 0.1 0.2 0.002

3 0.2 0.1 0.004

What are the reaction orders with respect to reactants A and B and what is the order of the reaction overall?

The reaction orders can be found with the generalized formula:

Reaction order = {Log (rate 2/rate 1)} / {Log (concn 2/concn1)}

e.g. For NO2- = Log (2) / Log(2) = 1

From a rate law we can calculate the rate of reaction using the rate constant and initial reactant concentrations. We now need an equation that allows us to determine the concentration of reactants and products at any particular time

Zeroth Order Reactions

12.4 The Change in concentration with Time

Consider the reaction: A → products

Rate = - Δ [A] = k [A]o = k Differential Rate LawΔt

Intergrating this differential rate law gives:

[A]t - [A]o = -kt Ao is the initial concentration of A (at t = 0)At is the concentration of A at any time t after

From a rate law we can calculate the rate of reaction using the rate constant and initial reactant concentrations. We now need an equation that allows us to determine the concentration of reactants and products at any particular time

First Order Reactions

12.4 The Change in concentration with Time

Consider the reaction: A → products

Rate = - Δ [A] = k [A] Differential Rate LawΔt

Intergrating this differential rate law gives:

ln [A]t = -kt Ao is the initial concentration of A (at t = 0)[A]o At is the concentration of A at any time t after

Since ln[A]t/[A]o = ln[A]t - ln[A]o

We can get this equation in the form y = mx +c by re-arranging:

ln[A]t = -kt + ln[A]o

Plotting ln[A]t against t should give a straight line with slope = -k,and intercept = ln[A]o

Second Order Reactions

Again Consider the reaction: A → products

Rate = - Δ [A] =k [A]2 Intergrate to give:Δt

1 = kt + 1[A]t [A]o

So plotting 1/[A]t vs. t will be linear for a second order reaction

Half-Life

[A]t = 0.5[A]o

ln[A] t = -kt½ln[A]o

ln 0.5 = -kt½

= 0.693 = t½

k

First Order Reactions

Temperature and Rate

Kinetics Review

aA + bB → cC + dD Rate (r) = -1 Δ[A] = -1 Δ[B] = 1 Δ[C] = 1 Δ[D]a Δt b Δt c Δt d Δt

r = k[A]m[B]n

Zeroth order First order

Second orderArrhenius equation

[A]t - [A]o = -kt ln[A]t = -kt + ln[A]or= k r= k[A]

r= k[A]21 = kt + 1[A]t [A]o ln k = -Ea/RT + ln A

ln 0.5 = -kt½

t½ = 1k[A]o

k = Ae-Ea/RT R = 8.314 J/ mol K (T absolute)

Arrhenius Equation

ln k = -Ea/RT + ln A

Reaction Mechanisms

It provides an alternative pathway (mechanism), it alters either A or Ea or both

Catalysis

A catalyst increases the rate of a reaction (by lowering the Activation Energy), without being consumed in the reaction

Homogeneous Catalyst

Present in the samephase as the reactants

Heterogeneous Catalyst

Present in a different phase as the reactants (often metals)

Heterogeneous Catalysts

Exist in a different Phase to the reactants

For example catalytic hydrogentation of alkenes with a Ni catalyst and Catalytic Converters.

Reactants are adsorbed onto the surface of the metalReactants are free to move around the surfaceReactions happen (new sigma bonds form) on the surface

The products desorb

Enzyme Catalysis

Substrate (yellow) binds to enzyme (purple) in an active site

Each enzyme catalyses a specific reaction in the same way a key fits a given lock

The product is produced and the enzyme is unchanged.

An enzyme can increase a reaction rate up to 1018 times!

The product(s) leaving the active site is the rate determining step, once the products have left the site can be filled by another substrate molecule