Chemistry 100

Chapter 14 - Chemical Kinetics

The Connection Between Chemical Reactions and Time

Not all chemical reaction proceed instantaneously!!!

2 A B combination reaction

Can we quantify the length of time it takes for this (or any) chemical reaction to occur?

Practical examples of how long!

H2(g) + ½ O2 (g) H2O (l) Þ Very Slow

N2O(g) N2 (g) + ½ O2 (g) Þ SLOW combustion reactions fast process TNT exploding very fast reaction Food spoilage Drug decomposition

Chemical Kinetics

Chemical kinetics is concerned with determining the speed or rate at which a reaction occurs.

How is the reaction rate affected by temperature? states of reactants? amount of reactants? catalyst? surface area of the reacting species?

Example

Br2 (aq) + HCOOH (aq) ® 2 Br - (aq) + 2 H+ (aq) + CO2 (g)

Define the average rate

initialfinal

initial2final22

tt

]Br[]Br[

t

]Br[

A Sample

ReactionBr2 (aq) + HCOOH (aq) 2 Br – (aq) + CO2 (g) +

2 H+ (aq) Note – orange colour fades as reaction

proceeds.

t / s [Br2] / M

0 0.0120

50 0.0101

100 0.00846

150 0.00710

200 0.00596

250 0.00500

300 0.00420

350 0.00353

400 0.00296

Average Rate Data

Avg. Rate (150 s)

Avg. Rate (100 s)

Avg. Rate (50 s)

3.27 x 10-5 3.54 x 10-5 3.80 x 10-5

2.76 x 10-5 3.00 x 10-5 3.28 x 10-5

2.31 x 10-5 2.50 x 10-5 2.72 x 10-5

1.93 x 10-5 2.10 x 10-5 2.28 x 10-5

1.62 x 10-5 1.76 x 10-5 1.92 x 10-5

  1.47 x 10-5 1.60 x 10-5

    1.34 x 10-5

Instantaneous Rates

td]Brd[ 2

It’s best to define an instantaneous ‘speed of reaction’

Plot of the [Br2] vs. time

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0 100 200 300 400 500

time / s

[Bro

min

e]

/ M

Instantaneous Rate Data

Time (s) Rate (M/s)

0 4.19 x 10-5

50 3.52 x 10-5

100 2.95 x 10-5

150 2.48 x 10-5

200 2.08x 10-5

250 1.75 x 10-5

300 1.47 x 10-5

400 1.03 x 10-5

Plot of the ln [Br2] vs. time

-11.600

-11.400

-11.200

-11.000

-10.800

-10.600

-10.400

-10.200

-10.000

0 100 200 300 400 500

time / s

[Bro

min

e]

/ M

The Rate Law

Relates rate of the reaction to the reactant concentrations and rate constant

For a general reaction

a A + b B + c C ® d D + e E

rate = k[A]x[B]y[C]z

The exponents (x,y, and z) are called the reactant orders.

The Rate Constant

The rate constant relates the ‘speed’ of the chemical reaction to the instantaneous reactant concentration.

k = constant for constant temperature The rate of the reaction is dependent on

reactant concentration RATE CONSTANT IS INDEPENDENT OF THE

REACTANT CONCENTRATION.

The Reaction Orders

Determine the superscripts (x, y, and z) for a non-elementary chemical reaction by experimentation.

S x + y + z = reaction ordere.g. x = 1; y = 1; z = 0

2nd order reaction (x + y + z = 2)x = 0; y = 0; z = 1 (1st order reaction)

x = 2; y = 0; z = 0 (2nd order)

Reaction Rates and Reaction Stoichiometry

Look at the reaction

O3(g) + NO(g) ® NO2(g) + O2(g)

t

]O[+ =

t

]NO[+ =

t

[NO]- =

tO- = rate 223

Another Example

ttt

2Cl

1

1NO

2

1NOCl

2

1- rate

2 NOCl (g) 2 NO + 1 Cl2 (g)

WHY? 2 moles of NOCl disappear for every 1 mole Cl2 formed.

The General Case

a A + b B ® c C + d D

rate = -1 [A] = -1 [B] = +1 [C] = +1 [D] a t b t c t d t

Why do we define our rate in this way?- removes ambiguity

- obtain a single rate for the entire equation, not just for the change in a single reactant or product.

The Isolation Method of Obtaining Rate Laws

a A + b B ® c C + d D

rate = k[A]x[B]y

Fix the concentration of one reactant (say reactant A).

We then perform a series of experiments to examine how changing the [B] affects the initial reaction rate?

rate = (constant) [B]y

Isolation Method (cont’d)

Now we fix the concentration of reactant B. We then perform another series of experiments

to examine how changing the [A] affects the initial reaction rate?

rate = (constant) [A]x

Types of Reactions

The rate law gives us information about how the concentration of the reactant varies with time

How much reactant remains after specified period of time?

First Order Reaction

A product

rate = -D[A]/ D t = k[A] How does the concentration of the

reactant depend on time?

k has units of s-1

ktAA

o

ln

The Half-Life of a First Order Reaction

For a first order reaction, the half-life t1/2 is calculated as follows.

k6930

t 21

./

Radioactive Decay

Radioactive Samples decay according to first order kinetics.

This is the half-life of samples containing e.g. 14C , 239Pu, 99Tc.

Example 01

1414 NC

Second Order Reaction

A + B ® products Rate = k[A][B]

A ® products Rate = k[A]2

Reaction 1 is 1st order in A and B and 2nd order overall

Reaction 2 is 2nd order in A

The Dependence of Concentration on Time

For a second order process where rate = k[A]2

ktA1

A1

o

Half-life for a Second Order Reaction.

[A] at t = t½ = ½ [A]0

021

21o0

Ak1

= t or

kt + A1

= /2A

1

][

][][

/

/

A Pseudo-First Order Reaction

Example hydration of methyl iodideCH3I(aq) + H2O(l) CH3OH(aq) + H+(aq) + I-(aq)

Rate = k [CH3I] [H2O]

Since we carry out the reaction in aqueous solution [H2O] >>>> [CH3I] / [H2O] doesn’t change by a lot

Since the concentration of H2O is essentially constant

rate = k [CH3I] [constant]

= k` [CH3I] where k` = k [H2O]

Pseudo first order since it appears to be first order, but it is actually a second order process.

Collision Theory of Kinetics

With few exceptions, the reaction rate increases with increasing temperature.

Chemical reactions take place due to collisions between reactant molecules

i.e. rate µ number of collisions / unit time

A2 + B2 product rate = k[A2][B2]

The Reaction Profile

How does the energy of the reactants vary during the reaction sequence?

The Activation Energy The minimum amount of

energy need for initiation of a chemical reaction is the activation energy (Ea).

Colliding reactant molecules possess kinetic energy > the activation energy or Ea.

The Activated Complex

The species temporarily formed by the reactant molecules – the activated complex.

A small fraction of molecules usually have the required kinetic energy to get to the transition state The concentration of the activated

complex is extremely small.

The Arrhenius Equation

/RTE - A ln k ln a

• Arrhenius showed how the rate constant depended on temperature.

A is called the frequency factor – an estimate of the number of reactive collisions in the system

Ea is the activation energy

12

a

1

2

T

1 -

T

1

R

E -

k

kln

Reaction possesses a large activation energy small rate constant Slow reaction!!

Measure k at several different temperatures

Activation Energies and the Arrhenius Equation

R = 8.314 J/(K mole)

T in Kelvin units!!!

Arrhenius Equation (cont’d)

The Arrhenius equation is best suited for studying reactions between simple species (atoms, diatomic molecules).

The orientation of the reactants (how they collide) becomes very important when the species get bigger.

Catalysts

So far, we have considered one way of speeding up a reaction increasing T usually increases k.

Another way is by the use of a catalyst.

A catalyst - a substance that speeds up the rate of the reaction without being consumed in the overall reaction.

· look at the following two reactions

A+B ® C rate constant k

A+B ® C rate constant with catalyst is kc

· NOTE: RATE WITH CATALYST > RATE WITHOUT CATALYST

Types of Catalyst

We will briefly discuss three types of catalysts. The type of catalyst depends on the phase of the catalyst and the reacting species. Homogeneous Heterogeneous Enzyme

Homogeneous Catalysis

The catalyst and the reactants are in the same phase

e.g. Oxidation of SO2 (g) to SO3 (g) 2 SO2(g) + O2(g) ® 2 SO3 (g) SLOW

Presence of NO (g), the following occurs.

NO (g) + O2 (g) ® NO2 (g)

NO2 (g) + 2 SO2 (g) ® 2 SO3 (g) + NO (g)FAST

SO3 (g) is a potent acid rain gas

H2O (l) + SO3 (g) H2SO4 (aq)

Note the rate of NO2(g) oxidizing SO2(g) to SO3(g) is faster than the direct oxidation.

NOx(g) are produced from burning fossil fuels such as gasoline, coal, oil!!

Heterogeneous Catalysis

The catalyst and the reactants are in different phases adsorption the binding of molecules to

the surface to a surface. Adsorption on the surface occurs on

active sites. An active site is a place where reacting

molecules are adsorbed and physically bond to the metal surface.

The hydrogenation of ethene (C2H4 (g)) to ethane

C2H4 (g) + H2(g) C2H6 (g) Reaction is energetically favourable

rH = -136.98 kJ/mole of ethane. With a finely divided metal such as Ni

(s), Pt (s), or Pd(s), the reaction goes very quickly .

Common Heterogeneous Catalysts

Two other important heterogeneous catalysis processes petroleum cracking (refining crude oil) catalytic converters very efficient in

reducing exhaust emission when hot; cold is another story!

Enzyme Catalysis

Enzymes - proteins (M > 10000 g/mol) High degree of specificity (i.e., they will

react with one substance and one substance primarily

Living cell > 3000 different enzymes

The Lock and Key Hypothesis

Enzymes are folded into fixed configurations.

According to Fischer, active site is rigid.

The substrate’s molecular structure exactly fits the “lock” (hence, the “key”).

Simplified Model for Enzyme Catalysis

E º enzyme; S º substrate; P º product

E + S ® ES

ES ® P + E

rate = k [ES] The reaction rate depends directly on

the concentration of the substrate.

Rate Laws for Multistep Processes

Chemical reactions generally proceed via a large number of elementary steps - the reaction mechanism

The experimentally established rate law must reflect the reaction rate of the slowest elementary step Þ the rate determining step (rds)

What do we mean by an rds?

A commuter goes through a two step process to get to work in Halifax.

(1) highway ® MacKay Bridge Toll booth

(2) toll booth ® downtown

MacKay Bridge Toll Booth

Overall reaction

highway ® downtown

Situation 1. highway clogged, toll booth is fast.

Situation 2. fast highway, clogged toll booth.

The Rate Determining Step (rds)

Situation 1 - clogged highway is the slowest step in the commuting process (rds).

Situation 2 - the clogged toll-booth is the slowest step in the commuting process (the rds).

Speed of overall process (highway ® downtown) depends which step is slowest! Which is the rate-determining step.

Elementary steps and the Molecularity

Any chemical reaction occurs via a sequence of elementary steps.

Kinetics of the elementary step only depends on the number of reactant molecules in that step! Molecularity the number of reactant

molecules that participate in elementary steps

The Kinetics of Elementary Steps

Classes of elementary steps

Akrate productsA

B Akrate productsBA

A bimolecular step

A unimolecular step

For the step

BAkrate productsBA2 2

A termolecular (three molecule) step.