b18pa_ap - chemical kinetics - prof mckendrick - lectures 1-4 handout.pdf

8/14/2019 B18PA_AP - Chemical Kinetics - Prof McKendrick - Lectures 1-4 handout.pdf

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B18PA/AP

Introductory Chemical Kinetics

Prof McKendrick

8 lectures

2 tutorials (weeks 7 and 8)

4 Webtests

(weeks 5 -8; deadlines = Sun midnight, weeks 6- 9)

Recommended text

Elements of Physical Chemistry, Atkins and de Paula, 5e

Chapters 1, 10, 11

Course Outline

Motivation - Why is kinetics important?

Basic definitions

Effects of concentration on reaction rate

Order of Reaction Differential/Integrated Rate Laws

Connection of Rate Law to Mechanism

ec o empera ure on reac on ra e Arrhenius Equation

Collision Theory

Transition State Theory


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Motivation

For any chemical system not at equilibrium, can ask

How farwill it go?

Why does it react?

How fast will it go?

How does it get there?

MotivationVery many important systems are not at equilibrium

e.g.

organic materials in air

the atmosphere itself

biochemical systems

geochemistry


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Motivation

Knowing or predicting the rates of chemical reactions is

crucial for understanding e.g.

The atmosphere

Biochemistry

Pharmacology

Motivation

Optimization of chemical

production

Laboratory synthesis of new

compounds and materials

Decay of forensic specimens -


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Basic definitions

Rate of reaction In simplest terms

More generally,

rate at each instant

= slope of concentration

against time

vgenerally varies as time (and

concentration) varies

v(normally) has dimensions ofconcentration / time

Rate of reaction

Accounting for stoichiometry

A little care is needed to specify which species vrefers to

[NO2]

/molL-1

e.g.

If we know vfor any

one species, we know the

others from stoichiometry

[O2]

[N2O

5]C

oncentration

Time / s


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Rate of reaction

A consistent definition of rate will always result from

dividing by the stoichiometric coefficients in a balanced

reaction

e.g. for

Note that the rate for a reaction going in the forward

direction is always positive

Factors influencing reaction rates

concentration

temperature

(external) pressure

surface area

presence of a catalyst


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Effect of concentration on reaction rate

For most reactions, the rate depends on the concentration

of reactants

e.g. as above for A products

rate falls as [A] falls

The differential rate law

For a single reactant, this relationship can be expressed

through the dif ferential rate law

This often but not alwa s has the sim le form


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A note on units...

The units in any physical equation must be the same on

both sides of the equation

or simply view as

hence the units of kmust beOrder, n Units of k

0 mol L-1 s-1

1 s-1

2 mol-1 L s-1

etc.

n mol1-n Ln-1 s-1

Determining the order of reaction

Given a set of data of [A] against time, you could

determine rate, v, as a function of [A] by estimating the

slopes of [A] v. t

attempt to find the correct order by plotting a series of

graphsPlot against result conclude

v [A] linear first order (n = 1)

k= slope


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Determining order of reaction e.g. decomposition of ethane at high temperature (700C)

v/10 10mol L 1s 18.57

5.05

2.94

time/s [C2H6]/106 mol L10 1.60

1000 0.942

2000 0.548

1.72

1.01

0.59

3000 0.321

4000 0.188

5000 0.110

2.0

Determining order of reaction

[C2H6] v. time rate v. [C2H6]

10

0.5

1.0

1.5

2H

6]/10-6m

olL-1

5

/10-10

molL

-1s

-1

0 2000 40000.0

[C

time / s

0.0 0.5 1.0 1.50

v

[C2H

6] / 10

-6mol L

-1


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Determining the order of reaction

It is possible to avoid the trial-and-error by recognising that

if

then by taking natural logs

and so a plot of lnv against ln[A] will be a straight line

with slope = n

the rate constant is found from the intercept = lnk

E.g. lnvv ln[C2H6] from above

Determining the order of reactionDetermining the order of reaction

1

2

10-10

molL-1 s

-1)

18

-2 -1 0 1-1

ln(v/

ln([C6H

6] / 10

-6mol L

-1s

-1)


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It is possible (and in fact much more common) to determine

the orderand rate constant directly from [A] against time,

Integrated rate equations

without needing to find v(i.e. estimating slopes)

Consider

As tgets smaller,

[A]

curve is smoother In limit t 0,

curve is exact

timet

Integrated rate equations

The algebraic equivalent is to integrate

differential

rate law

integrated rate

law (expression)

[A] v. t can then be analysed directly

requires an advance assumption of the order


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Integrated rate laws

e.g. 1st order A products

First order integrated rate law

integrated rate law

or

t


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First order integrated rate law A further useful property is the half-life, t1/2

= time taken for [A]0 [A]0/2

Insert t = t1/2 ; [A] = [A]0/2

in

gives

Uniquely for 1st-order,

this is independent of [A]0

Half-lives for first order reactions

basis of radiocarbon dating

In upper atmosphere 14N + n 14C +p

Carbon-14 (14C) is radioactive; t1/2 = 5730 years

Photosynthetic organisms absorb 14C (via CO2):

passed on to those higher in the food chain

so 14C :12C ~ that of atmosphere (~1.3 x 10-12)

When organism dies,[14C] decays in a first-order way

ideally

but note additional variations in 14C in real life


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Consider now second order A products

Second order integrated rate laws

Integrated rate law

so plot 1/[A] against t

t


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Distinction first and second order

For reactions with the same

initial rate

2nd order slows down more

rapidly than 1st order

t1/2 not constant for 2nd order


Zero order A products

so, by inspection (or by integrating)

[A] against t [A]

t1/2

time


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Zero order reactions

zero-order reactions are less common, but include e.g.

reactions at surfaces

e.g.

at high pressure of NH3rate limited by the available

sites on the W surface

processing of ethanol by the

human liver(!)

See tutorial Week 7, Q2

Rate equations, single reactants:Rate equations, single reactants:

summarysummary

Order Differential

Rate Law

Integrated

Rate

Expression

Linear

Plot

Typical

Units

of k

Half-life

0

1ln[A] v. t s-1][

][Ak

Ad=

kteAA

= 0][][2ln

30

2

n ( 1)


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Multiple Reactants

All the examples of rate laws above involve a single

reactant

In general, there will be multiple reactants: A, B, etc.

Al l concentrations change simultaneously

Rate law often (though again not always) has simple form

Multiple reactants : A+ B products

Integration of the rate law is not as straightforward

e.g.

consider the case of first orderin each of A and B

= second orderoverall the differential rate law is

its solution leads to


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Multiple reactants

These difficulties can be avoided (if experimentally

practical) using the isolation method

Arrange all concentrations to be in excess except one

Excess concentrations remain ~constant Variation is isolated to a sing le reactant

e. .

Arrange [B] in excess

Multiple reactants : A+ B products

So the integrated rate law approximates as follows:

[ ] [ ] [ ] [ ]( )ktAB

AA

BB00

0

0ln =


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Multiple reactants

is an 'effective' or 'pseudo-first o rder rate constant for

the loss of [A].

repeat experiment at several

values of [B]0

k

true second-order k

[B]0

E.g. Year 2 Organic Lab

Hydrolysis of a series of p-nitrophenol benzoate esters

Isolation methodIsolation method

O

NO2O

Cl

O

NO2O

CH3O

O

NO2O

C13H9NO4Mol. Wt.: 243.21

C13H8ClNO4Mol. Wt.: 277.66

C14H11NO5Mol. Wt.: 273.24

spectrometry) in the presence of excess [OH-]

pseudo-1st order kinetics

36


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Method of init ial rates

The same general analyses above can be applied to a

series of

initial rates v0 as a function of initial concentrations [A]0

Some advantages where e.g.

e c

Multiple reactants Isolation method also widely used with initial rates to

establish orders for multiple reactants

e.g. H O (aq) + 3I-(aq) + 2H+(aq) I -(aq) + 2H O

Exper-

iment

No.

Initial concentrations / mol L-1 Initial rate

/ 10-6 mol

L-1 s-1[H2O2] [I-] [H+]

1 0.010 0.010 0.00050 1.15

2 0.020 0.010 0.00050 2.30

. . . .

4 0.010 0.010 0.00100


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Elementary reactions

To begin to understand the relationship between

mechanisms and rate laws, need to distinguish

overall reaction elementary reaction

Unimolecular reactions

Elementary 1st order reactions of type

Since every A behaves independently

rate is simply no. of A molecules

e.g.


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Bimolecular reactions

Elementary 2nd order reactions of type

rate is proportional to the number of pairs of reactants

. .

SN2 reactions:

dimerisation (in solution):

exchange reactions:

etc.

A first look at mechanisms

The rate laws for overall reactions can be deduced, in

principle, from those of their individual steps

n exac rea men may e cu mposs e or a u e

simplest mechanisms.

e.g. combustion of methane

overall

but mechanism

But even such complex systems can be treated numerically


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A first look at mechanisms

Simpler systems are often tractable analytically

especially with the use (where justified) of simplifying

assumptions

e.g.

rate-determining steps

rapid pre-equilibrium

(steady-state approximation - see B19PC)

Analysing mechanisms: examples

(CH3)3CBr + OH- (CH3)3COH + Br

Observed rate law

1st-order in [(CH3)3CBr] Zero-order in [OH-]

- ' '


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2NO2Cl(g) 2NO2(g) + Cl2(g)

Observed rate law

1st order in NO2Cl and overall

Another 2-step mechanism


NO2(g) + CO(g) NO(g) + CO2(g)

Observed rate law

2nd order in [NO2] Zero-order in [CO]

-


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Analysing mechanisms: examples H2(g) + I2(g) 2 HI(g)

1st order in [H2] and in [I2]

Mechanism

simple bimolecular?


But note again that not all apparently simple reactions

have simple rate laws

e.g.

H2(g) + Br2(g) 2 HBr(g)

Looks similar to H2 + I2 but...

Rate law

Such complicated laws are typical of chain reactions

(analyse via the steady-state approximation see B19PC)

b18pa_ap - chemical kinetics - prof mckendrick - lectures 1-4 handout.pdf

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