Lecture 5. Chemical kinetic. Rate of reaction

Prepared by PhD Falfushynska H.

Type of chemical reactions after numbers of stages

SimpleSimpleone elemental step

ComplexComplexSeveral steps

Bilateral: АА В ВParallel or competitive

reactions:: ВВА А

ССConsecutive:: АА→В→С→В→СConjugation:: АА

DD СС

ВВ Е Е

Nuclear chain reaction

A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions to take place.

A possible nuclear fission chain reaction. 1. A uranium-235 atom absorbs a neutron and fissions into two new atoms, releasing three new neutrons and a large amount of binding energy. 2. One of those neutrons is absorbed by an atom of uranium-238, and does not continue the reaction. However, one neutron does collide with an atom of uranium-235, which then fissions and releases two neutrons and more binding energy. 3. Both of those neutrons collide with uranium-235 atoms, each of which fissions and releases a few neutrons, which can then continue the reaction.

Rice-Hertzfeld Free Radical Chain Reaction MechanismRice-Hertzfeld Free Radical Chain Reaction Mechanism

)()()( 43 gCOgCHgCHOCH Overall Reaction:

Proposed Mechanism:

ationterchainHCCH

npropagatiochainCHCOCHCHCHOCH

initiationchainCHOCHCHOCH

k

k

k

min2 623

3433

33

3

2

1

?][ 4

dt

CHd

Classification of chemical reactions

homogeneous reaction (occur in a single phase (gaseous, liquid, or solid)::

N2 (g) + H2 (g) → NH3 (g)

heterogeneous reaction (occur in different phase)::

Mg (s) + HCl (aq) → MgCl2 (aq) + H2 (g)

topochemical reactions (occurs at the boundary of solid phases

СuO + C Cu + CO t

• The balanced chemical equation provides information about the beginning and end of reaction.

• The reaction mechanism gives the path of the reaction.

• Mechanisms provide a very detailed picture of which bonds are broken and formed during the course of a reaction.

Elementary Steps• Elementary step: any process that occurs in a single

step.

Reaction MechanismsReaction Mechanisms

Elementary Steps• Molecularity: the number of molecules present in an

elementary step.– Unimolecular: one molecule in the elementary step,– Bimolecular: two molecules in the elementary step, and– Termolecular: three molecules in the elementary step.

• It is not common to see termolecular processes (statistically improbable).

Reaction MechanismsReaction Mechanisms

Rate Laws for Elementary Steps• The rate law of an elementary step is determined by

its molecularity:– Unimolecular processes are first order,– Bimolecular processes are second order, and– Termolecular processes are third order.

Rate Laws for Multistep Mechanisms• Rate-determining step is the slowest of the

elementary steps.

Reaction MechanismsReaction Mechanisms

Rate Laws for Elementary Steps

Reaction MechanismsReaction MechanismsReaction MechanismsReaction Mechanisms

Mechanisms with an Initial Fast Step

2NO(g) + Br2(g) 2NOBr(g)

• The experimentally determined rate law can be:

d[NOBr]/dt = kobs[NO]2[Br2] (or) = kobs’[NO][Br2]

• Consider the following mechanism

Reaction MechanismsReaction Mechanisms

NO(g) + Br2(g) NOBr2(g)k1

k-1

NOBr2(g) + NO(g) 2NOBr(g)k2

Step 1:

Step 2:

(fast)

(slow)

General MechanismGeneral Mechanism

DCBA Overall Reaction:

Proposed Mechanism:

DBM

CMA

k

k

k

2

1

1Where: D = observable product

M = intermediate

Rate of reaction should be determine by change of concentration and pressure

against time

measure P over time

time Br2 + HCOOH → 2Br- + 2H+ + CO2

2H2O2 → 2H2O + O2

14

Measurement of Reaction Rates

Chemical Method

The concentration of a reactant or product as a function of time

Reaction vessels

At constant T

At intervals Slows down or stop the reaction

Rapidly analyze chemical compositions of the mixture

Cooling the sample

removing a catalyst

Diluting the mixture

Adding a species

Reaction Rate and Stoichiometry• For the reaction

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

we know

• In general foraA + bB cC + dD

Reaction RatesReaction Rates

dt

d

dt

d OHHCClHCRate 9494

dt

d

ddt

d

cdt

d

bdt

d

a

DCBARate

1111

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

dt

d

dt

d OHHCClHCRate 9494

2 2

2

2

2 2

[ ]Average Rate

[ ]Instantaneous Rate= -

NO NO O

NO

td NO

dt

Rate lawRate law

Rate of heterogeneous Rate of heterogeneous reactionreaction

depends on surface and depends on surface and concentrations of reagents in gas concentrations of reagents in gas

and sollutionand sollution:V = kSС

СаО(т) + СО2(г) = СаСО3(т)

V = kSпит.(СаО) С(СО2)

Background on Rates & Mechanisms

• Main Factors which influence reaction rate:– Concentrations of Reactants - Rates usually increase as reactant

concentrations increase. – Reaction Temperature - An increase in temperature increases

the rate of a reaction.– Presence of a Catalyst (not all rxns have catalysts)

• A catalyst is a substance which increases the rate of a reaction without being consumed in the overall reaction.

• The concentration of the catalyst or its surface area (if insoluble) are variables which influence the rate.

• Some catalysts are incredibly complex - like enzymes; and others are quite simple: H+ + H2O + CH2 = CH2 ------) CH3-CH2-OH + H+

– Type of Reactants– “Surface Area of Insoluble Reactant”

Exponents in the Rate Law• For a general reaction with rate law

we say the reaction is mth order in reactant 1 and nth order in reactant 2.

• The overall order of reaction is m + n + ….• A reaction can be zeroth order if m, n, … are zero.• Note the values of the exponents (orders) have to be

determined experimentally. They are not simply related to stoichiometry.

Concentration and RateConcentration and Rate

nmk ]2reactant []1reactant [Rate

First Order Reactions (to one component)

The Change of Concentration with TimeThe Change of Concentration with Time

0lnln CktC CNCHNCCH Co

39.198

3

Isomeric Transformation of Methyl Isonitrile to Acetonitrile

23

First-Order Reactions

2/1tHalf-life:

2/1tt oAA ][2/1][

tkA

AA

oln

2/1][

][2/1ln tk

A

AA

o

o

693.02ln2/1 tkA First-order reaction

2/12/1ln tkA

The time needed for [A] to drop to half its value

Akt /693.02/1 Independent of [A]o

A useful indication for the chemical reaction rate

Second Order Reactions

The Change of Concentration with TimeThe Change of Concentration with Time

0

11

Ckt

C

)(2

1)()( 2

3002 gOgNOgNO Co

Pseudo-Order Reaction Law

3 2 2

233

33 0 0 0

0 0 3 0

' ' 233

5 6 3 3

[ ][ ][ ][ ]

[ ] 1.0 10 [ ] 1.0 [ ] 1.0

[ ] [ ] [ ]

[ ][ ] ( [ ][ ] )

BrO Br H Br H O

d BrORate k BrO Br H

dt

BrO M Br M H M

Br H BrO

d BrOk BrO k k Br H

dt

Integrated Rate Law － zero order

0

0

[ ]

[ ]

0

0

[ ][ ] = ( )

[ ]

[ ] [ ]

[ ] [ ]

a a a

A

aA

a

a

aA P

d ARate k A k k ak

dt

d A k dt

A A k dt

A A k dt

Summary of Rate Laws to One-ComponentSummary of Rate Laws to One-Component

First-Order Second-Order Zeroth-Order

differential rate law (-dC/dt)

kC kC2 k

EquationC = Co·e-kt

ln C = -kt + ln Co

1/C = kt + 1/Co C = -kt + Co

Linear Equation ln C vs. t 1/C vs. t C vs. t

Linear Plot

Half-Life ln(2)/k 1/kCo Co/2k

Units on k time-1 M-1 time-1 M time-1

m = -k

b = ln Co

m = k

b = 1/Co

m = -k

b = Co

IV. Determination of OrderOrder - from units of k: If you are given the units of the

rate constant for a reaction, then you will know the overall order (slide 14). Not too common.

Order by Method #1 - from altering M: Measure initial rates keeping one reactant constant and change the concentration of another; observe the rates; calculate order as illustrated in the next few slides.

Order by Method #2 - from integrated rate expression: Use calculus & integrate the rate expression between the limits of time = 0 & time = t. By plotting out the variables of these integrated rate expressions you can determine the order. This will be shown in the lecture, and you will be doing this in the kinetics lab.

Application in pharmacy• Evaluation of drug stability of liquid dosage

forms

A typical plot of log rate constant as a function of pH for a drug (codeine sulfate) which undergoes both acid and base catalysis. Modifi ed from M.F. Powell, J.Pharm. Sci.75, 901