§9.2 Reaction rate and rate equation

The rate (r) of a chemical reaction is defined as the change

in concentration of a reactant or a product per unit time.

There are two kinds of reaction rates:

2 1

2 1

[A]=

c cr

t t t

2.1 expression of reaction rate

mean rate

instantaneous rate:

[A]dr

dt

Physical meaning:

the slope of the [A] ~ t curve at time t. t1 t

c

t

c

t1 t2

c1

c2

N2 + 3H2 == 2NH3

2

2

H

H

dcr

dt2

2

N

N

dcr

dt 3

3

NH

NH

dcr

dt

It is apparent that 2 2 3N H NH

1 1

3 2r r r

When expressed using different species, the rate of the reaction

may attain different values, which is not convenient and

sometimes may even cause confusion.

Definition: extent of reaction or advancement ()

i i,0

i

n n

where i is the stoichiometric coefficient of the reaction.

Definition: The true rate of the reaction or rate of conversion (J):

dt

dJ

aA + bB gG + hH

For general reaction:

aA + bB gG + hH

When the extent of reaction is d

GA B Hdndn dn dnd

a b g h

GA B H1 1 1 1dndn dn dndJ

dt a dt b dt g dt h dt

When the reaction takes place in a container with constant volume

Define rate V

Jr

dt

dn

hdt

dn

gdt

dn

bdt

dn

adt

dJ HGBA 1111

dt

d

hdt

d

gdt

d

bdt

d

ar

]H[1]G[1]A[1]A[1

dt

cdr i

i

][1

Unit: mol m-3 s-1

2.2 measurement of reaction rate

Physical meaning:

slope of the c ~ t curvei

r1

dt

cd i ][kinetic curve

0

tdt

dcr

ttdt

dcr

Initial rate

Rate at any time

tt = 0 t = t

c

The key subject of kinetic study is to measure the concentration of some species after arbitrary time intervals.

The concentration of the species can be measured using either chemical or physical methods.

CH3COOC2H5 + NaOH

CH3COONa + C2H5OH

The reaction can be stopped by removing

of CH3COOC2H5, and the consumption of

NaOH can be determined by chemical

titration.

For example:

t = 0 t = t1 t = t2

The change in physical properties of the reaction system

which relates to the concentration of reactants or products can

be usually chosen as indicator of the progress of the reaction.

The first successful example for measuring concentration of reactant

physically was made by Wilhelmy in 1850 .

He determined the residual concentration of sucrose by measuring

the change of the rotation angle of a beam of plane-polarized light

passing through the hydrolysis solution (optical activity).

C12H22O11 + H2O C12H22O11 + C12H22O11

sucrose glucose fructose

Substance sucrose glucose fructose

[]D25 +66.5 o +52 o - 92 o

The rotation angle of the 1:1

mixture of glucose and fructose

is –20 o

We still use in it in our physical

chemistry laboratory t1 t2

20

[]

[]2

[]1

66.5

t

CH3COOC2H5 + NaOH

CH3COONa + C2H5OH

CH3COOC2H5 + NaOH

CH3COONa + C2H5OH

the rate of which can be monitored using pH meter or conductometer.

N2O5 = N2O4 + 0.5 O2N2O5 = N2O4 + 0.5 O2

When this reaction takes place in a container with constant

volume, the rate of the reaction can be monitored by measuring

the pressure change. And when this reaction takes place under

constant pressure, the advance of the reaction can be monitored

by measuring the volume increase. dilatometer.

Stretch of epoxy group

FTIR spectroscopy

The physical parameters usually used for monitoring

reaction process includes volume, pressure, electric

conductance, pH, refractive index, thermal conductivity,

polarimetry, spectrometry, chromatography, etc.

Analyzing methods:

1) Static method

2) Flow method

1) Real time analysis

2) Quenching

All the above methods are valid only for reactions with half-lives

of at least a few seconds, i.e., “slow” reaction. For fast reaction of

half-lives ranging between 100 ~ 10-11 s, special methods are

required.

Stable flow: l t

Flow method

Difficulties in study on kinetics

Mixer detector

Moving direction

2.3 Rate equation and the law of mass action

The concentration-dependence of rate:

r = r(ci) = r(cA, cB, cC…)

Where ci represents concentration of individual specie present

in rate equation.

In many instances, the rate of a reaction is proportional to

the concentrations of the reactants raised to some power.

CBA

A cckcdt

dc

rate equation

Rate law

For example:

H2 + I2 = 2 HI 1 12 2[H ] [I ]r k

H2 + Cl2 = 2 HCl 1 0.52 2[H ] [Cl ]r k

AA B C

dcr kc c c

dt

Where rate coefficient/constant (k) is a proportionality constant

/coefficient independent of concentration.

The exponent shows the effect of concentration on the reaction

rate. In 1895, Noyes defined them as partial order of the reactant.

, is the partial order of the reaction with respect to A or B, respectively.

1 0.52 2[H ] [Cl ]r k

This implies that the reaction obeying rate law is first-order in H2 and

0.5-order in Cl2.

the sum of the partial order n = + + +… is the overall order of the reaction, or more simply, the reaction order.

The overall order is 1.5.

1 0.52 2[H ] [Cl ]r k

2SO2 + O2 2SO3

13 2

2 3

[SO ]2 [SO ][SO ]

dr k

dt

is first-order in SO2, -0.5-order in SO3 and 0.5 order overall.

n, , , , etc., different from the stoichiometric coefficient, may

be integers, decimals, of plus or minus values.

Rate law must be determined from measurements of reaction

rate and cannot be deduced from the reaction stoichiometry.

For elementary reaction, = a, = b, etc.

AA B C

dcr kc c c

dt A

A B Ca b cdc

r kc c cdt

Partial order = stoichiometric coefficient

Reaction order = number of molecules involved in the reaction

For example: 2I + H2 = 2HI

22

1 [I][I] [H ]

2

dr k

dt

Law of mass action valid only for elementary reaction

An exercise

2A k1

k2

B + C D

E

k3

k4

dt

d ]A[

dt

d ]B[

dt

d ]C[

dt

d ]D[

dt

d ]E[

Group work:

Write the differential form of rate equation and deduce the

integration rate equations of reactions with simple orders.

A member of a chosen group will be asked to deduce the

equation on blackboard this Thursday.