i. r. levine, pp. 528-533 17.1 reaction kinetics; 17.2 ... · advance of the reaction can be...

§9.2 Reaction rate and rate equation

I. R. Levine, pp. 528-533

17.1 reaction kinetics;

17.2 measurement of reaction rates

The rate (r) of a chemical reaction is

defined as the concentration change of a

reactant or a product per unit time.

(1) Expression of reaction rate

instantaneous rate: [A]dr

dt

t1 t

c

2 1

2 1

[A]=

c cr

t t t

mean rate

t

c

t1 t2

c1

c2

Physical meaning:

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

Initial instantaneous rate?


N2 + 3H2 == 2NH3

2

2

H

H

dcr

dt 2

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

What is its Unit?



N2 + 3H2 == 2NH3

For general reaction:

aA + bB gG + hH

When the extent of reaction is d

GA B Hdndn dn dn

da 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 or in solution

without change of solution volume

Define rate V

Jr



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) Measurement of reaction rate

Physical meaning:

slope of the c ~ t curve

i

r

1

dt

cd i ][kinetic curve

0

tdt

dcr

Initial rate

ttdt

dcr

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:

Can other methods can be adopted to

follow the concentration change of NaOH?



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 .



C12H22O11 + H2O C6H12O6 + C6H12O6

sucrose glucose fructose

Substance sucrose glucose fructose

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



CH3COOC2H5 + NaOH

CH3COONa + C2H5OH

the rate of which can be monitored

using pH meter or conductometer.

N2O5 = 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

groupFTIR 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.



Flow method

Difficulties in study on kinetics

Stable flow: l t

Mixer detector

Moving direction



(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 1

2 2[H ] [I ]r k

H2 + Cl2 = 2 HCl

1 0.5

2 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 0.5

2 2[H ] [Cl ]r k

the sum of the partial order n = + +

+… is the overall order of the reaction,

or more simply, the reaction order.

This implies that the reaction obeying

rate law is first-order in H2 and 0.5-

order in Cl2.

The overall order is 1.5.



AA B C

dcr kc c c

dt

2SO2 + O2 2SO3

1

3 22 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

AA B C

a b cdcr kc c c

dt

Partial order = stoichiometric coefficient

Reaction order = number of molecules

involved in the reaction

For example:

2I + H2 = 2HI

2

2

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-1:

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.

First-order second-order third-order zeroth-order

1A Pk

2

2

A + B P

2A P

k

k

3

3

3

3A P

2A + B P

A + B + C P

k

k

k

0A Pk



i. r. levine, pp. 528-533 17.1 reaction kinetics; 17.2 ... · advance of the reaction can be...

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