Chapter 5 Chemical Kinetics Part 2 free study material by TEACHING CARE online tuition and coaching classes

 

 

 

Note : ®          The activation energy is found to increase with the lowering of temperature i.e., at lower temperatures the activation energy tends to increase.

(2)  Transition state theory

• According to transition state theory the activated complex is supposed to be in equilibrium with the reactant
• Once the transition state is formed it can either return to the initial reactants or proceeds to form the
• Assuming that once formed the transition state proceeds to products we can say that rate is proportional to concentration of transition state. Mathematically, Rate µ Transition state; Rate= Constant × Transition state

a

• The activation energy for the forward reaction, (E ^f ) and the activation energy for the reverse reaction

(E^r ) are related to the enthalpy (DH) of the reaction by the equation DH = E ^f – E^r .

a                                                                                                                                                                                                                                     a              a

• For endothermic reactions, DH > 0, so that E^r < E ^f

a              a

• For exothermic reaction, DH < 0, so that E^r > E ^f .

a              a

Note : ®           Exothermic reaction requires less activation energy than the endothermic reaction. Therefore an exothermic reaction proceeds at a faster rate than the endothermic reaction.

• Kinetic stability of fuels : Combustion of fuels is highly exothermic reaction yet these can be safely stored in contact with oxygen or air. The stability of fuels is due to high activation energy of these combustion

• E_a cannot be zero (if suppose E_a =0 then according to Arrhenius equation k = A i.e., every collision between molecules leads to be chemical This is not true.)

A general approximate rule or the effect of temperature on reaction rates is that the rate of a reaction becomes

almost double for every 10o C rise in temperature. This is also called temperature coefficient.

Temperature coefficient = kt + 10 kt

Temperature coefficient : Temperature coefficient of a reaction is defined as the ratio of rate constants at two temperatures differing by (generally 25°C and 35°C) 10.

 

Or

 

The temperature coefficient for most of the reactions lies between 2 and 3 i.e. the rate of reaction increase by

a factor of 2 to 3, for every 10 ^o C rise in temperature.

 

 

 

 

Arrhenius proposed a quantitative relationship between rate constant and temperature as,

 

k = Ae – Ea / RT

…..(i)

 

The equation is called Arrhenius equation in which constant A is known as frequency factor. This factor is

 

related to number of binary molecular collision per second per litre.

Ea is the activation energy. T is the absolute

 

temperature and R is the gas constant. Both A and logarithm equation (i) may be written as,

Ea  are collectively known as Arrhenius parameters. Taking

 

log k = log A – Ea 2.303 RT

…..(ii)

 

 

 

The value of activation energy

(Ea )

increases, the value of k decreases and therefore, the reaction rate

 

decreases. When log k plotted against

1 , we get a straight line. The intercept of

T

 

this  line  is   equal   to   log   A     and   slope  equal  to

 

Ea = -2.303 R ´ slope .

• Ea

2.303 R

.    Therefore

 

Rate constants for the reaction at two different temperatures T and T ,

1               2

 

…..(iii)

 

 

where k1 and k2 are rate constant at temperatures T1

and T2

respectively (T2 > T1 ) .

 

Note : ®           Generally rate of reaction increases with increase in temperature but remember for the reaction

2NO + O₂ ® 2NO₂;      the rate decreases slightly with increase in temperature because it has small negative temperature coefficient.

• When E_a= 0, the rate of reaction becomes independent of temperature (E_a= activation energy)

Example : 17 In the Arrhenius equation for a certain reaction, the values of A and Ea are 4 ´ 10¹³ sec ^–1 and 9.86 kJ mol ^–1

respectively. If the reaction is of first order, at what temperature will its half life period be 10 minute

 

 

(a) 311.34 K                               (b) 31.134 K                               (c) 411.34 K                       (d) 41.134 K

[IIT 1990]

 

Solution : (a)  According to Arrhenius equation, k = Ae ^–Ea / RT or log k = – Ea ´  1                

 

k = 0.693 = 0.693 = 1.155 ´ 10^–3

A         RT

2.303

 

t1 / 2

10 ´ 60

 

\ log 1.155 ´ 10^–3

4 ´ 10¹³

= –         98.6 ´ 10³

8.314 ´ T ´ 2.303

or – 16.54 = –         98600      

8.314 ´ 2.303 T

 

or T =            98600           = 311.34 K.

8.314 ´ 2.303 ´ 16.54

Example : 18 A first order reaction is 50% completed in 30 minutes at 27°C and in 10 minutes at 47°C. Calculate the activation energy of the reaction.

 

 

 

 

(a)

46.8 kJ mol ^–1

(b)

43.8 kJ mol ^–1

50.8 kJ mol ^–1

60.8 KJ mol ^–1

 

Solution : (b)  Let us first calculate k₁ and k ₂ at temperatures 27°C and 47°C. We know that t1 / 2 = 0.693

k

or k = 0.693

t1 / 2

 

At 27°C, t_{1/ 2} = 30 min ; k1 = 0.693 = 0.0231

30

At 47°C, t_{1/ 2} = 10 min ; k 2 = 0.693 = 0.0693

10

 

Now, log k2 =

 

E_a       é 1 – 1 ù ;

 

log 0.0693 =

E_a             é 1   –   1 ù

 

 

k1      2.303R ê T1

T2 ú

0.0231

2.303 ´ 8.314 êë 300

320 úû

 

ë

û

log 3 =

E_a             é      20      ù

 

Þ 0.4771 =

Ea ´ 20

 

 

2.303 ´ 8.314 êë 300 ´ 320 úû

or Ea = 0.4771´ 2.303 ´ 8.314 ´ 300 ´ 320

20

2.303 ´ 8.314 ´ 300 ´ 320

 

= 43848 Jmol ^–1 or 43.8 kJ mol ^–1 .

 

Example : 19 The rate of reaction becomes 2 times for every

10^o C

rise in temperature. How the rate of reaction will

 

 

 

 

Solution: (b)

increases when temperature is increased from 30^o C to 80^o C

(a) 16                                 (b) 32                                 (c) 64                           (d) 128

kt + 10 = rt + 10 = 2 .

 

 

kt                         rt

 

For an increase of temperature to 50^o C , i.e., 5 times, the rate increases by 2⁵

times, i.e., 32 times.

 

Example : 20 The rate constant, the activation energy and the Arrhenius parameter of a chemical reaction at

25^o C

are

 

3.0 ´ 10^–4 s^–1, 104.4 kJ mol^–1 and 6.0 ´ 10¹⁴ s^–1 respectively. The value of the rate constant as T ® ¥ is

 

 

(a)

2.0 ´ 10¹⁸ s^–1

(b)

6.0 ´ 10¹⁴ s^–1

(c) Infinity                     (d)

[IIT 1996]

3.6 ´ 10³⁰ s^–1

 

 

Solution: (b)

k = Ae ^{–Ea / RT} ; At T ® ¥

i.e.,

1 ® 0 ;

T

k = A = 6 ´ 10¹⁴ sec ^–1

 

Example : 21 The activation energy of a reaction is 9kcal / mole . The increase in the rate constant when its temperature is raised from 295 to 300 K is approximately                                                                                        [Pb. CET 1988] (a) 10%                                          (b) 50%                              (c) 100%                      (d) 28.8%

 

 

Solution: (d)

log k 2 =

 

Ea            é T2 – T1 ù =    9000    é 300 – 295 ù = 0.1103

 

 

k         2.303 R ê T T      ú       2.303 ´ 2 êë 295 ´ 300 úû

1                                   ë     1   2    û

 

 

Hence

k 2 = 1.288 or k  = 1.288 k

i.e., increase = 28.8%.

 

k

2                              1

1

• The study of reaction pathway or mechanism of a reaction is very important aspect of kinetics of
• In some reactions, intermediates formed which accumulate during the early period of the reaction, reach to the maximum concentration and then react and give the final
• The necessary condition for a mechanism is that it must lead to the correct

(1)  Reaction involving first order consecutive reactions

 

 

 

• In such reactions, the reactions form a stable intermediate compound before they are finally converted into the
• For example, reactants (R) are first converted to intermediate (I) which is then converted to product (P) as

R ¾¾^k1  ® I ¾¾^k¾2  ® P ;  Therefore, the reaction takes place in two steps, both of which are first order i.e.,

 

Step I : Step II :

R ¾¾^k1  ® I

I ¾¾^k¾2  ® P

 

This means that I is produced by step I and consumed by step II. In these reactions, each stage will have its own rate and rate constant the reactant concentration will always decrease and product concentration will always increase as shown in fig.

• Reaction involving slow step : When a reaction occurs by a sequence of steps and one of the step is slow, then the rate determining step is the slow For example in the reaction

1                 2

R ¾¾k1  ® I ;  I ¾¾k2  ® P ,  if k   << k    then I is converted into products as soon as it is formed, we can say that

– d[R] = d[P] = k  [R]

dt             dt           1

• Parallel reactions : In such type of reactions the reactants are more reactive, which may have different

 

orders of the reactions taking place simultaneously. For example, in a system containing

NO2

and

SO2 , NO2    is

 

consumed in the following two reactions,

2NO2  ¾¾^k1 ® N 2 O4 ;

NO2  + SO2  ¾¾^k¾2  ® NO + SO3

 

The rate of disappearance of

NO2

will be sum of the rates of the two reactions i.e.,

 

– d[NO2 ] = 2k [NO ]2 + k

[NO  ][SO  ]

 

dt                 1               2

2               2                 2

 

Absorption of radiant energy by reactant molecules brings in photophysical as well as photochemical changes. According to Einstein’s law of photochemical equivalence, the basic principle of photo processes, each reactant molecule is capable of absorbing only one photon of radiant energy. The absorption of photon by a reactant molecule may lead to any of the photo process.

 

 

 

The chemical reactions, which are initiated as a result of absorption of light, are known as photochemical reactions. In such cases, the absorbed energy is sufficient to activate the reactant molecules to cross the energy barrier existing between the reactants and products or in other words, energy associated with each photon supplies activation energy to reactant molecule required for the change.

(1)  Characteristics of photochemical reactions

• Each molecule taking part in a photo process absorbs only one photon of radiant energy thereby increasing

its energy level by hv or hc

l

• Photochemical reactions do not occur in dark.
• Each photochemical reaction requires a definite amount of energy which is characteristic of a particular wavelength of For example, reactions needing more energy are carried out in presence of UV light (lower

l , more E/Photon). A reaction-taking place in UV light may not occur on exposure to yellow light (lower l and lesser E/Photon)

• The rate of photochemical reactions depend upon the intensity of radiation’s
• The DG values for light initiated reactions may or may not be negative.
• The temperature does not have marked effect on the rate of light initiated

(2)  Mechanism of some photochemical reactions

• Photochemical combination of H₂ and Cl₂ : A mixture of H 2and Cl 2 on exposure to light give rise to

 

the formation of HCl, showing a chain reaction and thereby producing absorbed.

10⁶ to 10⁸ molecules of HCl per photon

 

2                 2

H    + Cl   ¾¾sunl¾ig¾ht  ® 2HCl

The mechanism leading to very high yield of HCl as a result of chemical change can be as follows. Chlorine molecules absorb radiant energy to form an excited molecule which decomposes to chlorine free radicals (Cl) to give chain initiation step.

 

Light absorption step :

Cl2  ¾¾^hv ® Cl2*

(Excited molecule)…………. (i)

 

Chain initiation step :

Cl  *  ® Cl ·  + Cl ·

……..(ii)

 

2

The chlorine free radical then combines with H ₂

molecule to form HCl and

H ·  free radical. The H ·

free

 

radical so formed again combines with another chain propagation step.

Cl2

molecule to give HCl and

Cl ·

free radical back resulting into

 

Chain propagation step :

Cl ·  + H   ® HCl + H ·

2

2

H · + Cl  ® HCl + Cl ·

……..(iii)

 

The combination of two Cl · free radicals leads to chain terminating step.

 

Chain terminating step :

Cl ·  + Cl ·  ® Cl

……..(iv)

 

2

• Photochemical combination of H₂ and Br₂ : The combination of H2

and Br2

to form HBr in presence

 

of light is also an example of chain reaction like photochemical combination of H₂

and

Cl₂ . Here two

Br2

 

molecules absorb photon, however, inspite of chain reaction only one molecule of HBr is formed for each 100 photon absorbed by 100 molecules of Br₂ . The mechanism of reaction is given below.

 

H2 + Br2

¾¾lig¾ht  ® 2HBr

 

 

 

 

Mechanism :

Light absorption step :

Chain initiation step :

 

Br + hv ® Br *

2

2                                2

2

Br * ® Br · + Br ·

 

……..(i)

……..(ii)

 

Chain propagation step :

Br * + H

® HBr + H ·

……..(iii)

 

 

 

 

 

Chain termination step :

H * + Br ® HBr + Br ·

2

2

Br · + Br · ® Br

……..(iv)

……..(v)

 

The lower values of HBr formation per photon of light absorbed has been attributed to the fact that step (III) is highly endothermic and thus before step (III) can take place most of the bromine free radicals recombine as per step

 

• to give

Br₂ molecule and thus providing less feasibility for step (IV) i.e. steps regenerating free radicals. Also the

 

decomposition of HBr increases with increase in temperature.

• Quantum yield (or quantum efficiency) : The quantum efficiency or yield (f )

of a photochemical

 

reaction may be expressed as,

f = No. of molecules reacted or product formed No. of photon absorbed

 

 

• Application of photochemistry : Photochemistry has significant role in our daily life. Some of the photochemical reactions commonly known as cited below,

(i) Photosynthesis in plants                                             (ii) Photography

(iii) The formation and destruction of ozone layer     (iv) Photoetching in electronic industry

(v) Many polymerization reactions.                                 (vi) Modern printing technology

(vii) Free radical combinations to obtain many compounds.

• Damaging effect of photochemistry : As already discussed, the destruction of ozone layer by chloro- fluorocarbon is due to photochemical decomposition of these compounds. The fading away of colours in coloured fabrics is due to the photochemical decomposition of colouring material (i.e. dyes) used in printing

Note : ®          Generally ultraviolet or visible radiation’s are used for carrying out such type of reactions because their photons possess energies approximately of the order of 420 kJ per mol which is comparable to mole of the bond energy. Thus UV radiation energy is capable of breaking the bonds. On the other hand IR radiation’s are generally not used because their photons possess energy of the order of 60 kJ per mole which is quite less for breaking the bonds.

• Destruction of ozone layer : The formation and dissociation of ozone keeps a balance of ozone and

 

oxygen in the ozone layer. However the diffusion of chloro-fluorocarbon such as

CFCl3  and  CF2 Cl2

 

• · ·                                 ·

 

into   the   ozone   layer   are   destroying   the   ozone.

Cl2 + hn ® CF2 Cl+ Cl ;          Cl+ O3   ® ClO+ O2 ;

 

• ·

Cl O + O₃ ® Cl+ 2O₂ . Chloro-fluorocarbons are used as aerosol repellents and as refrigerants.

Hence, ozone layer which acts as an umbrella for earth is being continuously destroying by the harmful UV radiation’s coming from the sun.

 

 

 

 

Rates of chemical reactions differ form very slow to very fast. The rates of moderate speed reactions lying in between these two extreme reactions. However, rates of some instantaneous reactions are so fast that they occur within 10^–12 second or in even less time. For example,

 

• Neutralization reactions have half life of 10^–10 sec ; H ⁺

• OH^–

® H O

 

(aq.)

(aq.)

2   (l)

 

• Photosynthesis has half life of 10^–12 sec ;

6CO2 + 6H2O ¾¾^chlo¾^rop¾^h¾^yll ® C6 H12O6  + 6O2

hv

 

• Some precipitation reactions have very short half life; AgNO3 + KCl ® AgCl ¯ +KNO3
• Isomerisation of retinal in vision has half life of 10^–12 sec

Rates of such reactions cannot be studied by ordinary methods because change in concentration cannot be measured during this short interval of time. However, modern techniques such as flow methods, relaxation methods, flash photolysis, laser technique and spectrophotometric methods are used to study such fast reactions.

 

• Photosynthesis in plants : Plants obtain their food for growth by the combination of

CO2  and

H2O   in

 

presence of chlorophyll and light (a fast reaction) which leads to the preparation of carbohydrate and this phenomenon is known as photosynthesis. The studies on photosynthesis involve flash photolysis technique. The following mechanism has been proposed for photosynthesis. First step of the reaction mechanism involves the excitation of chlorophyll molecule by absorbing photon of red light. The excited chlorophyll molecule transfers its

 

energy in the form of an electron to nearby reactant molecule A within 10^–12

accepts this energy is known as electron acceptor.

second. The reactant molecule which

 

Chlorophyll ¾¾^hv ® Chlorophyll^*  ;

(Excited molecule)

Chlorophyll^* + A ¾¾® Chlorophyll + A^– + Energy

( A is CO₂ or H ₂O)

 

The electron acceptor (A) transfer this electron to another electron acceptor molecule (B). A^– + B ® A + B^– + E

The process leads to release of energy which is used for the series of reaction to yield the synthesis of energy

rich molecule of carbohydrates from CO2 and water. 6CO + 6H O ¾¾¾® C H  O  + 6O

Energy

• Isomerisation of retinal in vision : The mechanism involves two steps
  • The retinal molecule (a light sensitive molecule present in the retina of eye) gets excited on exposure to light and undergoes geometrical isomerization and the energy absorbed is stored as chemical The process takes place within 10^–12 sec .

 

• As soon as the first step gets completed, the retinal is converted back into its original form within 10^–12

and the energy released is used to send signals to the brain which ultimately causes the sensation of vision.

Differences between Photochemical and Thermochemical reactions

sec

 

 

Photochemical reactions	Thermochemical reactions
These reactions are initiated by light radiation.	These reactions are initiated by heat energy.
They cannot occur in dark.	They do occur in dark.
Temperature does not have any significant effect on the rates of	The temperature does have a marked effect on the rates of these
such reactions and temperature coefficient is low.	reactions and temperature coefficient is generally high.
The value of DG may be +ve or – ve.	DG is – ve for such reactions.

 

 

Important tips

 

Chemiluminiscence : It is the emission of light in chemical reaction at ordinary temperature e.g., the light emitted by

glow worms (fire flies) is due to the oxidation of a protein Luciferin present in them.

Fluorescence and Phosphorescence : There are some substances which when exposed to light or radiation, absorbs light and immediately start re-emitting the energy. The glow continue as long as the source of light is there. Such substances are called fluorescent substances and phenomenon as fluorescence e.g., fluorite (CaF₂), fluorescein dye etc.

On the other hand, there are some substances which continue to glow for some time even after the source of light is cut off. Such substances are called phosphorescent substances and phenomenon as phosphorescence e.g., Zinc sulphide and sulphides of other alkaline earth metals.

Bioluminiscence : Certain living organisms emit light and show the phenomenon of chemiluminiscence. It is known as Bioluminiscence e.g., light emission in fire flies.

 

Example of fourth order reaction,

4 KClO3

⇌ 3KClO₄ + KCl

 

Grothus-Draper law : When light falls on a substance, a part of light is absorbed, a part is reflected and a part is transmitted. Only that part of light which is absorbed causes a particular reaction to occur.

Stark’s Einstein law of photochemical equivalence : According to this law, every atom or molecule taking part in a photochemical reaction absorbs only one quantum of radiation. (E = hn ) . The energy absorbed by one mole of reacting molecules is known as one Einstein.

Free energy (DG) for thermochemical reactions is always negative but remember, DG for photochemical reactions may not always be negative. It is because a part of the light energy absorbed by the reactants is converted into free energy of the

products. In the following photochemical reactions for which DG is positive and still they are spontaneous

• Ozanisation of oxygen (b) Synthesis of carbohydrates (c) Decomposition of HCl to H₂ and Cl₂

There are some substances which when added to a reaction mixture helps to start the photochemical reaction but do not undergo any chemical change are called photosensitizer and this process is called photosensitization. A photosensitizer simply acts as a carrier of energy. For example (i) Dissociation of H₂ in the presence of mercury vapours. (ii) Photosynthesis in presence of chlorophyll.

 

 

 

 

 

***