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Revision Notes on Chemical Kinetics:

Rate of Reaction:

  • Rate of change of extent of reaction is the rate of reaction.

  • Rate of reaction is positive for product and negative for reactant.

  • For reaction aA →bB
    Rate =1/b(Δ[B]/ Δ t)  = -1/a (Δ [A]/ Δt)

  • It goes on decreasing as the reaction progress due to decrease in the concentration(s) of the reactant(s).

  • Unit of rate of reaction : mol L-1 s-1

  • The rate measured over a long time interval is called average rate and the rate measured for an infinitesimally small time interval is called instantaneous rate.

  • In a chemical change, reactants and products are involved. As the chemical reaction proceeds, the concentration of the reactants decreases, i.e., products are produced.

  • The rate of reaction (average rate) is defined as the change of concentration of any one of its reactants (or products) per unit time.

Order of Reaction


 

For reaction aA + bB + ….. → cC+ ….

R ∝[A]m[B]or R = k[A]m[B]n….

Where m and n may or may not be equal to a & b.

m is order of reaction with respect to A and n is the order of reaction with respect to B.

m + n +… is the overall order of the reaction.

Elementary Reaction:

  • It is the reaction which completes in a single step.

  • A reaction may involve more than one elementary reactions or steps also.

  • Overall rate of reaction depends on the slowest elementary step and thus it is known as rate determining step.

Molecularity of Reaction:

  • Number of molecules taking part in an elementary step is known as its molecularity.

  • Order of an elementary reaction is always equal to its molecularity.

  • Elementary reactions with molecularity greater than three are not known because collisions in which more than three particles come together simultaneously are rare.

Chemical Reaction

Molecularity

PCl5  →  PCl3 + Cl2   

Unimolecular

2HI  →  H2 + I2 

Bimolecular

2SO2 + O →  2SO3

Trimolecular

NO + O3  →  NO2 + O2

Bimolecular

2CO + O2  →  2CO2

Trimolecular

2FeCl3 + SnCl2 → SnCl2 + 2FeCl2

Trimolecular

 

Differential and Integrated Rate Laws:

Zero Order Reactions:

Characteristic of Zero Order Reaction

For Reaction: A → Product

[A]0-[A]t  = k0t

Where,

[A]0 = Initial concentration of A

[A]t = Concentration of A at time t.  

k=  Rate constant for zero order reaction.

Half Life:

t1/2 = [A]0/2k

Unit of rate constant = mol dm-3s-1

Examples: 

  •  Enzyme catalyzed reactions are zero order with respect to substrate concentration.

  •  Decomposition of gases on the surface of metallic catalysts like decomposition of HI on gold surface.

First Order Reactions:

Characteristic of First Order Reaction

A → Product

(Δ [A] /A) = -k1Δt

 or k1=( 2.303/ t)log ([A]0 / [A]t

Half Life:

t1/2 = 0.693/k1

Half life is independent of the initial concentration of the reactant for a first order reaction.

Units of k1 =  s-1

Examples:

N2O5   2NO2 + 1/2O2

Br2  2Br

2HNO3  2NO + H2O

 H2O2 H2O + 1/2O2 

Pseudo First Order Reactions:

These are the reactions in which more than one species is involved in the rate determining step but still the order of reaction is one.

Examples:

  • Acid hydrolysis of ester: CH3COOEt + H3O+ →CH3COOH + EtOH 

  • Inversion of cane sugar:

  

  • Decomposition of benzenediazonium halides C6H5N=NCl +H2O → C6H5OH +N2 +HCl

Half – Life of a nth Order Reaction:

kt1/2 =  (2n-1-1)/(n-1)[A0]n-1

Where, n = order of reaction ≠1

Parallel  Reactions:

The reactions in which a substance reacts or decomposes in more than one way are called parallel or side reactions.

reaction-in-which-a-decomposes

If we assume that both  of them are first order, we get.

-\frac{d[A]}{dt} = (k_1 +k_2) [A] =k_{av}[A]

k1 = fractional yield of B × kav

k2 = fractional yield of C × kav

If k1 >  k2 then

A → B main and

A → C is side reaction

Let after a definite interval x mol/litre of B and y mol/litre of C are formed.

\frac{x}{y} =\frac{k_1}{k_2}

i.e

\frac{\frac{d[B]}{dt}}{\frac{d[C]}{dt}} =\frac{k_1}{k_2}

This means that irrespective of how much time is elapsed, the ratio of concentration of B to that  of C from the start (assuming no B  and C in the beginning ) is a constant equal to k1/k2.

Sequential Reactions:

This reaction is defined as that reaction which proceeds from reactants to final products through one or more intermediate stages. The overall reaction is a result of several successive or consecutive steps.

A → B → C and so on

A\overset{k_1}{\rightarrow}B\overset{K_2}{\rightarrow}C

-\frac{d[A]}{dt} = k_1[A]…....(i)

\frac{d[B]}{dt} = k_1[A]-K_2[B]…......(ii)

\frac{d[C]}{dt} = k_2[B]….......(iii)

Integrating equation (i), we get

[A]-[A]_oe^{-k_1t}

 

   

   

 

Arrhenius Equation:

k = A exp(-Ea/RT)

Where, k = Rate constant

A = pre-exponential factor

Ea = Activation energy

     ln k vs 1/T plot for Arrhenius Equation 

Temperature Coefficient: 

The temperature coefficient of a chemical reaction is defined as the ratio of the specific reaction rates of a reaction at two temperature differing by 10oC.

μ = Temperature coefficient= k(r+10)/kt

Let temperature coefficient of a reaction be ' μ ' when temperature is raised from T1to T2; then the ratio of rate constants or rate may be calculated as

\frac{k_T_2}{k_T_1}=\mu ^\frac{{T_2-T_1}}{10} =\mu ^{\frac{\Delta T}{10}}

log\frac{k_T_2}{k_T_1}=\mu ^\frac{{T_2-T_1}}{10} =\Delta T log\mu

\frac{k_T_2}{k_T_1}= antilog[\frac{\Delta T}{10 }] log\mu

Its value lies generally between 2 and 3.

Collision Theory of Reaction Rate

  • A chemical reaction takes place due to collision among reactant molecules.

  • The number of collisions taking place per second per unit volume of the reaction mixture is known as collision frequency (Z).

  • The value of collision frequency is very high, of the order of 1025 to 1028 in case of binary collisions.

  • Every collision does not bring a chemical change.

  • The collisions that actually produce the products are effective collisions.

  • The effective collisions which bring chemical change are few in comparison to the form a product are ineffective elastic collisions, i.e., molecules just collide and

  • disperse in different directions with different velocities.

  • For a collision to be effective, the following two barriers are to be cleared.

  1. Energy Barrier

  2. Orientation Barrier

Radioactivity:

All radioactive decay follow 1st order kinetics

For radioactive decay A ->B

-(dNA/dt) =l NA

Where, l =  decay constant of reaction

NA  = number of nuclei of the radioactive substance at the time when rate is calculated.

Arrhenius equation is not valid for radioactive decay.

Integrated Rate Law: Nt = Noe-lt

Half Life:  t1/2= 0.693/λ

Average life time: Life time of a single isolated nucleus, tav= 1/λ

Activity: Rate of decay

A = dNA/dt, Also, At = Aoe-lt

Specific Activity: activity per unit mass of the sample.

Units: dps or Becquerrel

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