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]ⁿ 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.

Differential and Integrated Rate Laws:

Zero Order Reactions:

For Reaction: A → Product

[A]₀-[A]_t  = k₀t

Where,

[A]_{0 =} Initial concentration of A

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

k₀  =  Rate constant for zero order reaction.

Half Life:

t_1/2 = [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:

A → Product

(Δ [A] /A) = -k₁Δt

 or k₁=( 2.303/ t)log ([A]₀ / [A]_t) 

Half Life:

t_1/2 = 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:

kt_1/2 =  (2^n-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.

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

k₁ = fractional yield of B × k_av

k₂ = fractional yield of C × k_av

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.

i.e

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

…....(i)

…......(ii)

….......(iii)

Integrating equation (i), we get

Arrhenius Equation:

k = A exp(-E_a/RT)

Where, k = Rate constant

A = pre-exponential factor

E_a = Activation energy

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 10^oC.

μ = Temperature coefficient= k_(r+10)/k_t

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

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 1^st order kinetics

For radioactive decay A ->B

-(dN_A/dt) =l N_A

Where, l =  decay constant of reaction

N_A  = 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: N_t = N_oe^-lt

Half Life:  t_1/2= 0.693/λ

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

Activity: Rate of decay

A = dN_A/dt, Also, A_t = A_oe^-lt

Specific Activity: activity per unit mass of the sample.

Units: dps or Becquerrel