Reaction Of Various Orders

(i) Zero order reactions

A reaction is said to be zero order if its rate is independent of the conc. of the reactants, consider the general reactions

A → Products

If it is reac. of zero order

or d[A] = -K dt

Integrating both sides, we get

[A] = -Kt + I ………………….. (i)

where I is a constant of integration

At t = 0, [A] = [A]₀

∴ [A]₀ = I

Substituting this value of I in equation (i), we get

 [A] = -Kt + [A]_{0  .....(i)}

or Kt = [A]₀ - [A]

K = 1/t {[A]₀ -[A_t]}......(iii)

Some important characteristics of reaction of zero order.

(i) Any reaction of zero order must obey equation (ii). As it is a equation of straight line
(y = mx + c), the plot of [A] versus t will be a straight line with slope = -K and intercept on the conc. axis = [A]₀ as shown in figure

(ii) Half reaction period:

Unit of K:

Examples of zero order reaction

(i) Photochemical reaction between hydrogen and chlorine

(ii) Decomposition of N2O on hot platinum surface :

(iii) Decomposition of NH₃ in presence of molybdenum or tungsten

First order reaction

A reaction is said to be of the first order if the rate of the reaction depends upon one conc. term only.

Consider the reaction

A → Products

Let ‘a’ be the conc. of A at the start and after time t, the conc. becomes (a – x), i.e., x has been changed into products. The rate of reaction after time ‘t’ is given by the expression

or

Upon integration of above equation,

where c is integration constant

when t = 0, x = 0

c = -log_ea

Putting the value of ‘c’,

If the initial concentration is [A]₀ and the concentration after time t is [A], then putting a = [A]₀ and (a – x) = [A], equation becomes

This equation can be written in the exponential form as

Some important characteristics of first order reaction

(a) A change in conc. unit will not change the numerical value of K. Let the new unit be n times the first one.

So

(b) Graphical method:

(c) Half life period:

The time taken for any fraction of the reaction to be completed is independent of the initial concentration.

Half – Life of a nth Order Reaction:

To find out the t½ for a nth order reaction where n ≠1.

Therefore for a nth order reaction, the half life is inversely related to the initial concentration raised to the power of (n–1).

Note:

It can be noted that for a zero order reaction t_1/2 = [A]₀/2k

Examples of first order reaction

(i) Decomposition of H₂O₂ in aqueous solution

(ii)

(iii)

Unit of rate constant

where n = order of reaction

Related Topics

1. Order Reaction

2. Some Complex First Order Reaction