# Order of Reaction

Order of Reaction is defined as the number of molecules whose concentration (changes) determines the rate of reaction. In other words, it is the sum of the powers of the concentration of reactants in the rate equation (rate law).

## Order of Reaction

Consider a reaction,

As determined from rate law. Rate = K [NO]2 [O2]1

Therefore Order of reaction with respect to NO is 2.

Order of reaction with respect to 2 is 1.

The overall order of reaction is 2 + 1 = 3.

## First Order of Reaction

Reactions whose rate is determined by the change of one concentration term only are known as first order reactions.

Consider a general reaction of the first order

The rate of such reaction at any moment will thus be given by the expression

Where CA is the concentration of the reactant A at the moment when the rate of reaction is determined and K is rate constant, a specific rate constant or velocity constant.

Examples

Since the slow (rate determining) step involves only one molecule, the order of reaction is 1 and not 2, although reaction is usually written as

where a = Initial concentration of the substance

x = Amount of substance decomposed in time t

Thus (a – x) = Amount left at time t.

The exponential form of the expression for the first-order reaction is

[ a – x ]=[a]e-kt

### Characteristics of first order reaction

1. The rate of reaction. The rate of reaction is directly proportional to the concentration of the reacting substance.
2. First order rate constant. It is a characteristic constant of a particular reaction at a given temperature. It does not depend on the initial concentration of the reactants, time of reaction and extent of reaction. Its unit is time-1, i.e. if t is expressed in seconds, K is expressed in seconds-1, if t is expressed in minutes, K is expressed in minutes-1. The value of K does not change with concentration units because a/(a – x) will be same whatever be the units of concentration.
3. A plot of log a/(a-x) versus time is linear passing through origin with slope = – K/2.303
4.  Half-life Period (Half-life time, t1/2). The half-life of a reaction is the time required to convert the original concentration of the reactant to half.

For first order reaction, at half-time i.e., at t1/2, x becomes a/2. Therefore, putting t = t1/2 and A = a/2 in eq. (i) we get

Note that half-life time of a first order reaction is constant and independent of the initial concentration of the reactant.

## Second Order of Reaction

Reactions whose rate is determined by the change of two concentration terms.

For example, for a general reaction

### Characteristics of Second order reaction

(i) The rate of reaction is directly proportional to the square of the concentration of the reacting substance.

(ii) The unit of second order rate constant is litre mole-1 time-1. The value of K depends upon the unit in which concentration of the reactant(s) is expressed.

(iii) The half-life of a second-order reaction is inversely proportional to the initial concentration of the reactants i.e., t1/2∝1/a (cf. half-life period of a first order reaction is inversely proportional to K and independent of a).

(iv) When a graph is plotted between t and 1/(a – x), a straight line is obtained; the slope of the line gives 1/K.

## Zero Order of Reaction

Reactions whose rate is not affected by concentration or in which the concentrations of the reactants do not change with time.Thus the rate of such reactions remains Constant.

Rate = K

Many photochemical reactions (e.g. formation of HCl from H2 and Cl2) and some heterogeneous reaction (e.g. decomposition of hydrogen iodide and ammonia on the surfaces of gold and tungsten) are the examples of zero order reactions.

### Characteristics of zero order reaction

(i) The rate of reaction is independent of the concentration of the reacting substance.

K=x / t

The concentration of products increases linearly with time. The plot of the concentration of products with time is a straight line passing through the origin.

(ii) The unit of zero order rate constant is mole litre-1 time-1.

(iii) The half-life is directly proportional to the initial concentration of the reactants.

t1/2 ∝ a

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