# Determination of order of Reaction

There are at least four different methods to ascertain the order of a reaction.

(i)       Integration method: This method consists in performing the reaction between required amounts of the reactants. The products formed are analysed from time to time and the concentration of reactant is determined. These values are substituted in equations for various order reactions.

E.g.

$k = \dfrac{2.303}{t} \log_{10} \dfrac{a}{a- x}$ ………(for first order reaction)

$k = \dfrac{1}{t} \times \dfrac{x}{a(a- x)}$ ……………(For second order reaction)

$k = \dfrac{1}{2t} \times \dfrac{x(2a- x}{a^2(a- x)^2}$ …….(For third order reaction)

and the order of reaction is then known by that equation which gives constant value of velocity constant, k.

This method is the commonest method for determining the order of the reaction.

(ii)        Graphical Method: We know that the reaction velocity in a first order reactions varies as one concentration term; while in second order reactions, the rate is determined by variation of two concentration terms and so on. Mathematically,

For a first order reaction: $\dfrac{dx}{dt} = k(a- x)$

For a second order reaction: $\dfrac{dx}{dt} = k(a- x)^2$

For a third order reaction: $\dfrac{dx}{dt} = k(a- x)^3$

In general, For a nth order reaction: $\dfrac{dx}{dt} = k(a- x)^n$

Here it is assumed that the initial concentrations of the reactants are same.

The various values of $\dfrac{dx}{dt}$ are plotted against (a — x) and if I the graph so obtained is a straight line then the reaction will be of first order. But if straight line is obtained by plotting $\dfrac{dx}{dt}$ and $(a- x)^2$, then the reaction is of second order. Similarly if a straight line is obtained between $\dfrac{dx}{dt}$ and $(a- x)^3$, it will be a third order reaction.

(iii)       Isolation method: In this method all the reactants are taken in very large excess except one and the order of the reaction is determined by the first method. The concentrations of the substances taken in excess are considered to be constant. The sum of the orders, obtained by the process of isolation of each reactant is the order of the reaction. The method may be illustrated by the reaction between sodium formate and silver acetate.

$\underset{\text{silver acetate}}{2CH_3COOAg} + \underset{\text{sod. Formate}}{HCOONa} \to 2Ag \downarrow + CO_2 \uparrow + CH_3COOH + CH_3COOONa$

When silver acetate is taken in large excess, then the reaction is of first order, but when sodium formate is taken in excess the reaction is of second order. Hence the reaction is of third order.

(iv)        Half period reaction Method: In this method, the time at which one-half of the substance has disappeared is determined and the experiment is repeated with different initial concentrations of the reactants. The order is then known with the help of the following facts:

$t_{1/2} \propto \dfrac{1}{a^{n- 1}}$

Order of Reaction $n = 1 + \dfrac{( \log t_{1/2} )_1 - (\log t_{1/2} )_2}{ \log a_2 - \log a_1}$

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