The following methods are employed to determine the rate law, rate constant and order of reaction.

**1. GRAPHICAL METHOD**

This method is used to determine the rate law of the reaction which involves only one reactant species. The various steps involved are:

(i) The concentrations of reacting substance are determined at different time intervals by some suitable method.

(ii) A graph is plotted between concentration and time.

(iii) For the plot of concentration vs. time, the instantaneous rates corresponding to different concentrations are determined by drawing tangents to the curve and subsequently calculating their slopes as discussed earlier (instantaneous rate).

(iv) Different graphs are now plotted between:

(a) reaction rate vs. concentration or

(b) reaction rate vs. (concentration?_ or in general,

(c) reaction rate vs. (concentration f. where n = I. 2, 3 and so on.

If a straight line is obtained in the first case, it means the rate is directly proportional to concentration of the reactant This in turn means that the rate law is given as,

rate= k [Reactant]

and therefore its order is one.

Similarly, if a straight line is obtained in second case. then

rate= k [Reactant]2

and its order is two.

**EXPERIMENTAL DETERMINATION OF ORDER BY GRAPHICAL METHOD**

Let us explain the above method, in details, by taking the example of decomposition of dinitrogen pentaoxide,

2N_{2}O_{5}(g) à 4NO_{2}(g) + O_{2}(g)

As the above reaction involves gaseous reactants and products, therefore, it is convenient to observe the changes in the pressure, accompanying the reaction. From the measured values of total pressure, first the partial pressure of N_{2}O_{5} is calculated and then the concentration in moles per litre of N_{2}O_{5} is determined. The molar concentrations of N_{2}O_{5} at different time intervals so obtained are given in Table 20.2.

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**Table 20.2. Concentration-Time Data for Decomposition of N _{2}OsCg)**

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Time (min) [N _{2}O_{5}J (mol dm-3)

0 1.12 x 10^{-2}

10 1.13 x 10^{-2}

20 0.84 x 10^{-2}

30 0.62 x 10^{-2}

40 0.46 x 10^{-2}

50 0.35 x10^{-2}

60 0.26 x 10^{-2}

70 0.19 x 10^{-2}

80 0.14 x 10^{-2}

Thereafter, the rates for reactions (Table 20.3) at different time intervals is obtained by calculating the slope of the tangent of the curve in Fig. 20.21. (obtained by plot of [N_{2}O_{5}1 as a function of time).

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