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.

** **

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

** ** 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).

**Table 20.3. Rate Data for Decomposition of N _{2}O_{5}(g)**

[N

_{2}O

_{5}] (mol dm

^{-3}) Rate (mol dm

^{-3}min

^{-}1)

1.13 x 10^{-2} 34 x 10^{-5}

0.84 x 10^{-2} 25 x 10^{-5}

0.62 x 10^{-2} 18 x 10^{-5}

0.46 x 10^{-2} 13 x 10^{-5}

0.35 x 10^{-2} 10 x l0^{-5}

0.26 x 10^{-2} 8 x 10 ^{-5}

0.19 x 10^{-2} 6 x 10 ^{-5}

0.14 x 10^{-2} 4 x 10 ^{-5}

**Fig. 20.22. Rate of decomposition of N _{2}O5 as a function of [N_{2}O_{5}]**

Now two graphs are drawn by plotting

(i) rate against concentration of Np5 i.e., [N_{2}O_{5}] as shown in Fig. 20.22 and

(ii) rate against square of concentration of N_{2}O_{5} i.e. , [Np_{5}]2 as shown in Fig. 20.23.

We find that a straight line is obtained in the first case which means that

and thus, the rate law expression is given as

rate = k [N_{2}O_{5}]

Also, the value of rate constant k, evaluated from rate data (Table 20.2) is,

K = RATE / [N_{2}O_{5}] = 3.0 x 10 ^{-2} min ^{-1}

**fig. 20.23. Rate of decomposition of N _{2}O_{5} as a function of [N_{2}O_{5}]^{2}.**

**2.1NITIAL RATE METHOD**

The graphical method described above involves, complications if the reaction involves more than one reactant. For such cases, a simple alternative method, i.e., Initial Rate Method is employed. The method involves the determination of the order of different reactants separately.

Initial reaction rate refers to the rate at the beginning of the reaction. It may also be taken as the rate over the first feasible and smallest possible time interval. From the data obtained, the order with respect to particular reactant is calculated. (See example 20.14 to 20.17.)

The same procedure is then repeated by devising another – set of experiments of the same reaction in which the concentration of the second reactant is varied whereas those of others are kept constant. Then, by a similar method as discussed above, the initial rates for different experimental runs and hence the order with respect to the second reactant is determined. The results then put together give the rate law expression.