Experimental Methods For Determining Order Of Reactions

Order of reaction is an experimental quantity and it can be determined by following methods.

1. Method of hit and trial

In this method kinetic data of a given reaction is collected in a lab. Then concentration of reactants and products at different time interval is determined. Then rate constants are calculated at different time intervals using rate equations for required order of reaction. 

If the value of rate constants at different time intervals are same with a particular order expression, then that will be the order of reaction. 

2. Half-life method

In this method, half-lives of a reaction with different initial concentration are determined. From the collected data we calculate order of reaction. Suppose

t₁  is half-life with initial concentration a_1, t₂  is half-life with initial concentration a₂ and, general equation for half-life is. So,         

dividing t₁ and t₂

taking natural log on both sides

 e.q.7.1

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1.      3. Graphical method

In graphical method, reaction is performed with a known initial concentration of reactant. Then, concentration of reactants and products are monitored periodically. Then a graph is plotted concentration vs time. The slope of the graph will give the rate of reaction. The rates are plotted against concentration according to different order of reactions.

General expression will be                                                 

e.q.7.2

Where n= order of reaction. 

Figure 7.1: Graph for determination of order of reaction

4. Differential method/initial rate method

It was proposed by Von’t Hoff so also known as Von’t Hoff differential method. A differential rate expression is used in which rate is related to concentration. In this method, rate of reaction is directly proportional to the concentration raised to power a number (order of reaction).

Rate ∝ [A]ⁿ

Rate = K[A]ⁿ

Here [A]= concentration “C”.

For a given reaction                            R     →       P

Rate of reaction wit concentration C1 is R1 and rate of reaction with concentration C2 is R2. The differential rate equations will be:

R1=KC1 ⁿ                                         and                              R2=KC2 ⁿ

As K is independent of the concentration and n is also  constant equations will be

             lnR1 = lnK + nlnC1         e.q.7.3

            lnR2 = lnK + nlnC2           e.q.7.4

Subtracting e.q.7.4 from e.q.7.3 we got

where n= order of reaction.

5. Isolation method

It is also known as Ostwald isolation method. It is used for complicated reactions. In this method one of the reactant is isolated by taking other in excess and rate become independent of the reactants in excess.  If

A         +          B        +        C       →       P

If A is isolated then B, C will be taken in excess. Rate will depend on the concentration of A.

A   → P

Then order of reaction w.r.t isolated reactant can be determined by any of the above four methods. Similarly the order of reaction w.r.t other reactants (B, C) will be determined.

If order of reaction when

A is isolated is n_A

B is isolated is n_B

C is isolated is n_C

Then overall order of reaction will be

n=  n_A + n_B + n_C

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Transition State Theory

Half-Lives Of Order Of Reactions (t1/2)

Third Order Reactions