### kinetics(1st order/2nd order), Arrhenius equation

**Reaction kinetics**

The rates of the chemical reactions are given by the rate law classifying the reactions as zero order, first, 2nd or higher order reactions. For zero order chemical reaction the rate is independent of the concentration of the reactants so that the rate is proportional to the [A]0 where [A] is the concentration of any reactant A. Introducing the proportionality constant *k*, the rate constant, rate law can be given as:

Rate = *k*

The situation is different when the rate of the chemical reaction depends upon the initial concentration of one or more reactants. In the former case the reactions are categorized as first order reactions i.e. the rate of reaction is dependent on the concentration of a single reactant raise to the power n (the value of n determined experimentally) while in the latter case the reactions can be termed as 2nd, 3rd or mixed order reactions. However most of the reaction we come across are 2nd order reactions, the higher order reactions being rare.

Consider a general equation for a 1st order reaction:

A (reactant) P (product)

The rate law can be expressed as:

Rate = *k** *[A]1

The units of the rate constant *k** *can be determined by putting the units of “Rate” (mol/dm3 s-1) and concentration [A] (mole/dm3) in the above equation which comes out to s-1.

In a 2nd order reaction the rate of the chemical reaction can be modulated by the concentration of the two reactant species. The general equation can be written as:

A + A P

In this case the rate of reaction can be shown as:

Rate = *k** *[A]2

The situation is different when the two dissimilar reactants affect the reaction rate, the rate law in that situation will be given by:

Rate = k[A][B] corresponding to the chemical reaction A + B → P. The units of the rate constant *k** *will come out to bemol-1dm3 s-1.

**Arrhenius equation and the rates of reactions**

Arrhenius equations predicts the relation of the rate constant with the temperature of the reaction system. The exponential form of the equation is given by:

*k** * = Ae – *E*a/RT

Where *E*a is the activation energy, T is the temperature, A is the frequency factor, indicating the frequency of collision between molecules and R is the general gas constant. If the graph is plotted between the rate constant of the reaction (determined at various temperatures) and 1/T an exponential curve is obtained. However in order to determine the value of the activation energy of a reaction the equation is usually converted into linear form by taking the ln of the both sides of equation:

ln*k** *= lnA – *E*a / RT

A graph is then plotted between ln*k** *on the y-axis and 1/T on the x-axis giving a straight line whose slope equal to –*E* a/R.Substituting the value of R (8.314 J/K), the value of *E*a can be determined. The value of the intercept on the y-axis provides information about the frequency factor A.

However If it is not possible to determine the rate constant at several temperatures, *E*a can be calculated by just working at two temperatures and the rate constant values are designated as*k*1 and *k*2 at T1 and T2 respectively. The two equation can be written as:

ln*k**1** *= lnA – *E*a / RT1

ln*k**2** *= lnA – *E*a / RT2

Dividing the two equation we get:

ln k2/k1 = *E*a / R (1/ T1 – 1/ T2)

By putting the values of rate constants, temperatures and R, *E*acan be calculated.