# Chemical Kinetics - Order Of A Reaction | Graphical Representation

## Methods of Determination of Order of a Reaction:

The important methods used for the following:

**1. Graphical representation/method **

A graphical method based on the respective rate laws can also be used.

If the plot of log (a-x) versus 't' is a straight line, the reaction follows second order.

If the plot of 1/(a-x)^{2} versus 't' is a straight line, the reaction follows third order.

In general, for a reaction of nth order, a graph of 1/(a-x)^{n-1} versus 't' must be a straight line.

**For example of nth order reaction **

** or **

So, from this it is evident that a plot of vs (a – x)^{n} will be straight line passing through the origin and will have its slope equal to k, the rate constant of reaction.

This equation demands that a plot of vs log (a – x)^{n} will be straight line of the slope equal to n, order of reaction and intercept equal to log k. For first order reaction this slope will be 1 as shown.

The equation may be rearranged as

log (a – x) =

Thus, a plot of log(a – x) vs. t will be straight line with slope equal to and intercept equal to log a, if the reaction is of first order.

**2. ****Method of integration (Hit and trial method)**

The most simple method is the one in which the quantities a, x and t are determined and substituted in the kinetic equations of various orders. The equation which gives the most constant value for the specific rate constant (k) for a series of time intervals is the one corresponding to the order of reaction. If all the reactants are at the same molar concentrations, the kinetic equations are:

k = 2.303/t log_{10}a/((a-x) ); for first order reactions.

k = 1/t [1/((a-x))-1/a]; for second order reactions.

k = 1/t [1/(a-x)^{2} -1/a^{2} ]; for third order reactions.

### What is Arrhenius equation?

**Answer:** In Chemical reactions, it is a well-known fact that raising the temperature increases the reaction rate. An equation that represents the dependence of the rate constant k of a reaction on the absolute temperature T is well known as **Arrhenius Equation**.

**k = A * exp (–Ea/RT)**

In its original form the pre-exponential factor **A** and the activation energy **Ea** are considered to be temperature-independent.

**Where**

**k** = rate constant, **Ea** = activation energy, **R **= 8.314 [ J • mol -1 • K -1 ]

**T **= absolute temperature in degrees Kelvin, ** A **= pre-exponential or frequency factor

**Note* [A = p • Z**, where Z is the collision rate and p is a steric factor. (Z turns out to be only weakly dependant on temperature.)]

### What is the unit of k for nth order reaction?

**Answer: ** Suppose A is concentration of reactant.

** Rate => ( d[A]/dt ) = k[A]n ** where [A] is in mol / lit and t is in sec

**(mol/lit) / sec = k (mol/lit)n
Units of k = mol1-n litn-1 sec-1 **

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