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# Reaction Order

Order of any reaction can be measured with respect to each of the reactants in the reaction. Order of any reaction is the exponential power to which the concentration of a reactant is raised.

In the given reaction :

a A + b B $\rightarrow$ c C + d D

There are more than one reactants, and so the reaction order is determined with respect to A and then subsequently with B.

As discussed earlier, the rate law is expressed as rate (r) = k [A]m [B]n, and here, the exponent 'm' denotes the order of the reaction with respect to reactant A while, the exponential value 'n' denotes the order of the reaction with respect to reactant B.
The resultant reaction order is now (m + n). Here, we need to note that the exponents 'm' and 'n' do not represent the stoichiometric coefficients 'a' and 'b' of the reaction. Order of any reaction is experimentally determined. Order of any particular reaction need not have an integral value. It could be a fraction or even negative. Different types of reactions can display different orders.

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## Zero Order Reaction

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The zero order reaction means that the rate of the reaction does not depend upon the concentration of the reactant. If a reaction rate is independent of the concentration of the reactant then the reaction is considered as zero order reaction.

Consider the reaction, $R \to P$

For a zero order reaction the rate of the reaction is give by
1. The rate of the reaction = k [R] 0
2. The unit for the rate constant of the zero order reaction is Mole L‑1s-1
3. The half life of the zero order reaction is directly proportional to the initial concentration of reactant.  $t \frac {1} {2}$ $\propto [R]_{o}$
Where [R]o is the initial concentration of the reactant.

The integrated rate equation for the zero order reaction is given by

k = $\frac {([R]­_{-o} –[R])} {t}$

Where t is the time taken for the initial concentration [R]o to get converted into [R].

Some examples of zero order reaction are :
1. Hydrogen reacting with Chlorine to form hydrogen chloride in presence of light.
2. Catalytic decomposition of ammonia into nitrogen gas and hydrogen gas on a surface is also a zero order reaction.
3. Decomposition of N2O with catalyst as platinum.

## First Order Reaction

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When the rate of the reaction depends on the first power of the reactant concentration in the rate equation, then the reaction is said to follow first order kinetics. The change in the concentration of only one reactant will affect the rate of the reaction. For example consider the reaction :

$A + B \to products$

For the first order reaction :

Rate of the reaction = k[A]

The rate of the reaction depends on the concentration of only A. Change in concentration of B is not going to affect the rate of the reaction.

The rate of the reaction is zero order with respect to B. The rate of the reaction can otherwise also be written as :

Rate of the reaction = k[A][B]o

### Characteristics of First Order Reaction

1. When the concentration of A is increased by 4 times then the rate of the reaction is also increased by 4 times. In general, an increase in concentration of the reactant by n times increases the rate of the reaction by n times.
2. The unit of the rate constant for the first order reaction is s-1. This implies that the rate constant does not depend on the concentration of the reactant.
3. The time taken for half the reactant to get reacted, the half life time of the first order reaction is independent of the concentration. This means that half life period of the first order reaction is constant.

### Examples of First Order Reaction

1. All radioactive reaction and disintegration follow the first order reaction.
2. The gas phase decomposition of sulfuryl chloride also follows the first order reaction.
3. Hydrolysis of cane sugar (sugar) in the presence of acid also follows the first order kinetics.

## Second Order Reaction

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When the rate of the reaction depends on the second power of the concentration term in the rate equation, then the reaction is called as the second order reaction. If there are two reactants in the rate equation and if the rate of reaction depends on the first power of the two reactants, then also it is called as the second order reaction

For example consider the reaction

2A $\to$ products ----(1)

Rate of the reaction = k[A]2

Or for this reaction

A + B $\to$ products

The Rate of the reaction =k [A][B]

The reaction depends on the concentration of both A and B and is a second order reaction.

### Characteristics of Second Order Reaction

1. When the concentration of A is increased by 2 times in reaction (1), then the rate of the reaction is increased by 4 times. In general an increase in concentration of the reactant by n times increases the rate of the reaction by n2 times.
2. The unit of the rate constant for second order reaction is mole-1 L s-1. This implies that the rate constant depends on the concentration of the reactant.
3. The time taken for half the reactant to get reacted, the half life time of the second order reaction is inversely proportional to initial concentration of the reactant.

## Third Order Reaction

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When the rate of the reaction depends on the third power of the concentration term in the rate equation then the reaction is called as the third order reaction.

For example consider the reaction

3A $\to$ products ----(2)

Rate of the reaction = k[A]3

The rate of the reaction depends on the third power of the reactant concentration and hence it is called as the third order reaction.

### Characteristics of third order reaction

1. When the concentration of A is increased by 2 times in reaction (2), then the rate of the reaction is increased by 8 times. In general, an increase in concentration of the reactant by n times increases the rate of the reaction by n3 times.
2. The unit of the rate constant for second order reaction is mole-2 L2 s-1. This implies that the rate constant depends on the concentration of the reactant.
3. The time taken for half the reactant to get reacted, the half life time of the third order reaction is inversely proportional to the square of the initial concentration of the reactant.

## Pseudo First Order Reaction

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In a chemical reaction involving more than one reactant, the overall order of the reaction would be more than 1. But the reaction can be converted into a lower order reaction by taking excess concentrations of all the reactants except any one of the reactant. The new order of the reaction is called as the pseudo order of the reaction. Thus for a second order reaction,
A + B $\to$ products

Rate of the reaction =k [A][B]

When one of the reactants concentration, consider B, is in excess by 10 to 100 times the other reactant A, then the reaction follows first order kinetics and it purely depends on the concentration of the A.

The Rate of the reaction =k’ [A]
Where k’ is called as the pseudo first order rate constant.

## Overall Reaction Order

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Consider the following reaction

aA + b B $\to$ products

Rate of the reaction =k [A]q[B]r

The overall order of the reaction is q + r. q is the order with respect to A and r is order with respect to B. q and r are experimentally determined quantities and it may be equal to or less than a and b respectively.
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