Question

Define ‘order of a reaction’.

Answer 1

Hint: We have to know that reaction order represents the number of species whose concentration directly affects the rate of reaction. We have to remember that there are a lot of methods used to determine the order of a reaction some of them are initial rate method, Integral method and differential method. Among these types of methods, the differential method is the easiest method.

Complete step by step answer:
The order of reaction is not dependent on the stoichiometric coefficients corresponding to every species in the balanced reaction.
We have to know that the order of a chemical reaction is expressed with the help of concentrations of reactants and not with concentrations of products.
The value of the order of reaction can be in the form of a whole number or a fraction. The order of the reaction could be zero.
We can define that the order of the chemical reaction is the sum of the power of concentration of reactants in the rate law expression.
For a reaction, $xA + yB \to P$
Rate = $k{\left[ A \right]^x}{\left[ B \right]^y}$
By adding the power of the concentration of reactants we get the order of the reaction.
Order = \[x + y\]
The exponents x and y represent the orders of the reactions. The order of the reaction is generally a small positive integer. The sum of the orders of the reaction is called the overall order of the reaction.
Types of order of reaction:
Zero order reaction:
A reaction which is independent of the reactant(s) concentration is known as zero order reaction.
For a zero order reaction we can write the rate law of zero order reaction as,
Rate$ = k{\left[ A \right]^ \circ }$
Here, k represents the rate constant and A represents the concentration of the reactant species.
First order reaction:
For the reaction, \[N{H_4}N{O_2} \to {N_2} + 2{H_2}O\]
The rate of the reaction is $k = \left[ {N{H_4}N{O_2}} \right]$ and we can see the power of the concentration of reactant is one and the order of the reaction is 1. We call these kinds of reactions a first order reaction.
Second order reaction:
For the reaction, \[NO + {O_3} \to N{O_2} + {O_2}\]
The rate of the reaction is $k = \left[ {NO} \right]\left[ {{O_2}} \right]$ and we can see the power of concentration of $NO$ is one and power of concentration of ${O_2}$ is one. Adding both the powers $\left( {1 + 1 = 2} \right)$, order of the reaction is 2. We call these kinds of reactions a second order reaction.
Third order reaction:
For the reaction, \[2NO + B{r_2} \to 2NOBr\]
The rate of the reaction is $k = {\left[ {NO} \right]^2}\left[ {B{r_2}} \right]$ and we can see the power of concentration of $NO$ is two and power of concentration of $B{r_2}$ is one. Adding both the powers $\left( {2 + 1 = 3} \right)$ the order of the reaction is 3. We call these kinds of reactions a third order reaction.
Fractional order reaction:
For the reaction, $C{H_3}CHO \to C{H_4} + CO$, the order of the reaction will be 1.5 with respect to aldehyde.
Initiation: $C{H_3}CHO \to \bullet C{H_3} + \bullet CHO$
Propagation: $ \bullet C{H_3} + C{H_3}CHO \to C{H_3}CO \bullet + C{H_4}$
$C{H_3}CO \bullet \to \bullet C{H_3} + CO$
Termination: $2 \bullet C{H_3} \to {C_2}{H_6}$
In the steady state, the formation rate and destruction of methyl radicals are same, so that
$\dfrac{{d\left[ { \bullet C{H_3}} \right]}}{{dt}} = {k_i}\left[ {C{H_3}CHO} \right] - {k_t}{\left[ { \bullet C{H_3}} \right]^2} = 0$,
So that concentration of methyl radical satisfies,
$\left[ { \bullet C{H_3}} \right]\alpha {\left[ {C{H_3}CHO} \right]^{\dfrac{1}{2}}}$
The reaction rate is equal to the rate of the propagation steps that form the main reaction products as methane and carbon monoxide:
$\dfrac{{d\left[ {C{H_4}} \right]}}{{dt}} = {k_p}\left[ { \bullet C{H_3}} \right]\left[ {C{H_3}CHO} \right]\alpha {\left[ {C{H_3}CHO} \right]^{\dfrac{3}{2}}}$
Here $\left[ { \bullet C{H_3}} \right]$ is free methyl radical.
Therefore, the order of the reaction is $\dfrac{3}{2}$.
We call these reactions as fractional order reactions.

Note: We can say in fractional order reactions, the order of the reaction would be a non-integer which represents chemical chain reaction or other complex reaction mechanism.
We can rationalize the order of a chain reaction with the steady state approximation for the concentration of reactive intermediates such as free radicals.