Molecularity and Order of Reaction

Molecularity of Reaction

A chemical reaction that takes place in one and only one step i.e., all that occurs in a single step is called elementary reaction while a chemical reaction occurring in the sequence of two or more steps is called complicated reaction. The sequence of steps through which a complicated reaction takes place is called reaction – mechanism. Each step in a mechanism is an elementary step reaction.

The molecularity of an elementary reaction is defined as the minimum number of molecules, atoms or ions of the reactants(s) required for the reaction to occur and is equal to the sum of the stoichiometric coefficients of the reactants in the chemical equation of the reaction. 

In general, molecularity of simple reactions is equal to the sum of the number of molecules of reactants involved in the balanced stoichiometric equation.

or

The molecularity of a reaction is the number of reactant molecules taking part in a single step of the reaction.

e.g.,

The minimum number of reacting particles (molecules, atoms or ions) that come together or collide in a rate determining step to form product or products is called the molecularity of a reaction.

For example, decomposition of H₂O₂ takes place in the following two steps:

The slowest step is rate-determining. Thus from step 1, reaction appears to be unimolecular.

There are some chemical reactions whose molecularity appears to be more than three from stoichiometric equations, e.g. 

•  4HBr + O₂ → 2H₂O + 2Br₂

• 2MNI₄^- + 16H⁺ + 5C₂ O₄^2- →  2Mn²⁺ + 10CO₂ + 8H₂O

In the first reaction molecularity seems to be '5' and in the second reaction molecularity seems to be '23'. Such reactions involve two or more steps; each step has its own molecularity not greater than three, e.g., in first reaction.

Molecularity of each of the above steps is 2.

Reaction between Br^- and H₂O₂ in acidic medium:

The overall reaction is

2Br^- + H₂O₂ + 2H⁺ → Br² + 2H₂O

The proposed mechanism is

(b)  Reaction between NO₂ and F₂:

The overall reaction is

2NO₂ + F₂ → 2NO₂F

The proposed mechanism is

The reaction is bimolecular. 

Reactions of higher molecularity (molecularity > 3) are rare. This is because a reaction takes place by collision between reactant molecules and as number of reactant molecules i.e. molecularity increases the chance of their coming together and colliding simultaneously decreases.

Refer to the following video for order and molecularity of reaction 

Order of Reaction

The mathematical expression showing the dependence of rate on the concentration(s) of reactant(s) is known as rate-law or rate-expression of the reaction and sum of the indices (powers) of the concentration terms appearing in the rate law as observed experimentally is called order of reaction. To understand what is order of reaction, consider the reaction

2NO(g) + 2H₂(g) →  N₂(g) + 2H₂O (g)

Kinetic experiment carried out at 1100 K upon this reaction has shown following rate data.

From the Expt. No.1 and 2, it is evident that rate increases 4 fold when concentration of NO is doubled keeping the concentration of H₂ constant i.e.

• Rate [NO]² when [H₂] is constant again from Expt. No.2 and 3, it is evident that when concentration of H₂ is doubled keeping the concentration of NO constant, the rate is just doubled i.e.

• Rate [H₂] when [NO] is constant

• From Expt. (1) and Expt. (3), the rate increases 8-fold when concentrations of both NO and H₂ are doubled simultaneously i.e.

• Rate  [NO]² [H₂]

• This is the rate-law of reaction as observed experimentally. In the rate law, the power of nitric oxide concentration is 2 while that of hydrogen concentration is 1. So, order of reaction w.r.t. NO is 2 and that w.r.t. H₂ is 1 and overall order is 2 + 1 i.e. 3.

Note that the experimental rate law is not consistent with the stoichiometric coefficient of H₂ in the chemical equation for the reaction. This fact immediately suggests that the reaction is complicated and it does not occur in single step as written. In order to explain the rate law, following mechanism has been proposed.

• NO + NO  N₂O₂ (fast and reversible)

• N₂O₂ + H₂  →  N₂O + H­₂O (slow)

• N₂O + H₂ →  N₂ + H₂O (fast)

Let us see how this mechanism corresponds to the rate law as found experimentally and mentioned above.

• The step II being the slowest step is the rate-determining step. Thus, rate of overall reaction or rate of formation of N₂, will be equal to the rate of step II or rate of formation of H₂O. So, we have according to Law of Mass Action.

• Rate of overall reaction = Rate of step II = k [N₂O₂] [H₂]

• Where k = rate constant of step II.

• N₂O₂ being intermediate for the overall reaction, its concentration has to be evaluated in terms of the concentration(s) of reactant(s) and this can be done by applying Law of Mass Action upon the equilibrium of Step I. Thus,

where K_C = equilibrium constant of Step II. Putting this value of concentration of N₂O₂ in the above rate expression, we get

Rate reaction = k×K_c× [NO]² [H₂]

or   Rate of reaction = k¹[NO]² [H₂]

Rate of reaction  [NO]² [H₂]

Where k×K_c = k¹ = another constant, rate constant of overall reaction.

Note that from the knowledge of any two out of k, K_c and k¹, the rest one may be calculated.

We are again turning to our topic “order”. In general, if rate law of a reaction represented by the equation.

aA + bB →  Products

is experimentally found to be as follows:

Rate [A]^m [B]ⁿ

Then   

order w.r.t. A = m

order w.r.t. B = n

overall order = m + n

It is to be noted that ‘m’ may or may not be equal to ‘a’ and similarly. ‘n’ may or may not be equal to ‘b’. m and n are experimental quantities and their values which really depend on the reaction-mechanism and experimental condition, may not be predicted by just seeing the chemical equation of the reaction. Reactions with some kind of chemical equations may differ in this rate laws and hence order. An example of this is as follows.

Order of reaction may also be defined as follows.

Number of molecules of the reactant(s) whose concentration changes during the chemical change is called order of reaction.

For example, the reaction

CH₃COOC₂H₅ + H₂O CH₃COOH + C₂H₅OH

is a bimolecular reaction but its order is ‘one’. This is because during the reaction only the concentration of ester decreases with time.

The concentration of water in the reaction mixture (usually a dilute aqueous solution of ester mixed with dilute aqueous acid) being in large excess as compared to ester, does not decrease appreciably or measurably during the reaction.

The first order behaviour of this reaction can be derived in the following way.

Applying Law of Mass Action upon the above reaction.

Rate [CH₃COOC₂H₅] [H₂O]

or   Rate = k[CH₃COOC₂H₅] [H₂O]

Where k is the rate constant of the above bimolecular reaction.

Since concentration of water remains practically constant. So,

K[H₂O] = k¹ = another constant or observed rate constant of the reaction.

So,

Rate = k¹ [CH₃COOC₂H₅]

This is first-order kinetics i.e. order in respect of ester is ‘1’ and that in respect of water is ‘zero’.

The reaction is an example of pseudounimolecular (or pseudo first order).

Thus, a second order reaction conforms to the first order if out of the reactants one is present in large excess and the reaction is called pseudounimolecular.

Some typical linear plots for the reactions of different orders:

Plots rate vs concentrations [Rate = k(conc.)ⁿ]

From the study of the kinetics of many simple reactions, it is observed that for a large number of reactions, the molecularity and order are the same. Some examples are given below to justify this point.

• Dissociation of N₂O₅.

N₂O₅ → N₂O₄ +  O₂

Order = 1, Molecularity = 1

• Dissociation of H₂O₂.

H₂O₂ → H₂O +  1/2O₂

Order = 1, Molecularity = 1

• Dissociation of HI,

2HI → H₂ + I₂

Order = 2, Molecularity = 1

• Formation of NO₂.

2NO + O₂ → 2NO₂

Order = 3, Moelcularity =3 
 

Pseudo- Order Reactions

Reactions whose actual order is different from that expected using rate law expression are called pseudo-order reactions; e.g.,

RCl + H₂O → ROH + HCl

Expected rate law:

Rate = k[RCl] [H₂O]       Expected order = 1+1 =2

Actual rate law:

Rate = k'[RCl];               Actual order = 1

Water is taken in excess; therefore, its concentration may be taken constant. The reaction is, therefore, pseudo first order. Similarly, the acid catalysed hydrolysis of ester, viz.,

RCOR' + H₂O ↔  RCOOH + R'OH

follow first order kinetics:

Rate = k[RCOOR']

It is also a pseudo-first order reaction. 
 

The Main differences between Molecularity and Order of Reaction