# Deducing Rate Law from a Given Data

According to Collision Theory a chemical reaction takes place due to collisions between the particles of the reactants. The number of reacting species (atoms, ions or molecules) which must collide simultaneously in order to bring about the chemical reaction is called molecularity of the reaction. The molecularity of the reaction can be 1, 2 or 3. For example,

(i) The decomposition of ammonium nitrite is a unimolecular reaction.

NH4 NO2 à N2 + 2H2O

(ii) The reaction involving simultaneous collision between two species is a bimolecular reaction. For example, dissociation of HI is a bimolecular reaction.

2HI (g) à H2(g) + I2 (g)

(iii) In the same way, the reaction between NO and O2 is a trimolecular reaction because it involves collisions among three species

2NO + O2 à 2NO2

In all the above chemical reactions molecularity is simply the sum of molecules of the different reactants as represented by the balanced chemical equation. Such reactions are known as elementary reactions. For most of the reactions, the molecularity does not exceed three. It is because the chances of simultaneous collisions between three or more particles are rare. Large number of chemical reactions show that the balanced equation may contain four or more species/molecules/ ions participating in the reaction. Some common examples are:

On the basis of balanced equations the molecularity of above reactions is 4, 5 and 23 respectively.

Since, molecularity greater than three is not possible, therefore, the above reaction does not involve the simultaneous collision of all the reacting species in a single step. In fact, such chemical reactions proceed through a sequence of steps. Each step is an elementary step and involves the simultaneous collision of two or three species only. Such chemical reactions which proceed through more than one steps are termed as complex reactions. The detailed description of various steps of the complex chemical reaction is called mechanism of the reaction. For example, the reaction,

4HBr + O2 à 2H2O + Br2

Occurs by the following steps :

Step 1.

The different steps of the given reaction are written based upon the experimental evidence like detection of the presence of some shortlived intennediates, etc. All the above steps are known to proceed at different rates.

RATE LAW OR RATE EQUATION

The determination of the rate law expression of a complex reactions is not an easy task. Its determination requires,

(i) Information about the number of moles of reactants consumed during the reaction.

(ii) A knowledge of the intermediates produced during the reaction and how much they accumulate during the early period of reaction.

(iii) The rate data to be supplemented by different techniques so that the certain elementary steps are verified to the maximum.

In complex reactions thus the rate expression written on the basis of the overall balanced equation has no significance at all. It merely represents a theoretical expression. The true rate expression for such complex reactions can be evaluated on the basis of the experimental data only. For example, in the reaction between NO2 and F2 to yield nitry l fluoride (NO2F), i.e.,

2NO2(g) + F2(g) à 2NO F(g)

Experimental1y, it has been observed that the rate of this reaction is proportional to the product of single concentration term of NO2 and F2. Thus, experimental rate of there action or the actual rate of reaction is given as

rate = k [NO2] [F2]

A mathematical expression that gives the true rate of a reaction in terms of concentration of the reactants, which actually influence the rate, is called Rate Law. For a general reaction,

aA + bB à cC  + dD

where a, b, c and d are the stoichiometric coefficients of reactants and product’>. The rate expression for this reaction is

Rate = [A]x + [B]Y = K [A]x [B]y

It is known as rate constant or velocity constant or specific reaction rate. If the concentration of all reacting species is taken as unity then, rate  = k   reaction rate.

DIFFERENCES BETWEEN RATE AND RATE CONSTANT

Rate of Reaction                                             Rate Constant of Reaction

l. It is the speed at which the                          l. It is constant of proper reactants

are converted into                                           tionality in the rate law

the products at any moment                           expression.

of time.

2. It depends upon the                                    2. It refers to the rate of

concentration of reactant                                 reaction at the specific point

species at that moment of                                 when concentration of

time.                                                                        every reacting species is

unity.

3. It generally decreases with                                     3. It is constant and does not

the progress of reaction                                   depend on the progress of

the reaction.

RATE CONTROLLING STEP

As pointed out that the complex reaction proceeds through more than one steps. Let us now understand that which of these steps can be used to write the rate expression. Out of various steps can the reaction the slowest step will decide the rate of overall-reaction because the reaction cannot take place faster than the slowest step. Thus, the slowest step of the complex reaction is called the Rate Controlling Step or Rate Determining Step. A few examples are discussed to illustrate the above point(s) more clearly:

Reactions Involving Slow Steps

(i) Thermal decomposition of nitrous oxide

2N2O à 2N2 + O2

On the basis of experimental data it is observed that the rate of this reaction depends on the single power of concentration of N2O. Thus, a possible mechanism of the reaction may be proposed as:

Thus, the rate law expression for the reaction can be written as

Rate = k [ N2O].

The above postulated mechanism is consistent with the rate law expression.

(ii) Thermal decomposition of dinitrogen pentaoxide

2N2O5 à 4NO2 + O2.

The rate of the above reaction is found to be dependent on single power of concentration of N2O5 Thus, the following mechanism can be proposed for this reaction.

The above reaction is a unimolecular reaction and the rate law expression will be

Rate = k [N2O5]

(iii) Reaction between nitric oxide and hydrogen

2NO + 2H2 à N2 + 2H2O

Experimentally, it is observed that the rate of this reaction depends upon square of concentration of NO and single power of concentration of H2 Consistent with this data the logical mechanism for the reaction may be written as:

The rate law expression for this reaction can be written as