UNIT 06 CHEMICAL KINETICS

Syllabus

·         Rate of Chemical Reaction

·         Theories of Chemical Kinetics

·         Mechanism of Reaction.

Chemical kinetics is the branch of chemistry  which deals with the study of the speeds or rates of chemical reactions. The decrease in free energy (DG < 0) is helpful in predicting the feasibility of chemical reactions. However, knowledge of free energy change of reaction does not give any  idea about the speed or rate of reaction. Chemical reactions can be categorised into three types depending upon the reaction rates.

1.  Very fast reactions : This type of reactions occur almost instantaneously. Mixing of solutions of sodium chloride and silver nitrate with instantaneous precipitation of silver chloride is an example of fast reactions

     AgNO₃(aq) + NaCl(aq) ® AgCl(s) + NaNO₃(aq)

The rates of such reactions (ionic reactions) cannot be determined easily. In such reactions, there is no chemical bonds are to be broken among the reactants.

2. Very slow reactions : This type comprises reactions which occur at a very slow rate. These reactions may require months or years for their completion. For example rusting of iron. The rates of such reactions are hardly of any physical importance.

3.  Moderately slow reactions :  This type refers to reactions in between the very fast (type1) and very slow (type 2) reactions. These reactions proceed at moderate speed which may be easily measured . Inversion of cane sugar and hydrolysis of starch are common examples of this type of reactions.

         C₁₂H₂₂O₁₁  +  H₂O ® C₆H₁₂O₆ + C₆H₁₂O₆

    2  (C₆H₁₀O₅) _n +  n H₂O ® n C₁₂H₂₂O₁₁

Such type of chemical reactions will be the main focus of our study in this chapter.

The branch of chemistry which deals with the study of reaction rates and their mechanism is called Chemical Kinetics. The kinetic studies not only help us to determine the reaction  rates but also describe the conditions by which the reaction rates can be altered.

RATE OF A CHEMICAL REACTION

The rate of a chemical reaction may be defined as the speed or velocity at which the reactants change into products. It may be defined as the change in any one of the reactants or products per unit time. Consider a hypothetical reaction :

                           A ® B

The rate of reaction may be expressed in either of the following  ways :

(i)      The rate of disappearance or decrease in concentration of A         ( reactants) :

(ii)  The rate of increase in concentration of B (products) :

          

            The decrease or increase in the concentration of reactants or products may be expressed in terms of change in their concentration during time interval , Dt, as :

  

where D[A] gives the decrease in concentration of A and D[B] represents increase in concentration of B. The square brackets around the substances are used to express the molar concentration ( mol/L) . It may be noted that in the case of concentration of reactants minus sign is used . This implies that the concentration of reactants is decreasing with time.

Significance of  negative sign

 The negative sign in the expression does not mean that the rate is negative, rather it indicates the decrease in concentration of the reactant. As we know that with the passage of time, the concentration of reactants decrease, therefore change in concentration , D[A] ( final conc. - initial conc.) will have a negative value. Since the rate of reaction is a positive quantity, thus, to get a positive rate, we put a - ve sign in the rate expression. Thus,

Rates of reactions involving same stoichiometric coefficients of reactants and products

Consider the gaseous reaction between nitrogen dioxide and carbon monoxide.

NO₂(g) + CO(g) ® CO₂(g) + NO(g)

In this case as the reactants and products appear in same stoichiometric proportions, therefore, the rate of reaction may be expressed in terms of rate of appearance of CO₂ and NO or alternately, in terms of rate of disappearance of NO₂ or CO whichever may be convenient, Thus, rate of reaction is given by :

Since nitrogen dioxide is a deep reddish brown gas , the rate of the reaction can be followed easily by measuring the change in the intensity of colour in the gaseous mixture in the given interval of time.

Reactions involving  different stoichiometric coefficients of reactants and products.

Consider the reaction

A + B ® 2 C

In this case, one mole of A reacts with one mole of B to form 2 moles of C. This means that the rates of disappearance of A and B are same, but the rate of appearance of C must be twice the rate of disappearance of A and B. Thus,

2 x Rate of disappearance of A = 2 x Rate of disappearance of B

                                      =  Rate of appearance of C

To get unique value of the reaction rate (independent of concentration chosen) , we divide the rate of reaction  defined with any of the reactants or products by stoichiometric coefficient of that reactant or product involved in the reaction. Thus for the above reaction,

                  

For example consider a gaseous reaction between hydrogen and iodine to give hydrogen iodide.

H₂(g)+ I₂(g) ® 2 H I (g)

The rate of the reaction can also be given in terms of rate of disappearance of one of the reactants H₂ or I₂ or in terms of rate of formation of HI.

          As the reactants (H₂ and I₂)and the products (HI)  have different stoichiometric coefficients , this means that every mole of H₂ and I₂ reacting we get two moles of HI. Thus the rate of formation of HI will be twice the rate of disappearance of H₂  or I₂. In order to avoid the difference in the two rates i.e., to get unique value of the reaction rate irrespective of the species selected, we divide the rate of change of concentration by stoichiometric coefficient of reactant or product involved in the reaction. Thus, we have :

Similarly for a hypothetical reaction :

a A  +  b B  ®    c C   +   d D

Average rate and instantaneous rate

            The average rate of a reaction is the change in concentration of reactants or products divided by the time interval during which the change occurs.

This concept of average rate is similar to mechanical speed. However, the concept of mechanical speed cannot be applied in measuring rates of reactions. This is due to the fact that in case of reactions, rate of reaction depends upon the concentration of reactants.  Since the concentrations of reactants are continuously decreasing as the reaction proceeds, the rate of reaction also keeps on decreasing with time. This means that the rate of reaction may not be remaining constant in the time interval which we measure. Since rate of reaction goes on changing from one moment to another , therefore, it is more appropriate to express the rate of reaction at a particular moment of time.  Such a rate is called instantaneous rate. For this purpose the time interval (Dt) is made infinitesimally small so that the change of concentration in that time interval almost remains uniform. Alternately, the average rate approaches the instantaneous rate as Dt becomes smaller and approaches zero.

Here d[A] or d[B] represents infinitesimally small changes in concentration of A or B in infinitesimally small interval of time dt. Thus , the average rate approaches the instantaneous rate as Dt becomes smaller and smaller i.e.

In general, if dx  represents very small (infinitesimally small) change in time dt , the rate of reaction may be expressed as :

If the rate is expressed in terms of concentration of any one of the reactants, which keeps on decreasing, the negative sign is used.

            For a general reaction,

a A  +  b B  ®    c C   +   d D

The rate of the reaction is defined as :

Let us write instantaneous rate expressions for some reactions.

  (i)          2 N₂O₅    ®   4 NO₂   +  O₂

The instantaneous rate expressions are :

Problems

1.         From the concentrations of R at different times given below, calculate the average rate of reaction :  R ® P during different intervals of time.

Time (s)	0	5	10	20	30
103 [R] mol / L	160	80	40	10	2.5

2.         The decomposition of N₂O₅ in CCl₄ solution at 318 K has been studied by monitoring the concentration of N₂O₅ in solution. Initially the concentration of N₂O₅ is 2.33 M and after 184 minutes , it is reduced to 2.08 M. The reaction takes place according to the equation :

2 N₂O₅ ®  4 NO₂ + O₂

Calculate the average rate of this reaction in terms of hours, minutes and seconds. What is the rate of production of NO2 during this period ?

3.         The concentration of a reactant changes from 0.03 M to 0.02 M in 25 minutes. Calculate the average rate of reaction using units of time both in minutes and seconds.

4.         Express the rates of the following reactions in terms of the concentration of reactants and products.

i)                PCl₅ ® PCl₃ + Cl₂

ii)      2 NO₂ + F₂ ® 2 NO₂F

iii)     N₂ + 3 H₂  ® 2 NH₃

iv)     2 N₂O₅       ® 4 NO₂  + O₂

5.         For the reaction :

                    2 N₂O₅ ® 4 NO₂ + O₂

       The rate of the reaction is expressed in three ways :

        Establish the relationship between k , k' and between

        k  and k''.

6.         For the reaction :

       2 NO₂  ® 2 NO + O₂

i)        Write  the expression for the rate of reaction.

ii)      If the rate of decrease of concentration of NO₂ is           4.0 x 10^-13 mol L^-1s^-1, what are the corresponding rates of increase in NO and O₂ concentrations ?

7.         The reaction :

            2 N₂O₅     ®    4 NO₂  +    O₂

        takes place in a closed flask. It is found that

        concentration of NO₂ increases by 20 x 10^-3 mol L^-1 in

        5 seconds. Calculate the rate of reaction and rate of

        change of concentration of N₂O₅.

8.         For the following reaction :

       4 NH₃(g) + 5 O₂(g) ® 4 NO(g) + 6 H₂O(g)

       if the rate expression in terms of disappearance of

       NH₃  is - D[NH₃] / Dt. Write the rate expression in

       terms of O₂ and H₂O.

Experimental determination of reaction rate

            The rate of reaction is determined by measuring the concentration of any of the reactants or products after a definite interval of time. A graph is then plotted between concentration and time. The rate of the chemical reaction is found by drawing a tangent to the curve at the point P (fig 1) corresponding to the desired moment of time. The slope of the tangent gives the rate of the reaction at that time.

Fig 1    Determination of rate of a reaction

where  DX  and Dt are intercepts as shown in Fig 1.

Calculation of average rate of the reaction

            The average rate of the reaction at any instant of time can be evaluated from the data of concentrations and time intervals as described below.

                Here two equidistant points are taken with respect to the time at which average rate is to be determined. The difference in concentrations corresponding to these points is calculated. The difference in concentration is divided by the time interval between the selected equidistant points. For example, the average rate at  time 't' can be calculated by measuring the change in concentration in time interval from t₁ to t₂ (where t₁ and t₂ are equidistant points about 't' as shown in Fig 2.

Fig 2 Measurement of average rate and

instantaneous rates of a reaction.

Thus,

On the other  hand, the instantaneous rate at time 't' is given by the slope of the tangent at point P.

It may be noted that instantaneous or average rate can also be determined by measuring the change in concentration or any other measurable property of product species as a function of time and then plotting the graph between concentration vs  time as illustrated in Fig 3.

Fig 3 Determination of Reaction rate

Problem

9.         The progress of a reaction A  ⇌n B with time is presented in figure.

       

        Determine :

(i)     the value of n

(ii)    the equilibrium constant K and

(iii)   the initial rate of conversion of A.

Factors affecting the rate of a chemical reaction

There are a number of factors which influence the rate of a reaction. Some of the important factors are :-

1. Concentration of the reacting species.
2. Temperature of the system.
3. Nature of reactant and products.
4. Presence of a catalyst.
5. Surface area.
6. Exposure to radiation.

1. Effect of concentration

When the reaction proceeds, the reactants are converted into the products and the concentration of reactants decreases while that of products increases. The general behaviour of the concentrations of the reactants and products is shown in Fig.4.

Fig 4 . Change in concentration of reactants and products with time.

The following observations can be made from the Fig 4.

i)        In the beginning of the reaction ( i.e., when time = 0 ), only reactants are present  so that the concentration of the product is zero. As the reaction progresses , the concentration of the products increases.

ii)      The change in concentrations of the various species takes place rapidly in the beginning but very slowly as the reaction approaches the final stage.

From the above observations, it can be concluded that, at the start of the reaction, the rate of the reaction is large. As the concentration of reactants decrease, it brings about the corresponding decrease in the rate of the reaction. This means that the rate of the reaction is directly proportional to the concentration of the reactants. For example, the rate of burning of wood depends on the concentration of oxygen. A piece of wood burns slowly in air(containing about 20% oxygen) but burns rapidly in pure oxygen (100% oxygen) because the concentration of oxygen in air is less     ( only 1/5 th of the concentration of pure oxygen). Therefore to increase the rate of a reaction, we should increase the concentration of one or all reactants and vice versa.

Units of rate of reaction

            As concentration is expressed in mol L^-1 and time in seconds or minutes, the units for reaction rate, therefore, are       mol  L^-1 s^-1 or mol L^-1 min^-1 or atm s^-1. For gaseous reactions, sometimes the concentrations of reactants and products are given in terms of partial pressures. Since the pressure is expressed in atmospheres, therefore the units of rate of reaction will be atm min^-1 or atm s^-1.

            The partial pressure of any gaseous components can be calculated  from the gas equation, PV = n R T or by the expression:

The partial pressure can also be converted into units of concentration in moles per litre by using the equation:

[Concentration ]  = (n/V) = (P/RT)

 

THE LAW OF MASS ACTION

The quantitative relationship between the rate of a reaction and molar concentration of the reacting substances was given by Guldberg and Waage (1867). The relationship is known as Law Of Mass Action. According to this law:

The rate at which a substance reacts is proportional to the active mass and the rate of a chemical reaction is directly proportional to the product of the active masses of the reactants.

     Active mass of a substance means the molar concentration

( i.e., number of moles per litre) involved in the reaction. The active mass of a substance A, is expressed either by C_A or by [A].

            Consider a simple chemical reaction of the type,

                A + B  ®  Products

The rate of the reaction according to the law of mass action is given as :

Rate of reaction , r a  [A] [B]

                            =  k  [A] [B]

              where [A] and [B] are molar concentrations of  reactants A and B respectively and k is a proportionality constant.

For a hypothetical reaction :

             a A + b B ® c C + d D

The rate of the reaction according to the law of mass action may be written as :

                Rate = k [A]^a [B]^b

Although the above rate expression  has written from balanced chemical equation, yet it may or may not give the actual dependence of the reaction rate on concentrations of reacting species.  The actual relationship between the concentrations of reacting species and the reaction rate is determined experimentally and is given by the expression called rate law expression.