,To know the rate of reaction at any time t, a tangent is drawn to curve at the point corresponding to that time and it is extended on either side so as to cut the axes, say at the point A and B. Then
is the time in which half of the substance has reacted.
substituting those values in equation (iii), we get
Octane Number
Gasoline is used as a fuel in internal combustion engines of motor cars and airplanes. In such engines, a mixture of gasoline vapors and the air is compressed by a piston within the cylinder of the...
Chemical Kinetics
Chemical Kinetics is the branch of science that deals with rate of reaction, factors affecting the rate of reaction and reaction – mechanism.
Different reactions occur at different rate. In fact a chemical reaction involves redistribution of bonds –– breaking of bond(s) in the reactant molecule(s) and making of bonds in the product molecule(s). The rate of a chemical reaction actually depends upon the strength of the bond(s) and number of bonds to be broken during the reaction. It takes longer time for the reactant molecules to acquire higher amount of energy which they do by collision. Hence reactions involving strong bond – breaking occur at relatively slower rate while those involving weak
bond – breaking occur at relatively faster rate. On the basis of rate, reactions are classified as.
- Instantaneous or extremely fast reactions i.e. reactions with half-life of the order of fraction of second.
- Extremely slow reactions i.e. reactions with half-life of the order of years.
- Reactions of moderate or measurable rate.
Ionic reactions are instantaneous. If a drop of silver nitrate solution is added to a solution of the chloride salt of any metal or solution of HCl, a white precipitate of silver chloride appears within twinkling of eye. This is because of the fact that in aqueous solution an ionic compound exists as its constituent ions. No bond needs to be broken during the reaction. Hence reaction takes no time to complete. The half life period of an ionic reaction is of the order of 10–10 s.
Na+ + Cl– + Ag+ + 
Free radicals being very unstable (reactive) due to the presence of unpaired electron, reactions involving free radicals also occur instantaneously. Thus, the reactions, are instantaneous.
CH3 + Cl2 → CH3Cl + ∙Cl
CH3 + ∙CH3 → H3C – CH3
Some molecular reactions involving reactant(s) containing odd electron completes within a fraction of second. The speed of such reactions is attributable to the tendency of the odd electron molecule (paramagnetic in nature) to transform into stable spin-paired molecule (diamagnetic) by dimerisation. An example of such reaction is the dimerisation of nitrogen dioxide into nitrogen tetraoxide as mentioned below.
NO2 + NO2 → N2O4
There are some molecular reactions which are known to be extremely slow. Their half-lives are of the order of several years. Some examples of the type of reactions are as given below:
4
[Cr(H2O)6]3+ + I– → [Cr(H2O)5I]2+ + H2O
Note that the first reaction given above is called “rusting of iron”. The second one is not ionic reaction as it appears at the first sight. Here in this reaction it is the co-ordinate bond between central metal ion i.e. Cr3+ (acceptor) and water molecule (donor) that is broken and covalent bond between Cr3+ and I– that is formed. The half-life of this reaction is in years.
Most molecular reactions especially organic reactions occur at measurable rate. The half-life of such reactions are of the order of minutes, hours, days. Examples of such reactions are numerous. Some of these are given below.
CH3COOC2H5 + H2O 
H2O2 (aq) 
2N2O5 
NH4NO2 (aq) 
In Chemical Kinetics we deal with the rates of only those reactions which occur with measurable rate i.e. which are neither too fast nor too slow. The rates of fast reactions are also determined using lasers.
Rate of Rxn
The rate of a reaction means the speed with which the reaction takes place. This is expressed either in terms of decrease in the concentration of a reactant per unit time or increase in the concentration of a product per unit time.
Rate of reaction
Or,
The term 
The above example indicates that the car has been driven with uniform rate but actually it has been driven sometimes faster and sometimes slower depending upon the condition of road. Thus, the overall rate is an average rate and the rate at which the car was moving at any instan
t, called instantaneous rate. The rate measured over a long time interval is called average rate and the rate measured for an infinitesimally small time interval is called instantaneous rate.
In general, for any reaction of the type
Average rate of reaction
Where [A] signifies the molar conc. of (A) and 
Average rate of reaction
The rate measured over a long time interval is called average rate. The rate of reaction (average rate) is defined as the change of concentration of any one of the reactants (or products) per unit time.
Average rate of reaction
Consider the reaction between CO and
This equation shows that one mole of CO reacts with one mole of 
Thus,
For the reaction,
When 2 moles of 
So
In general, for a reaction,
| With the progress of reaction the conc. of reactants decreases while that of product increases. According to law of mass action the rate of reaction decreases moment to moment as shown by graph of rate vs. time. Rate varies from moment to moment so rate of reaction has to be specified at a given instant of time called instantaneous rate |
Where dC is the infinitesimal change in conc. during infinitesimal time interval dt after time t i.e. between t and t + dt.
| Consider a reaction |
Thus the rate of reaction at time 10 minutes
Units of the rate of reaction
Since concentration is usually expressed in moles / time and time is taken in seconds or minutes, the unit of the rate of reaction is moles 
Law of mass Action
“At a given temperature, the rate of a reaction at a particular instant is proportional to the product of the active masses of the reactants at that instant raised to powers which are numerically equal to the numbers of their respective molecules in the stoichiometric equation describing the reaction”.
Active mass = molar concentration of the substance
= number of gm moles of the substance/Volume in litre
where W = mass of substance, M = molecular mass in grams.
V = volume in litres
Consider a simple reaction
If CA is the molar concentration or active mass of A at a particular instant, then
Where K is a proportionality constant or rate constant.
If CA = 1 then
Rate
Let us consider a general reaction
If [A] = [B] = 1 mole / lit, then
Rate = K
Rate of reaction at unit concentration of reactant is called rate constant.
The value of rate constant depends on :
- Nature of reactant
- Temperature
- Catalyst
Molecularity
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 the 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 required for the reaction to occur and is equal to the sum of the stoichiometric coefficient of the reactants in the chemical equation of the reaction. Thus, the molecularity of some elementary reactions is as mentioned below:
Elementary reactions Molecularity
Reactions with molecularity equal to one, two, three, etc; are called unimolecular, biomolecular, trimolecular, etc. respectively.
A complicated reaction has no molecularity of its own but the molecularity of each of the steps (elementary reactions) involved in the mechanism.
For example; consider the reaction; 
-
(fast and reversible)
-
(slow)
-
(fast)
The molecularity of each step in the mechanism is two so we say that the reaction takes in a sequence of three steps each of which is bimolecular. There is another way also. According to which molecularity of a complicated reaction is taken to be equal to the molecularity of the slowest step i.e. rate-determining step (r.d.s) in the mechanism.
For example, the reaction
is said to be unimolecular nucleophilic substitution (SN1). Since the reaction occurs in the sequence of the following three steps and the slowest step i.e. r.d.s. is unimolecular.
| (i) |  |
| (ii) |  |
| (iii) |  |
Reactions of higher molecularity (molecularity > 3) are rare. This is because a reaction takes place by a collision between reactant molecules and a number of reactant molecules i.e. molecularity increases the chance of their coming together and colliding simultaneously decreases
Order of Rxn
The mathematical expression showing the dependence of rate on the concentration of reactant 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 :
| Experiment Number | [NO](mole dm-3) | [H2](mole dm-3) | Rate (mole dm-3 s-1) |
| 1 | 5 x 10-3 | 2.5 x 10-3 | 3 x 10-5 |
| 2 | 1 x 10-2 | 2.5 x 10-3 | 1.2 x 10-4 |
| 3 | 1 x 10-2 | 5 x 10-3 | 2.4 x 10-4 |
From the experiment number 1 and 2, it is evident that rate increases 4 fold when conc. of NO is doubled keeping the conc. of H2 constant i.e. 
Order of reaction with respect to NO is 2 and with respect to H2 is 1 The overall order of reaction is 2 + 1 = 3. This order of reaction suggest that the reaction is complicated and it does not occur in single step. In order to explain this reaction following mechanism has been proposed.
(i)
(ii)
(iii)
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 of reactant and this can be done by applying law of mass action upon the equilibrium of step I.
Thus,
where Kc=equilibrium constant of step I, putting this value of concentration of N2O2 in the above rate expression, we get
(i) 
(ii) 
Further Reading :
- Reaction of Various Orders
- Some Complex First Order Reaction
Reaction whose actual order is different from that expected using rate law expression are called pseudo – order reactions,
eg.
Rate = K[RCI][H2O] , Expected order = 1 + 1 = 2
Actual rate law :Rate = K'[RCI], Actual order = 1 Water is taken in excess; therefore, its concentration may be taken constant. This reaction is therefore, pseudo first order. Similarly, the acid catalysed hydrolysis of ester, viz,
Rate = K[RCOOR']
It is also a pseudo first order reaction.
Difference between order and molecularity- Order is an experimental property while molecularity is the theoretical property.
- Order concerns with kinetics (rate law) while molecularity concerns with mechanism.
- Order may be any number, fraction, integral or even zero whereas molecularity is always an integer expecting zero.
A reaction is said to be zero order if its rate is independent of the conc. of the reactants, consider the general reactions
If it is reac. of zero order
or d[A] = -K dt
Integrating both sides, we get
[A] = -Kt + I ………………….. (i)
where I is a constant of integration
At t = 0,
Substituting this value of I in equation (i), we get
or
(i) Any reaction of zero order must obey equation (ii). As it is a equation of straight line
(y = mx + c), the plot of [A] versus t will be a straight line with slope 
| Half life period When |
(i) Photochemical reaction between hydrogen and chlorine
(ii) Decomposition of N2O on hot platinum surface :
(iii) Decomposition of NH3 in presence of molybdenum or tungsten
A reaction is said to be of the first order if the rate of the reaction depends upon one conc. term only.
Consider the reactionLet ‘a’ be the conc. of A at the start and after time t, the conc. becomes (a – x), i.e., x has been changed into products. The rate of reaction after time ‘t’ is given by the expression
or
Upon integration of above equation,
where c is integration constant
when t = 0, x = 0
Putting the value of ‘c’,
If the initial concentration is 
This equation can be written in the exponential form as
Some important characteristics of first order reaction
(a) A change in conc. unit will not change the numerical value of K. Let the new unit be n times the first one.
So
| Comparing it with y = mx + c Slope |
The time taken for any fraction of the reaction to be completed is independent of the initial concentration.
| when the half reaction is completed |
To find out the t½ for a nth order reaction where n ≠1.
∴ 
⇒ 
⇒ 
Therefore for a nth order reaction, the half life is inversely related to the initial concentration raised to the power of (n–1).
Note:It can be noted that for a zero order reaction t1/2 =
(i) Decomposition of H2O2 in aqueous solution
(ii)
(iii)
Unit of rate constant
where n = order of reaction
It may be observed that the increase in the total number of collision per unit volume per unit time (collision frequency) is not so much responsible for the higher reaction rate as is the increase in the fraction of effective collisions. Let us, for eg, calculate the increase in collision frequency when temperature increases from 298 to 308 K. As we know that collision frequency is directly proportional to the square root of absolute temperature, therefore, the rate of collision frequencies at these temperatures follows as
From the above ratio it is clear that there is a insignificant increase in the collision frequency. Hence it can not explain the observed increase in the ratio of the reaction with increase in temperature.
Let us now consider the effect of increase in temperature on the number of effective collisions.
Now, as we know that the rise in temperature increases the kinetic energy of the molecules. 
Note:
The reaction rate dependence on temperature can also explained by Vant Hoff’s equation.
The nature of reacting substances affect, the rates significantly. For e.g. the oxidation of ferrous (Fe+2) by KMnO4 in acidic medium is practically instaneous. On the other hand, oxidation of oxalate ions 
Catalyst
A catalyst is a substance, which increases the rate of a reaction without itself being consumed at the end of the reaction, and the phenomenon is called catalysis. There are some catalysts which decrease the rate of reaction and such catalysts are called negative catalyst. Obviously, the catalyst accelerating the rate will be positive catalyst. However, the term positive is seldom used and catalyst itself implies positive catalyst.
Catalyst are generally foreign substances but sometimes one of the product formed may act as a catalyst and such catalyst is called “auto catalyst” and the phenomenon is called auto catalysis. Thermal decomposition of KClO3 is found to be accelerated by the presence of MnO2. Here MnO2 (foreign substance) acts as a catalyst.
2KClO3 + [MnO2] → 2KCl + 3O2↑ + [MnO2]
MnO2 can be received in the same composition and mass at the end of the reaction. In the permanganate titration of oxalic acid in the presence of bench H2SO4 (acid medium), it is found that the titration in the beginning there is slow discharge of the colour of permanganate solution but after sometime the discharge of the colour become faster. This is due to the formation of MnSO4 during the reaction which acts as a catalyst for the same reaction. Thus, MnSO4 is an “auto catalyst” for this reaction. This is an example of auto catalyst.
2KMnO4 + 3H2SO4 + 5H2C2O4 → K2SO4 + 8H2O + 10CO2 + 2MnSO4
General characteristics of catalyst- A catalyst does not initiate the reaction. It simply fastens it.
- Only a small amount of catalyst can catalyse the reaction.
- A catalyst does not alter the position of equilibrium i.e. magnitude of equilibrium constant and hence ΔG0. It simply lowers the time needed to attain equilibrium. This means if a reversible reaction in absence of catalyst completes to go to the extent of 75% till attainment of equilibrium, and this state of equilibrium is attained in 20 minutes then in presence of a catalyst also the reaction will go to 75% of completion before the attainment of equilibrium but the time needed for this will be less than 20 minutes.
- A catalyst drives the reaction through a different route for which energy barrier is of shortest height and hence Ea is of lower magnitude. That is, the function of the catalyst is to lower down the activation.
| Ea = Energy of activation in absence of catalyst. E′a = Energy of activation in presence of catalyst. Ea – E′a = lowering of activation energy by catalyst. |
If k and kcat be the rate constant of a reaction at a given temperature T, and Ea and E′a are the activation energies of the reaction in absence and presence of catalyst, respectively, the
Since Ea > Ea′ so kcat • k. the ratio 
The rate of reaction in the presence of catalyst at any temperature T1 may be made equal to the rate of reaction in absence of catalyst but for this sake we will have to raise the temperature. Let this temperature be T2 then
or
The rate of disintegration of a given substance depends upon the nature of disintegrating substance and its total amount. The law of radioactive disintegration may be defined as the quantity of radioactive substance which disappears in unit time is directly proportional to the amount of radioactive substances present or yet not decayed.
The radioactive decay of the different radioactive substances differ widely. The rate of disintegration of a given substance depends upon the nature of disintegrating substance and its total amount. The law of radioactive disintegration may be defined as the quantity of radioactive substance which disappears in unit time is directly proportional to the amount of radioactive substances present or yet not decayed.
Rutherford introduced a constant known as half - life period. It is defined as “time during which half the amount of a given sample of the radioactive substance disintegrates”.
Half life periods vary from billions of years for some radio isotopes to a fraction of a second. Half life period is represented as t1/2. Let the initial amount of a radioactive substance be No. After one half life period (t1/2) it becomes = No/2. After two half life periods (2t1/2) it becomes = No/4 and after n half life periods (nt1/2) it becomes = (1/2)n N0. Thus, for the total disintegration of a radioactive substance an infinite time will be required.
Amount of radioactive substance left after n half life periods N = (1/2)n N0 and total time T = n × t1/2. Where n is a whole number.
Disintegration constant: A chemical reaction whose rate varies directly to the concentration of one molecular species only, is termed as first order reaction. Radioactive disintegration is similar to such a chemical reaction as one radioactive species changes into other. This can be represented as.
A → B
Suppose the number of atoms of a radioactive substance present at the start of observation, i.e., when t = 0, is No and after time t the number of atoms remaining unchanged is N. At this instant of very small number of atoms dN disintegrate in a small time dt; the rate of change of A into B is given -dN/dt. The negative sign indicates the number of atoms decreases as time increases.
Since rate of disintegration or change is proportional to the number of atoms present at that time, the relation becomes.
-dN/dt = λ.N …(i)
'λ' is called the disintegration constant or decay constant.
Evidently, -dN/N = λ.dt …(ii)
If dt = 1 second, λ =-dN/N … (iii)
Thus, λ may be defined as the fraction of the total number of atoms which disintegrates per second at any time.
Integrating equation (ii),
or, – log N = λt + C ……… (iv)
where C is the integration constant.
When t = 0, N = N0
Putting values in equation (iv)
– log N0 = C
Putting the value of C in equation (iv)
– log N = λt – log N0
or, log No – log N = λt
or, log 
or, 2.303 log10 
or, λ =
This equation is called kinetic equation and is obeyed by first order reactions.
Relationship between half life period and radioactive disintegration constant
When t = t1/2 N =
Putting the values in equation (v)
λ = 
So, λ = 
or, t1/2 =
Thus, half life period of a given radioactive substance does not depend on the initial amount of a radioactive substance but depends only on the disintegration constant of the radioactive element.
Average life Period (T)
Since total decay period of any element is infinity, it is meaningless to use the term total decay period for radioelement. Thus the term average life is used which is determined by the following relation.
Average life (T) =
Relation between average life and half - life
Average life(T) of an element is the inverse of its decay constant, i.e.,
T =
Substituting the value of λ =
Average life (T) = 1.44 × Half life (t1/2)
