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Chemical Kinetics

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Chemical Kinetics PDF Notes, Important Questions and Formulas

Chemical Kinetics

This branch of chemistry which deals with the study of rates of chemical reactions and the mechanism by which they occur. While studying reaction, one deals with:

  1. How fast (or slow) the reactants get converted into products
  2. The steps or paths through which the products are formed (reaction mechanism) Chemical reaction kinetics deals with the rates of chemical processes.

Any chemical process may be broken down into a sequence of one or more single-step processes known either as elementary processes, elementary reactions, or elementary steps. Elementary reactions usually involve either a single reactive collision between two molecules, which we refer to as a bimolecular step, or dissociation/ isomerisation of a single reactant molecule, which we refer to as a unimolecular step. Very rarely, under conditions of extremely high pressure, a termolecular step may occur, which involves simultaneous collision of three reactant molecules.

An important point to recognise is that many reactions that are written as a single reaction equation in actual fact consist of a series of elementary steps. This will become extremely important as we learn more about the theory of chemical reaction rates. As a general rule, elementary processes involve a transition between two atomic or molecular states separated by a potential barrier. The potential barrier constitutes the activation energy of the process, and determines the rate at which it occurs.

When the barrier is low, the thermal energy of the reactants will generally be high enough to surmount the barrier and move over to products, and the reaction will be fast. However, when the barrier is high, only a few reactants will have sufficient energy, and the reaction will be much slower. The presence of a potential barrier to reaction is also the source of the temperature dependence of reaction rates.

The huge variety of chemical species, types of reaction, and the accompanying potential energy surfaces involved means that the timescale over which chemical reactions occur covers many orders of magnitude, from very slow reactions, such as iron rusting, to extremely fast reactions, such as the electron transfer processes involved in many biological systems or the combustion reactions occurring in flames. A study into the kinetics of a chemical reaction is usually carried out with one or both of two main goals in mind:

  1. Analysis of the sequence of elementary steps giving rise to the overall reaction. i.e. the reaction mechanism.
  2. Determination of the absolute rate of the reaction and/or its individual elementary steps.

 Rate of a Reaction

In general, for a reaction: R → P, the behaviour of the concentration of the reactant and product, as the reaction proceeds is shown graphically

From the graph, it is clear that the concentration of the reactant decreases and that of the product increases as the reaction proceeds and the rate of the change of the concentration of the reactant as well as that of the product is also changing.

Rate of a reaction can, now, be defined in two ways:

Average Rate of reaction (rav) given by for the Reaction R → P:

Rav=begin mathsize 12px style negative fraction numerator straight capital delta left square bracket straight R right square bracket over denominator Δt end fraction equals fraction numerator straight capital delta left square bracket straight p right square bracket over denominator Δt end fraction end style

Units of Rate of a Reaction

Units of rate are concentration time-1. For example, if concentration is in mol L-1 and time is in seconds then the units will be mol L-1S-1. However, in gaseous reactions, when the concentration of gas is expressed in terms of their partial pressures, then the units of the rate equation will be atm s.

Relation between Various Rates:

In general for a reaction: aA + bB → cC + dD

The rate of reaction can be expressed as follows:

Rate=begin mathsize 12px style negative 1 over straight a fraction numerator straight d left square bracket straight A right square bracket over denominator dt end fraction equals negative 1 over straight b fraction numerator straight d left square bracket straight B right square bracket over denominator dt end fraction end style

begin mathsize 12px style equals plus 1 over straight c fraction numerator straight d left square bracket straight C right square bracket over denominator dt end fraction equals plus 1 over straight d fraction numerator straight d left square bracket straight D right square bracket over denominator dt end fraction equals straight K subscript straight r left square bracket straight A right square bracket to the power of straight m left square bracket straight B right square bracket to the power of straight n end style

Order of a reaction

By performing a reaction in actual in laboratory and carefully examine it, it is possible to express the rate law as the product of concentrations of reactant each raised to some power. For example consider the reaction: aA +bB → cC + dD.

The differential rate law is written as:

begin mathsize 12px style table attributes columnalign left end attributes row cell Rate equals negative 1 over straight a fraction numerator straight d left square bracket straight A right square bracket over denominator dt end fraction equals 1 over straight b fraction numerator straight d left square bracket straight B right square bracket over denominator dt end fraction end cell row cell space space space space space space space space equals plus 1 over straight c fraction numerator straight d left square bracket straight C right square bracket over denominator dt end fraction equals plus 1 over straight d fraction numerator straight d left square bracket straight D right square bracket over denominator dt end fraction equals straight k subscript straight r left square bracket straight A right square bracket to the power of straight m left square bracket straight B right square bracket to the power of straight n end cell end table end style

Where Kr is called as rate constant of the reaction or velocity constant or specific reaction rate.

K is a characteristic of a reaction at a given temperature. It changing only when the temperature. It changing only when the temperature changes.

The powers m and n are integers or fractions. m is called as order of reaction with respect to A and n is called as order of reaction with respect to B. The overall order of reaction = m + n Hence, the sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. The values of m and n are calculated from the experimental data obtained for a reaction and the powers m and n are not related to the stoichiometric coefficients of the reactants

Molecularity

As already discussed, the order of a reaction is an experimental concept.

A complex chemical reaction is understood in terms of various indirect steps called elementary processes. The study of a reaction in terms of elementary processes is called as reaction mechanism. Now various elementary steps occur at different rates. The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction.

In the rate determining step, when one molecule takes part, it is said to be a unimolecular reaction; two molecules take part, it is said to be a bimolecular reaction; three molecules take part, it is said to be a termolecular reaction.

Unimolecular:

  1. Cyclopropane → propene
  2. O3(g → O2(g) + O(g)
  3. N2O5(g) → N2O4(g)+1/2O2(g)

Bimolecular:

  1. NO(g)+O3(g) → NO2(g)+O2(g)
  2. 2HI(g) → H2(g) +I2(g)

Termolecular:

  1. 2N)(g)+O2(g) → 2NO2(g)

The probability that more than three molecules can collide and react simultaneously is very small. Hence, reactions with the molecularity three are very rare and slow to proceed. It is, therefore, evident that complex reactions involving more than three molecules in the stoichiometric equation must take place in more than one step.

KClO3+6FeSO4+3H2SO4 KCl+3Fe2 (SO4)3+3H2O

This reaction which apparently seems to be of tenth order is actually a second order reaction. This shows that this reaction takes place in several steps. Which step controls the rate of the overall reaction? The question can be answered if we go through the mechanism of reaction, for example, chances to win the relay race competition by a team depend upon the slowest person in the team. Similarly, the overall rate of the reaction is controlled by the slowest step in a reaction called the rate determining step.

  1. Order of a reaction is an experimental quantity. It can be zero and even a fraction but molecularity cannot be zero or a non integer.
  2. Order is applicable to elementary as well as complex reactions whereas molecularity is applicable only for elementary reactions. For complex reaction molecularity has no meaning. 103 Chemical Kinetics
  3. For complex reaction, order is given by the slowest step and molecularity of the slowest step is same as the order of the overall reaction.

For a reaction: A → B in the rate law: rate = k[A]m [B]n Neither the order of reaction (m + n) nor the molecularity of a reaction can be predicted from stoichiometric coefficient of a balanced reaction. The order of reaction is always to be determined experimentally and molecularity is determined theoretically after studying the reaction mechanism. However as a theoretical idea sometime, we can have an approximate order of reaction equal to molecularity (i.e., the number of molecules taking Part in slowest elementary for complex reactions).

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