Maharashtra Board Class 12 Chemistry Chapter 6 Chemical Kinetics PDF Download

6. Chemical Kinetics

Three important characteristics of chemical reactions include: extent of reaction, feasibility and its rate. In standard XI, we learnt how equilibrium constants predict the extent of reaction. In unit 3 of this text, we learnt how thermodynamic properties such as change in entropy or enthalpy tell us whether under the given set of conditions chemical reaction represented by chemical equation occurs or not. Chemical kinetics is a branch of chemistry which deals with the rate of chemical reactions and the factors those affect them.

A chemist wants to know the rates of reactions for different reasons. One, the study of reaction rates help us to predict how rapidly the reaction approaches equilibrium. Secondly it gives information on the mechanism of chemical reactions.

A number of reactions occur as a sequence of elementary steps constituting the mechanism of reaction.

6.2 Rate Of Reactions

The rate of reaction describes how rapidly the reactants are consumed or the products are formed.

6.2.1 Average Rate Of Chemical Reaction

The average rate of a reaction can be described by knowing change in concentration of reactant or product divided by time interval over which the change occurs. Thus,

Average rate = \(\frac{\text{change in concentration of a species}}{\text{change in time}}\) = \(\frac{\Delta c}{\Delta t}\)

Consider the reaction A \(\rightarrow\) B in which A is consumed and B is produced.

Average rate of consumption of A = \(-\frac{\Delta[A]}{\Delta t}\)

Average rate of formation of B = \(+\frac{\Delta[B]}{\Delta t}\)

Therefore, average rate of reaction = \(-\frac{\Delta[A]}{\Delta t}\) = \(+\frac{\Delta[B]}{\Delta t}\)

The rate of reaction represents a decrease in concentration of the reactant per unit time or increase in concentration of product per unit time. The dimensions of rate are concentration divided by time, that is, mol dm\(^{-3}\) sec\(^{-1}\).

6.2.2 Instantaneous Rate Of Reaction

To determine the instantaneous rate of a reaction the progress of a reaction is followed by measuring the concentrations of reactant or product for different time intervals. The changes in concentration are relatively fast in the beginning which later become slow. The concentration of a reactant or a product plotted against time are shown in Fig. 6.1 (a) and 6.1 (b). A tangent drawn to the curve at time t\(_{1}\) gives the rate of the reaction. The slope thus obtained gives the instantaneous rate of the reaction at time t\(_{1}\). The instantaneous rate dc/dt, is represented by replacing \(\Delta\) by derivative dc/dt in the expression of average rate. In chemical kinetics we are concerned with instantaneous rates.

For the reaction, A \(\rightarrow\) B,

Rate of consumption of A at any time t = \(-\frac{d[A]}{dt}\)

Rate of formation of B at any time t = \(\frac{d[B]}{dt}\)

Rate of reaction at time t = \(-\frac{d[A]}{dt}\) = \(\frac{d[B]}{dt}\)

For the reaction involving one mole of A and B each, the rate of consumption of A equals the rate of formation of B. This is not true for the reactions involving different stoichiometries. Consider, for example, a reaction:

A + 3B \(\rightarrow\) 2 C

When one mole of A is consumed three moles of B are consumed and two moles of C are formed. The stoichiometric coefficients of the three species are different. Thus the rate of consumption of B is three times the rate of consumption of A. Likewise the rate of formation of C is twice the rate of consumption of A. We write,

\(-\frac{d[B]}{dt} = -3\frac{d[A]}{dt}\) and \(\frac{d[C]}{dt} = -2\frac{d[A]}{dt}\)

With this

\(-\frac{d[A]}{dt} = -\frac{1}{3}\frac{d[B]}{dt} = \frac{1}{2}\frac{d[C]}{dt}\)

or rate of reaction = \(-\frac{d[A]}{dt}\) = \(-\frac{1}{3}\frac{d[B]}{dt}\) = \(\frac{1}{2}\frac{d[C]}{dt}\)

In general, For

aA + bB \(\rightarrow\) cC + dD,

rate = \(-\frac{1}{a}\frac{d[A]}{dt}\) = \(-\frac{1}{b}\frac{d[B]}{dt}\) = \(\frac{1}{c}\frac{d[C]}{dt}\) = \(\frac{1}{d}\frac{d[D]}{dt}\)

Teacher's Note

In India, many chemical factories use reaction rates to control production speed. For example, sugar factories monitor how fast sugar dissolves in water to get the best quality product.

Exam Trick

Remember: The rate is always shown with a minus sign for reactants (they decrease) and a plus sign for products (they increase). Just like your bank balance decreases when you spend money and increases when you earn.

Points to Remember

Rate tells how fast a reaction happens.
Concentration changes with time during a reaction.
We use special math symbols like Δ for change and d for instant change.
Rate of reaction has units like mol dm\(^{-3}\) s\(^{-1}\).
Reactants decrease and products increase during a reaction.

6.3 Rate Of Reaction And Reactant Concentration

The rate of a reaction at a given temperature for a given time instant depends on the concentration of reactant. Such rate-concentration relation is the rate law.

6.3.1 Rate Law

Consider the general reaction,

aA + bB \(\rightarrow\) cC + dD \(\quad\) (6.1)

The rate of reaction at a given time is proportional to its molar concentration at that time raised to simple powers or

Rate of reaction \(\propto\) [A]\(^{x}\) [B]\(^{y}\)

or

rate = k [A]\(^{x}\)[B]\(^{y}\) \(\quad\) (6.2)

where k the proportionality constant is called the rate constant, which is independent of concentration and varies with temperature. For unit concentrations of A and B, k is equal to the rate of reaction. Equation (6.2) is called differential rate law.

The powers x and y of the concentration terms A and B in the rate law not necessarily equal to stoichiometric coefficients (a and b) appearing in Eq. (6.1). Thus x and y may be simple whole numbers, zero or fraction. Realize that x and y are experimentally determined. The rate law in Eq. (6.2) is determined experimentally and expresses the rate of a chemical reaction in terms of molar concentrations of the reactants and not predicted from the stoichiometries of the reactants.

The exponents x and y appearing in the rate law tell us how the concentration change affects the rate of the reaction.

(i) For x = y = 1, Eq. (6.2) gives

rate = k[A][B]

The equation implies that the rate of a reaction depends linearly on concentrations of A and B. If either of concentration of A or B is doubled, the rate would be doubled.

(ii) For x = 2 and y = 1. The Eq. (6.2) then leads to rate = k[A]\(^{2}\)[B]. If concentration of A is doubled keeping that of B constant, the rate of reaction will increase by a factor of 4.

(iii) If x = 0, the rate is independent of concentration of A.

(iv) If x < 0 the rate decreases as [A] increases.

6.3.2 Writing The Rate Law

Consider the reaction,

2H\(_{2}\)O\(_{2}\)(g) \(\rightarrow\) 2 H\(_{2}\)O(l) + O\(_{2}\)(g).

If the rate of the reaction is proportional to concentration of H\(_{2}\)O\(_{2}\). The rate law is given by

rate = k[H\(_{2}\)O\(_{2}\)]

Teacher's Note

Rate laws are found by doing experiments, not by looking at the equation. In Indian labs, scientists use this method to make medicines and chemicals faster and cheaper.

Exam Trick

Remember: The power of a substance in rate law comes from experiments, not from the equation number. The equation number shows how many molecules react, but the power shows how concentration affects speed.

Points to Remember

Rate law must be found by experiment, not guessed from the equation.
The powers x and y can be whole numbers, fractions, or zero.
Rate constant k changes with temperature but not with concentration.
Each reactant's power is called its "order" in that reaction.
The rate law shows which reactant has the biggest effect on speed.

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