Overview of Chemical Kinetics

The branch of chemistry which deals with the study of rate of chemical reactions and the factors affecting them is called chemical kinetics.

The change in concentration of a reactant or product per unit time is called rate of reaction.

The rate of reaction measured over a given finite interval of time is called average rate of reaction.

The rate of reaction at a particular instant of time is called instantaneous rate of reaction.

The mathematical expression that relates the rate of reaction with the concentration of reactants is called rate law.

The proportionality constant present in the rate equation at a given temperature is called rate constant.

The sum of the powers of the concentration terms in the rate law expression is called order of reaction.

The number of reacting species that collide simultaneously in an elementary reaction is called molecularity.

A reaction whose rate is independent of the concentration of reactants is called zero order reaction.

A reaction whose rate is directly proportional to the first power of the concentration of a reactant is called first order reaction.

\[r=-\frac{\Delta[R]}{\Delta t}=\frac{\Delta[P]}{\Delta t}\]

\[r=-\frac{d[R]}{dt}\]

For reaction:

aA + bB → Products

Rate = k[A]^x[B]^y

Order = x + y

Rate = k

Integrated form:

[R] = [R]₀​ − kt

\[k=\frac{[R]_0-[R]}{t}\]

Units of k = mol L^⁻¹ s^⁻¹

Rate = k[R]

Integrated form:

ln[R] = ln[R]₀ ​− kt

\[k=\frac{2.303}{t}\log\frac{[R]_0}{[R]}\]

Units of k = s⁻¹

\[\mathrm{Rate}=\frac{\text{Concentration}}{\mathrm{Time}}\]

Unit = mol L⁻¹ s⁻¹

The rate of a chemical reaction at a given temperature is proportional to the product of concentrations of reactants, each raised to a power.

Mathematically,

Rate = k[A]^x[B]^y

Where:

• k = rate constant
• x, y = orders with respect to reactants
• x + y = overall order

Note: Order is determined experimentally.

The time required for the concentration of a reactant to become half of its initial concentration is called half-life of a reaction.

A reaction which is actually of higher order but behaves as a first order reaction because one reactant is present in large excess is called pseudo first order reaction.

The minimum amount of energy required by reacting molecules to form products is called activation energy.

The intermediate unstable species formed during a reaction at the top of the energy barrier is called activated complex.

The constant A in Arrhenius equation which represents the frequency of effective collisions is called frequency factor.

A substance which increases the rate of a reaction without itself undergoing permanent chemical change is called catalyst.

The number of molecular collisions occurring per second per unit volume is called collision frequency.

A collision in which molecules collide with sufficient energy and proper orientation to form products is called effective collision.

The minimum kinetic energy required by colliding molecules for an effective collision is called threshold energy.

Statement:
At a constant temperature, the rate of a chemical reaction is directly proportional to the product of the molar concentrations of the reactants, each raised to a power, which may or may not be equal to their stoichiometric coefficients.

Mathematical Expression:
For a reaction

aA + bB → Products

Rate = k[A]^x[B]^y

Where:

• k = rate constant
• x and y = orders with respect to A and B
• x + y = overall order of reaction

Important Points:

• Order is determined experimentally.
• Order may be zero, whole number, or fractional.
• Order is not necessarily equal to stoichiometric coefficients (except for elementary reactions).

Statement:
The rate constant of a reaction increases exponentially with increase in temperature and is given by the Arrhenius equation.

Mathematical Expression:

\[k=Ae^{-E_a/RT}\]

Taking logarithm:

\[\ln k=-\frac{E_a}{RT}+\ln A\]

Where:

• A = frequency factor
• Ea = activation energy
• R = gas constant
• T = temperature

Important Results:

• A plot of ln k vs 1/T is a straight line.
• Slope = −Ea/R
• Intercept = ln A
• Increase in temperature increases rate constant.

Statement:
According to collision theory, a chemical reaction occurs only when reacting molecules collide with sufficient energy and proper orientation.

Expression for Rate:

\[\mathrm{Rate}=Z_{AB}e^{-E_a/RT}\]

Including orientation factor:

\[\mathrm{Rate}=PZ_{AB}e^{-E_a/RT}\]

Where:

• ZAB = collision frequency
• Ea = activation energy
• P = steric factor

Important Points:

• Not all collisions are effective.
• Effective collisions require:

1. Energy ≥ activation energy
2. Proper orientation

Statement:
For a first order reaction, the half-life period is constant and independent of the initial concentration of reactant.

Expression:

\[t_{1/2}=\frac{0.693}{k}\]

Important Points:

• Half-life does not depend on initial concentration.
• Used in radioactive decay and decomposition reactions.
• Helps in determination of rate constant.