Revision: Chemical Kinetics JEE Main Chemical Kinetics

The rate of a chemical reaction may be defined as the change in concentration of any of the reactants or any of the products per unit time.

Rate of Reaction = `"Change in concentration of a reactant or a prodect"/"Time taken for the change"`

The rate of chemical reaction is defined as the change in concentration of reactant or product per unit time.

The rate of a chemical reaction may be defined as the change in concentration of any of the reactants or any of the products per unit time. Thus,

`"Rate of reaction" = "(Change in concentration of a reactant or a product)"/"Time taken for the change"`

The rate of change of concentration of either products or reactants per unit time is termed the rate of reaction.

Reactants ⟶ Products

It is the ratio of the total change in concentration of a reactant or product to the total time taken by the reaction.

\[r_{\mathrm{av}}=-\frac{\Delta[R]}{\Delta t}=+\frac{\Delta[P]}{\Delta t}\]

The rate of a reaction at any instant of time is called the instantaneous rate of reaction. It is equivalent to the small change in concentration (dx) in a small interval of time (dt).

Instantaneous rate of reaction,

\[r_{\mathrm{inst}}=\frac{-dx}{dt}\]

The reactions that have higher order true rate law but are found to behave as first order are called pseudo first order reactions.

\[\ce{CH3COOCH3 + H2O - CH3COOH + CH3OH}\]

Zero order reaction is the reaction whose rate is independent of the reactant concentration and remains constant throughout the course of the reaction.

Chemical kinetics is the branch of chemistry which deals with the study of chemical reactions with respect to the reaction rates, the effect of various arrangements of atoms and the formation of intermediates. It also describes the conditions in which rates can be altered.

or

The branch of chemistry which deals with the study of reaction rates and their mechanisms is called chemical kinetics.

The time in which concentration of reactant becomes half of its initial concentration is called half Life. It is denoted by `t_(1/2)`.

A reaction is zero order if the rate is independent of the concentration of the reactant.

A chemical reaction in which the rate of reaction depends solely linearly on the concentration of one ingredient is referred to as a first-order reaction.

A first-order reaction is a reaction whose rate depends upon the first power of the concentration of reactants, i.e., the rate is directly proportional to the concentration of reactants.

Half life of a reaction is defined as the time required for the reactant concentration to reach one half of its initial value.

The half-life t_1/2 is the time required for the concentration of a reactant to fall to half its initial value.

\[t_{1/2}\propto\frac{1}{[A_0]^{n-1}}\]

The Arrhenius equation is a mathematical expression to give a quantitative relationship between the rate constant and temperature.

Activation energy is the lowest energy necessary to commence a chemical reaction by disrupting the bonds of reactant molecules and creating the activated complex or transition state. It signifies the energy threshold that must be surmounted for a reaction to transpire. Activation energy is typically represented as E_a.

Activation energy may be defined as the excess energy that the reactant molecules (having energy less than the threshold energy) must acquire in order to cross the energy barrier and to change into the products.

\[\mathrm{Rate}=\frac{\text{Decrease in concentration of Reactant}}{\text{Time interval}}\]

\[=-\frac{\Delta[R]}{\Delta T}\]

\[\mathrm{Rate}=\frac{\text{Increase in concentration of Product}}{\text{Time interval}}\]

\[=+\frac{\Delta\left[P\right]}{\Delta T}\]

For a general reaction aA + bB → cC + dD:

\[\frac{dx}{dt}=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=+\frac{1}{c}\frac{d[C]}{dt}=+\frac{1}{d}\frac{d[D]}{dt}\]

Collision Theory explains why and how temperature increases the rate of reaction.

Microscopic Factors:

Factor 1: Collisional Frequency (Z):

• The number of collisions taking place per second per unit volume of the reaction mixture.
• Effective collision: Only those collisions that actually produce the products.

\[\mathrm{Rate}=\frac{dx}{dt}=Z\times\text{(fraction of effective collisions)}\]

Factor 2: Activation Energy:

• The minimum amount of extra energy required by a reacting molecule to get converted into an activated molecule (transition state).
• Ea = Threshold energy − Average energy of reactant molecules

Conditions for Effective Collision:

1. Colliding molecules must possess energy ≥ threshold energy.
2. Colliding molecules must have proper orientation at the time of collision.

Drawback of Collision Theory: It considers atoms/molecules to be hard spheres and ignores their structural features.

The rate of a reaction depends on:

A reaction is first order if the rate depends on the first power of concentration of one reactant.

For A → Products:

\[k=\frac{2.303}{t}\log\frac{a}{a-x}\quad\mathrm{or}\quad k=\frac{2.303}{t}\log\frac{[A]_0}{[A]}\]

Also: \[[A]=[A]_0\cdot e^{-kt}\]

Half-life:

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

• Half-life is independent of initial concentration — a defining feature of first order reactions.
• \[t_{75\%}=2\times t_{1/2}\]

Temperature Coefficient:

The temperature coefficient μμ is the ratio of rate constants at two temperatures differing by 10°C:

\[\mu=\frac{k_{T+10}}{k_T}=2\mathrm{~to~3}\]

The two reference temperatures are typically 35°C (308 K) and 25°C (298 K).

If R₁​ = reaction rate at T₁​ and R₂​ = reaction rate at T₂​:

\[\frac{R_1}{R_2}=\frac{\mu T}{10}\]

Arrhenius Equation:

\[k=A\cdot e^{-E_a/RT}\]

where:

• k = rate constant
• A = pre-exponential factor (frequency factor)
• EaEa​ = activation energy (J mol⁻¹)
• R = gas constant (8.314 J mol⁻¹ K⁻¹)
• T = temperature in Kelvin

The factor \[e^{-E_a/RT}\] is called the Boltzmann factor.

Logarithmic form:

\[\log k=\log A-\frac{E_a}{2.303RT}\]

A plot of log k vs 1/T is a straight line with:

\[\mathrm{Slope}=-\frac{E_a}{2.303R}\]

Intercept = log A

This is of the form y = mx + c.

Two-Temperature Form:

\[\log\frac{k_2}{k_1}=\frac{E_a}{2.303R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)=\frac{E_a}{2.303R}\left(\frac{T_2-T_1}{T_1T_2}\right)\]

• A catalyst increases the rate of reaction
• Works by lowering the activation energy (energy barrier)
• Helps reaction reach equilibrium faster
• Does not change the equilibrium position

A positive catalyst lowers the activation energy and hence increases the rate of reaction.