Third Order Reaction 

A third order reaction definition involves a type of chemical reaction where the rate of reaction depends on the concentration of three reactant molecules. The overall order of the reaction is the sum of the powers of the concentration terms in the rate law, and for a third-order reaction, this sum is three.

To understand a third-order reaction, it is essential first to understand the concept of the order of a reaction. 

The order of a reaction is known as the sum of the exponents of the concentration terms of all the reactants present in the rate law expression. 

The rate law typically takes the form 

Rate = k [A]^m [B]ⁿ, 

where [A] and [B] are the concentrations of the reactants, m and n are their respective orders, and k is the rate constant. The overall order of the reaction is the sum of m and n.

1.0Integrated Rate Equation for a Third-Order Reaction (Single Reactant)

Consider a third-order reaction: 

3A  →  products

Let:

• The initial concentration of A is a moles per liter.
• After time t, x moles of A have reacted.
• The concentration of A at time t becomes (a−x) moles per liter.

The rate law for a third-order reaction can be expressed as: Rate = k[A]³

Substituting the concentration of A at time t: Rate = k(a − x)³

Since the rate of the reaction is also given by the decrease in concentration of A over time:

$\frac{d[A]}{dt}=-k(a-x{)}^3$

Given that [A] = a − x

$\frac{dx}{dt}=k(a-x{)}^3$

Rearranging the equation, we’ll get:

k = $\frac{1}{t}.\frac{x(2a-x)}{2a^2(a-x{)}^2}$

2.0Characteristics of Third-Order Reactions

Dependence on Concentrations:

The rate of a third-order reaction can depend on the concentration of one reactant cubed, the concentration of two reactants where one is squared, or the concentration of three different reactants.

Rate Law:

The rate law for a third-order reaction can be expressed in different forms based on the specific reactants involved.

For one reactant: Rate = k[A]³

For two reactants: Rate = k[A]²[B]

For three reactants: Rate = k[A][B][C]

where k is the rate constant, and [A], [B], and [C] are the concentrations of the reactants.

Units of Rate Constant:

The units of the rate constant k for a third-order reaction are L²/mol²⋅s.

3.0Integrated Rate Law for Third-Order Reactions

The integrated rate law expresses the concentration of a reactant as a function of time. For a third-order reaction involving one reactant A:

A → products

The integrated rate law is:

$\frac{1}{2[A{]}^2}=kt+\frac{1}{2[A{]}_0^2}$

where:

• [A] is the concentration of the reactant at time t.
• [A]_0​ is the initial concentration of the reactant.
• k is the third-order rate constant.
• t is the time.

4.0Half-Life of a Third-Order Reaction

The half-life (t_1/2​) of a third-order reaction, which is the time taken for the concentration of a reactant to decrease to half its initial value, is given by:

$t_{\frac{1}{2}}=\frac{3}{2k[A{]}_0^2}$

This shows that the half-life of a third-order reaction is inversely proportional to the square of the initial concentration of the reactant. As the concentration of the reactant decreases, the half-life increases.

5.0Examples of Third Order Reaction

An example of a third-order reaction is the formation of triiodide ion in aqueous solution:

I₂  +  I⁻ + I⁻  →  I₃⁻

In this reaction, two iodide ions and one iodine molecule combine to form a triiodide ion. The rate law for this reaction would be:

Rate = k [I₂] [I⁻]²

Example: Reaction Between Nitric Oxide and Chlorine

Reaction: 2NO + Cl₂  → 2NOCl

Rate Law: R = k[NO]² [Cl₂]

Order of Reaction: The order of the reaction is determined by summing the exponents of the concentration terms in the rate law. 

Order: 2 + 1 = 3

So, the reaction between nitric oxide and chlorine is a third-order reaction.

Example: Reaction Between Nitric Oxide and Oxygen

Reaction: 2NO + O2 → 2NO₂

Rate Law: R = k[NO]₂ [O₂]

Order of Reaction: Again, the order of the reaction can be calculated by summing the exponents of the concentration terms in the rate law. 

Order = 2 + 1 = 3

So, the reaction between nitric oxide and oxygen is also a third-order reaction.

6.0Significance of Third-Order Reactions

Understanding third-order reactions is important in several fields, including:

• Chemical Kinetics: Provides insights into complex reaction mechanisms and how different reactants interact.
• Catalysis: Helps in designing efficient catalysts that can handle reactions involving multiple reactants.
• Environmental Chemistry: Useful for studying atmospheric and environmental processes where multi-molecular interactions are common.
• Industrial Processes: Important for optimizing reaction conditions in manufacturing and chemical production.