Order of Reaction

• The reaction rates vary with the concentration of the reactants.
• The experimental results show that the reaction rates do not always show similar concentration-dependences.
• In many cases, the rates are found to be proportional to the first power of concentration.
• There are many reactions in which the rates varied to the second or even third power of the reactant concentration.
• For a general reaction,

aA + bB + cC → Products

• The reaction rate is described by the expression

Rate = k [A]^p[B]^q[C]^r…………..(i)

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

The exponents (p, q and r) are called order of the reaction with respect to A, B and C respectively.

The sum p + q + r is called as the overall order of the reaction.

• Thus, the order of the reaction is equal to the sum powers of all the concentration terms in the rate law equation.
• In other words, the order may be defined as: The total number of concentration variables which determine the rate of any reaction is called the overall order of the reaction.
• The order of a reaction is generally a small integer, half integer or zero.
• The order of the reaction is obtained experimentally.
• As a matter of general rule, reaction order cannot be deduced from the stoichiometry of the reaction.
• However, if the reaction takes place in a single step, then the stoichiometric coefficient(s) of the reactant(s) in the balanced chemical equation give the order of the reaction with respect to the respective reactant.
• The overall order is then given by the sum of all the stoichiometric coefficients.

A) Zero Order Reactions

• The reaction whose rate does not depend upon the concentration of the reactant is called a zero order reaction.
• Thus, the reaction A→ Products is called  a zero order reaction if

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Rate = -d[A]/dt = k[A]⁰ = k……………………….(ii)

• Thus, the rate of a zero order reaction remains constant with time.
• Reaction of H₂ and Cl₂ over the surface of water is a zero order reaction.

   B) First Order Reactions

• The reaction for which the rate depends upon only one concentration variable is called the first order reaction.
• The reaction, A → Products is said to be first order, if the reaction rate is given by the equation,

Reaction rate = k[A]

• Thus, the reaction rate in such case changes linearly with the concentration of A (the reactant) i.e., if [A] is doubled, the reaction rate also gets doubled.
• This reaction is then said to be of first order i.e., order of the reaction is one.
• The reaction, aA + bB→ cC + dD, is said to be of first order, if the reaction rate is given by any of the following expressions.

R_t = k[A] or R_t= k[B]

• The reaction rate in such a case would vary linearly with the concentration of A or B.

C) Second Order Reactions

• The reaction in which two concentration variables affect the rate is called a second order reaction.
• The reaction, A → Products, is said to be of second order, if the reaction rate follows the following equation, Reaction rate = k[A]²
• In such a case, the reaction rate varies to the second power of the concentration of the reactant A.
• Thus, for  a second order reaction if the concentration of the reactant (A) is doubled, then the reaction rate gets increased by a factor of four.
• The reaction, aA + bB → Products is said to be second order, if the rate of reaction depends upon two concentration variables.

• In such a reaction, the following cases are possible:

• Some examples of second order reaction are:

2 NO₂ → 2 NO + O₂ [Nitrogen dioxide decomposes into nitrogen monoxide and an oxygen molecule.]

2 HI → I₂ + H₂ [Hydrogen Iodide decomposes into iodine gas and hydrogen gas].

2 NOBr → 2 NO + Br₂ [In the gas phase, Nitrosyl bromide decomposes into nitrogen oxide and                        bromine gas.]

References: 

i) https://brilliant.org/wiki/order-of-chemical-reactions/

ii) https://saylordotorg.github.io/text_general-chemistry-principles-patterns-and-applications-v1.0/s18-03-methods-of-determining-reactio.html

iii) https://www.shaalaa.com/question-bank-solutions/define-order-of-reaction-with-suitable-examples-rate-of-reaction-and-reactant-concentration_201927

Order of Reaction