Order of Reactions

The power to which the reactants concentration term in the rate equation is raised is known as order of chemical reaction. Every chemical reaction can be classified depending on reaction kinetics. Consider the following chemical reaction with a rate equation:

2A  +   B   →  C; the rate of reaction r= k (A)²(B)¹.

Here the reaction order is 2 with respect to A and it is 1 with respect to B. The total reaction order will be 2 + 1 =3.The order of reaction can be a whole number, zero or fraction. Reactions are divided into 4, based on reaction orders.

• Zero-Order Reaction
• First-Order Reactions
• Second-Order Reactions
• Higher-Order Reactions(Mixed-Order Reactions)

Zero-Order Reaction

Zero-Order Reactions have constant rate. It does not depend on the concentration of reactants. These reactions have rate law in which the exponential powers (raised power) of all the reactants are zero. Any number raised to zero is one (a⁰=1).According to zero –Order rate equation x = kt   or k = x/t = moles per liter time^-1.Zero –order reactions are commonly seen in thermal chemical decompositions.

First-Order Reactions

In first order reactions the rate of reaction is proportional to the concentration of the square of a single reactant or the product of concentrations of two reactants. Phenomenon of radioactive decay is a best example of first order reaction. The rate law of first order reaction is :

Rate = k (A).  The half life period of a first order reaction is independent of the initial concentration of reactants.

Second Order Reactions

In a Second-order Reaction (order=2), the rate is proportional to the concentration of square of single reactant. The rate law for a second -order reaction is:

Rate = k(A)² and the units of rate constant is  M^-1 sec^-1.

The half life of 2^nd order reaction also depends on the initial concentration of reactants.

t_1/2   =   1/k(B)_0.  These reactions can be reduced to pseudo-first-order rate equation and thus an integrated rate equation can be obtained.

Fixed-Order Reaction

These reactions have fractional order for their rate. A mixed second-order rate law can be expressed as: d(B)/dt   =   -k(A)(B).In these reactions the order of reaction changes in the course of reaction

Examples of order of reactions for complex reactions:

CH₃COOC₂H₅  +  OH^-   →  CH₃COO^-   +   C₂H₂O₅

Rate of the reaction,  r  =  k(CH₃COOC₂H₅)(OH)

Questions:

• Define Order of reactions?
• Express the rate law for a third-order reaction?