Rate equation

Rate Equation

The rate equation or rate law is a mathematical model that describes the relationship between the rate of a chemical reaction and the concentrations of its reactants. It is a fundamental concept in chemical kinetics, the study of rates of chemical processes.

Formulation

The rate equation is typically expressed in the form:

r = k[A]^m[B]^n

where:

• r is the rate of reaction,
• k is the rate constant,
• [A] and [B] are the concentrations of the reactants,
• m and n are the orders of reaction with respect to [A] and [B].

The rate constant k is specific to the reaction at a given temperature. The orders of reaction m and n are typically determined experimentally.

Zero Order Reactions

In a zero order reaction, the rate of reaction is independent of the concentration of the reactants. This means that the rate equation is simply:

r = k

First Order Reactions

In a first order reaction, the rate of reaction is directly proportional to the concentration of one of the reactants. The rate equation is:

r = k[A]

Second Order Reactions

In a second order reaction, the rate of reaction is proportional to the square of the concentration of one of the reactants, or to the product of the concentrations of two reactants. The rate equation is:

r = k[A]^2 or r = k[A][B]

Integrated Rate Equations

The integrated rate equation is derived from the rate equation and gives the concentration of the reactants as a function of time. The form of the integrated rate equation depends on the order of the reaction.

See Also

• Chemical kinetics
• Reaction rate
• Rate constant
• Order of reaction

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