Chemical kinetics, a topic in several chemistry courses, illustrates the connection between mathematics and chemistry. Chemical kinetics deals with chemistry experiments and interprets them in terms of a mathematical model. The experiments are perfomed on chemical reactions as they proceed with time. The models are differential equations for the rates at which reactants are consumed and products are produced. By combining models with experiments, chemists are able to understand how chemical reactions take place at the molecular level.
At the macroscopic level, chemical kinetics investigates the amounts reacted, formed, and the rates of their formation. At the molecular or microscopic level, chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states.
Rate
The term rate is often used to describe the change in a quantity that occurs per unit of time. For example, the rate of inflation is the change in the average cost of a collection of standard items per year.
Rate of reaction
It is the rate at which the reactants are transformed into the products of the reaction. The rate of a reaction is the change in the concentration of one of the reactants £G(X) that occurs during a given period of time £Gt.

Units for chemical reaction rates
Define and use proper units for chemical reaction rates For changes in amounts, the units can be one of mol/s, g/s, lb/s, kg/day etc.
For changes in concentrations, the units can be one of mol/(L s), g/(L s), etc.
With respect to reaction rates, we may deal with average rates, instantaneous rates, or initial rates depending on the experimental conditions.
Rate law
The relation between the reaction rate and the concentration of the reactants are called rate laws; that is, rate laws are expressions of rates in terms of concentrations of reactants. Rate laws apply to homogeneous reactions in which all reactants and products are in one phase (solution).
These rate laws can often be expressed mathematically in differential forms or in integrated forms; which are called differential rate laws and integrated rate laws respectively. Some rate laws are very simple and some are very complicated. A rate law may be determined experimentally or may be the result of a theoretical prediction, or both.
Often reactions are found to have rate laws of the form
Where k is constant, characteristic of a particular reaction, called the rate constant or the rate coefficient. The powers a,b, ¡K are also constants, a is the order with respect to A and b is the order with respect to B. Orders are commonly integers, but they do not have to be.
Common types of rate laws
The zero order rate law for the general reaction A ¡÷ P is written as
A first order rate law is one in which the rate is proportional to the concentration raised to the power of 1
A second order reaction has the concentration raised to the power of 2
Rate equation
The rate law or rate equation for a chemical reaction is an equation which links the reaction rate with concentrations or pressures of reactants and constant parameters (normally rate coefficients and partial reaction orders) The rate equation is a differential equation, and it can be integrated in order to obtain an integrated rate equation that links concentrations of reactants or products with time.