A first order chemical reaction is a reaction in which the rate of reaction is proportional to the concentration of only one reactant. This means that the rate of reaction increases as the concentration of the reactant increases, and decreases as the concentration decreases. The mathematical expression for the rate law of a first order reaction is given by:

r = k[A]

where r is the rate of the reaction, k is the rate constant of the reaction, and [A] is the concentration of the reactant A.

This rate law shows that the rate of the reaction is directly proportional to the concentration of the reactant A. The rate constant, k, is a proportionality constant that is specific to each reaction and is dependent on the temperature and other reaction conditions.

The half-life of a first order reaction is also important in understanding the behavior of the reaction. The half-life is defined as the time it takes for the concentration of the reactant to decrease to half of its initial concentration. For a first order reaction, the half-life is given by:

$t_{1/2} = \frac {0.693}{k}$

where t_1/2 is the half-life and k is the rate constant.

This equation shows that the half-life of a first order reaction is inversely proportional to the rate constant of the reaction. This means that the faster the rate of the reaction, the shorter the half-life.

One common example of a first order reaction is the radioactive decay of isotopes. Radioactive decay is a first order process because the rate of decay is proportional to the number of radioactive atoms present. The rate constant of radioactive decay is specific to each isotope and is often used to determine the age of rocks and fossils. However, radioactive decay is not a chemical reaction.

Another example of a first order reaction is the hydrolysis of esters. This is a chemical reaction that involves the reaction of an ester with water to produce an alcohol and a carboxylic acid. The rate of this reaction is proportional to the concentration of the ester, making it a first order reaction. This reaction is important in the production of soaps and detergents.

In conclusion, first order reactions are a type of chemical reaction in which the rate of reaction is proportional to the concentration of only one reactant. They are characterized by their rate law and half-life, which are dependent on the rate constant of the reaction. Understanding first order reactions is important in many areas of science and technology, including radioactivity*, pharmaceuticals, and environmental science.

*Radioactivity is an example of first order reaction but not of first order chemical reaction.