Half-life of a Reaction

During a chemical reaction, the reactant’s concentration decreases over time. The time taken to reduce it to half of its initial quantity is called the half-life of the reaction, abbreviated as t_1/2.

Consider the refrigerant trichlorofluoromethane, which depletes the ozone layer. Its atmospheric residence time is 45 years and it is banned in many countries. But how long does it take for the concentration to drop to 50%? To estimate a reactant’s concentration after an elapsed time, the half-life can be used.

The half-life differs for each reaction type. Depending on the reaction order, a general half-life expression can be derived from the integrated rate laws.

Consider the zero-order integrated rate law. At t_1/2, the reactant concentration is half of its initial concentration. On substitution of these parameters, an expression for the half-life is formulated.

The formula shows that the half-life for a zero-order reaction is dependent on and directly proportional to the initial reactant concentration. As the reactant concentration declines, the half-life continues to get shorter.

For a first-order reaction, the integrated rate expression is modified by substituting the time as t_1/2