kinetic+half+life

The half-life of a reactant in a chemical reaction is a measure of time in which exactly 50% of it is consumed.

There are two ways to determine the half-life of a reactant:
 * using a plot of concentration versus time
 * using the rate constant if the reactant order is known


 * Concentration vs. Time**

This technique can be used for any reactant, regardless of its order. Take a look at the following plot of [A] versus time:

The initial concentration of the reactant A is 30 mg/L at time zero. After one half-life, its concentration would be 15 mg/L. Then use the plot to determine the time at 15 mg/L (which would be approximately 4 hours). The half-life of A is 4 hours.

In this situation, the reactant order for A is unknown, so nothing can be said about its rate constant.


 * Half-Life from Kinetics**

Recall that in order to find reactant orders, you must have experimental data. Rate constants can be derived from the data as well.

If a reactant is __first-order__, it will obey the first-order half-life equation:

Therefore knowing the rate constant allows for the calculation of half-life, and vice versa.

A __second-order__ reactant will obey the second-order half-life equation:



In this equation, the initial concentration of the reactant must be known, as well as either the rate constant or half-life.