Changes in Concentration Over Time

As a reaction proceeds, the concentrations of the species involved (reactants and products) will
change. The value of the concentration of each reactant and product at different points in time can
in general be calculated if the rate law is known, although the mathematics needed to perform the
manipulations may be quite complicated, depending on the order of the reaction. The relationships
derived are often also not general enough to be of interest. The simplest cases, however, are worth
examining in more detail.

ZERO-ORDER REACTIONS

A zero-order reaction has a constant rate, which is independent of the reactants’ concentrations.
Thus, the rate law is: rate = k, where k has units of M s−1. The concentration of the reactants
decreases linearly over time, i.e., it decreases by the same amount in each period of time, until it is
completely used up. A plot of reactant concentration ([A]) versus time for a zero-order reaction is a
straight line with slope equal to negative k.

FIRST-ORDER REACTIONS

A first-order reaction (order = 1) has a rate proportional to the concentration of one reactant: