What is the shape of the graph for a first order reaction?

For a first-order reaction, the concentration of reactants decreases exponentially with time, leading to an important relationship that can be depicted graphically. The key characteristic of a first-order reaction is that when you plot the natural logarithm of the concentration of the reactant versus time, the resulting graph produces a straight line. This linear relationship has a slope that is negative and proportional to the rate constant of the reaction.

This linear representation is foundational because it simplifies the analysis of reaction kinetics and allows for easy determination of the rate constant, which can be obtained from the slope of the line. The equation that describes this relationship is:

[ \ln[A] = -kt + \ln[A]_0 ]

where ([A]) is the concentration of the reactant at time (t), ([A]_0) is the initial concentration, (k) is the rate constant, and (t) is the time. By rearranging this equation, you can clearly see the linear relationship.

In contrast, a first-order reaction does not produce a curved line or an exponential curve when you are plotting the natural logarithm of concentration against time; these graphical descriptions apply to different types of reactions or parameters. Therefore, the