What does the slope equal for a second order reaction graph?

For a second-order reaction, the relationship between the concentration of reactants and time can be analyzed using the integrated rate law. For a second-order reaction with respect to one reactant, the integrated rate equation is:

1/[A] = kt + 1/[A₀]

Here, [A] is the concentration of the reactant at time t, [A₀] is the initial concentration, k is the rate constant, and t is time.

When this equation is plotted in a linear form, with 1/[A] on the y-axis and time (t) on the x-axis, the slope of the line is equal to the positive value of the rate constant (k). Therefore, the slope of the graph representing a second-order reaction is positive k. This indicates that as time progresses, the concentration of the reactant decreases, leading to a corresponding increase in the value of 1/[A], consistent with the characteristics of a second-order reaction.

This understanding is crucial because it allows one to determine the rate constant from experimental data, thus aiding in kinetic studies of reaction mechanisms.