For a second order reaction, what is the correct plot?

For a second order reaction, the relationship that governs the reaction kinetics can be expressed as the rate of reaction being proportional to the square of the concentration of the reactant. Specifically, for a reaction involving a single reactant A, the integrated rate law is given by the equation:

1/[A] = kt + 1/[A]₀

In this equation, [A] is the concentration of the reactant at time t, k is the rate constant, and [A]₀ is the initial concentration. This means that if you plot 1/[A] versus time, you will obtain a straight line, indicating that the reaction follows second-order kinetics.

This linear plot confirms the nature of the reaction and allows for the determination of the rate constant k from the slope of the line. The intercept will correspond to the inverse of the initial concentration.

The other plotting options do not yield a linear relationship for a second order reaction:

• A plot of concentration vs. time for a second order reaction does not yield a linear plot and is not useful for determining rate constants.
• A plot of ln[A] vs. time is applicable to first order reactions, where the natural logarithm of concentration decreases linearly over time.