Data for a first-order decomposition give a straight line when ln[A] is plotted against time, described by ln[A] = -(0.0462 s^-1)t - 1.204. What is the rate constant of the reaction?

Core Concept

The integrated first-order law, ln[A] = ln[A]0 - kt, plots as a straight line with slope -k and intercept ln[A]0. Matching the fitted equation shows a slope of -0.0462 s^-1, so k = 0.0462 s^-1. The intercept corresponds to ln[A]0, so the starting concentration was e^(-1.204), about 0.30 M. One graph thus recovers both the rate constant and the initial concentration.