Integrated Rate Law Graphs

Graphical analysis of kinetic data identifies the order by finding which function of concentration gives a straight line against time. For a first order reaction the integrated rate law is ln[A] = ln[A_0] - kt, so a plot of ln[A] versus time is linear with slope -k. The observed straight line of ln[A] against time with a negative slope therefore signals first order kinetics, and the magnitude of the slope equals the rate constant. A zero order reaction gives a straight line for [A] itself, not its logarithm, against time. A second order reaction gives a straight line for 1/[A] against time. A third order reaction gives a straight line for 1/[A]^2 against time. This graphical method is a standard NCERT tool for determining order from experimental data. It is worth emphasising that this is not a special case but a representative example of how integrated rate law graphs operates throughout chemical kinetics. Working through the logic step by step, rather than memorising the result, makes it clear why first order governs the behaviour seen here. Plausibility check: the linear logarithmic plot reflects the exponential decay unique to first order kinetics, and the slope yielding a positive rate constant confirms the assignment.