An integrated rate law relates concentration to elapsed time after solving a rate equation with an initial condition. Its validity retains the assumptions of the underlying rate law, including fixed rate constants and appropriate stoichiometry. The second-order reaction reciprocal-concentration relation is one example; a different rate equation generally requires a different integrated rate law.[ref]
Chemistry 2e. §12.4, opening paragraph and “Second-Order Reactions”: concentration as a function of elapsed time
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