The First-Order Integrated Rate Law
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For a first-order reaction, the natural log of concentration falls linearly with time, so ln[A] plotted against time gives a straight line.
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Plotting ln[H2O2] against time during its decomposition produces a straight line, confirming first-order behavior.
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A curved ln[A]-versus-time plot rules out first order — it does not merely weaken the case for it.