Chemistry / Unit 9 Chem 1678 worked example, 60 to 90 seconds
Calculating a First-Order Rate Constant From a Measured Half-Life
The idea
Calculating a first-order rate constant from a measured half-life means substituting that half-life into the first-order relationship k = 0.693/t1/2, since 0.693 is the natural log of two.
In practice
Hydrogen peroxide's decomposition at 40 °C shows a half-life t1/2 of 2.16 × 10⁴ s, the quantity to substitute for the first-order relationship's t1/2 in seconds. Substituting into k = 0.693/t1/2 gives k = 0.693/(2.16 × 10⁴ s), where the units divide to leave inverse seconds, s⁻¹. Carrying that division through gives k ≈ 3.21 × 10⁻⁵ s⁻¹, consistent with the anchor's own reported value for this decomposition. The result's small magnitude and s⁻¹ units make sense for a reaction whose half-life spans hours, confirming the answer is physically reasonable.
Where people slip
This shortcut, k = 0.693/t1/2, holds only for first-order reactions — using it on a second- or zero-order half-life produces a rate constant with no correct meaning.
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