CHM-25

First-order half-life

t½ = ln 2 / k. Independent of the starting concentration.

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KineticsFirst-order kinetics

Governing equation

t_{1/2}=\ln 2/k

where

k: Rate constant (1/s)
t_{1/2}: Half-life (s)

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-25 — First-order half-life) is the form associated with First-order kinetics. Working symbols: $k$ $\rightarrow$ $t_{1/2}$ . From c = c0 e^{−kt}. Radioactive decay is the textbook first-order process.

Purpose

Purpose: compute

t_{1/2}

from

k

in Physical chemistry via

t_{1/2}=\ln 2/k

t½ = ln 2 / k. Independent of the starting concentration. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

k = 0.010\,\mathrm{1/s}

, the governing relation

t_{1/2}=\ln 2/k

yields

t_{1/2} = 69.315\,\mathrm{s}

. Irreversible first-order, constant k. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Rate constant k0.01 1/s

Outputs

Half-life t_{1/2}69.315 s

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Narration of this film

Irreversible first-order, constant k.

From c = c0 e^{−kt}. Radioactive decay is the textbook first-order process.

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