CHM-30

First-order half-life

Independent of concentration.

Reading speed

Physical chemistryfirst order

Governing equation

t_{1/2}=\\ln2/k

$k \in \left[1\times 10^{-4}, 1\right]$

where

k: k (1/s)
t_{1/2}: t½ (s)

The figure, part by part

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①

Governing law — red

t_{1/2}=\\ln2/k

$k \in \left[1\times 10^{-4}, 1\right]$

$k = 1\times 10^{-4}$ $t_{1/2} = 6931.5$

Along the curve

②

Domain of the variable — blue

k_{\min} = 1\times 10^{-4},\quad k_{\max} = 1

$k \in \left[1\times 10^{-4}, 1\right]$

$k = 1\times 10^{-4}$ $k = 1\times 10^{-4}$

Along the curve

③

Response curve — green

t_{1/2}=\\ln2/k

$k \in \left[1\times 10^{-4}, 1\right]$

$k = 1\times 10^{-4}$ $t_{1/2} = 6931.5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}t_{1/2}}{\mathrm{d}k}

$k \in \left[1\times 10^{-4}, 1\right]$

$k = 0.006$ $t_{1/2}^{\prime} = -5.47\times 10^{5}$

Along the curve

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-30 — First-order half-life) is the form associated with first order. Working symbols: $k$ $\rightarrow$ $t_{1/2}$ . Independent of concentration.

Purpose

Purpose: compute

t_{1/2}

from

k

in Physical chemistry via

t_{1/2}=\\ln2/k

Independent of 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}=\\ln2/k

yields

t_{1/2} = 69.31\,\mathrm{s}

. Independent of concentration. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

k k0.01 1/s

Outputs

t½ t_{1/2}69.31 s

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Narration of this film

Independent of concentration.

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