CHM-28

Arrhenius k

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Physical chemistryArrhenius

Governing equation

k=A e^{-E_a/RT}

$T \in \left[250, 800\right]$

where

A: A (1/s)
E_a: Ea (kJ/mol)
T: T (K)
k: k (1/s)

The figure, part by part

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①

Governing law — red

k=A e^{-E_a/RT}

$T \in \left[250, 800\right]$

$T = 250$ $k = 1.92\times 10^{-4}$

Along the curve

②

Domain of the variable — blue

T_{\min} = 250,\quad T_{\max} = 800

$T \in \left[250, 800\right]$

$T = 250$ $T = 250$

Along the curve

③

Response curve — green

k=A e^{-E_a/RT}

$T \in \left[250, 800\right]$

$T = 250$ $k = 1.92\times 10^{-4}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}k}{\mathrm{d}T}

$T \in \left[250, 800\right]$

$T = 253.5$ $k^{\prime} = 5.06\times 10^{-5}$

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-28 — Arrhenius k) is the form associated with Arrhenius. Working symbols: $A$ , $E_a$ , $T$ $\rightarrow$ $k$ . Activated rate.

Purpose

Purpose: compute

k

from

A

E_a

T

in Physical chemistry via

k=A e^{-E_a/RT}

Activated rate. 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

A = 1.000e+13\,\mathrm{1/s}

E_a = 80.000\,\mathrm{kJ/mol}

T = 350.000\,\mathrm{K}

, the governing relation

k=A e^{-E_a/RT}

yields

k = 11.487420\,\mathrm{1/s}

. Activated rate. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

A A10000000000000 1/sEa E_a80 kJ/molT T350 K

Outputs

k k11.487420 1/s

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Narration of this film

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