ORG-09

Arrhenius (organic)

k = A exp(−Ea/RT) for an organic elementary step.

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KineticsArrhenius

Governing equation

k=A\exp(-E_a/RT)

$T \in \left[250, 500\right]$

where

A: Pre-factor (1/s)
E_a: Activation energy (kJ/mol)
T: Temperature (K)
k: Rate constant (1/s)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

k=A\exp(-E_a/RT)

$T \in \left[250, 500\right]$

$T = 250$ $k = 1.74\times 10^{-7}$

Along the curve

②

Domain of the variable — blue

T_{\min} = 250,\quad T_{\max} = 500

$T \in \left[250, 500\right]$

$T = 250$ $T = 250$

Along the curve

③

Response curve — green

k=A\exp(-E_a/RT)

$T \in \left[250, 500\right]$

$T = 250$ $k = 1.74\times 10^{-7}$

Along the curve

④

Rate of change — amber

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

$T \in \left[250, 500\right]$

$T = 251.6$ $k^{\prime} = 3.66\times 10^{-8}$

Along the curve

Lecture brief

Historical brief

Hammett (1937) and Taft linear free-energy, E-factor green metrics, Woodward–Fieser UV and Claisen equilibria are how organic chemistry became predictive. The lab is substituent, waste and tautomer. This sheet (ORG-09 — Arrhenius (organic)) is the form associated with Arrhenius. Working symbols: $A$ , $E_a$ , $T$ $\rightarrow$ $k$ . Typical Ea: SN2 ~ 80 kJ/mol, radical H-abstraction ~ 30–40, Diels–Alder ~ 80–100.

Purpose

Purpose: compute

k

from

A

E_a

T

in Organic chemistry via

k=A\exp(-E_a/RT)

k = A exp(−Ea/RT) for an organic elementary step. Use it when a real organic chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

A = 1.000e+11\,\mathrm{1/s}

E_a = 85.000\,\mathrm{kJ/mol}

T = 350.000\,\mathrm{K}

, the governing relation

k=A\exp(-E_a/RT)

yields

k = 0.020639\,\mathrm{1/s}

. Constant A, Ea. T in kelvin. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Pre-factor A100000000000 1/sActivation energy E_a85 kJ/molTemperature T350 K

Outputs

Rate constant k0.020639 1/s

Reading speed

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Narration of this film

Constant A, Ea. T in kelvin.

Typical Ea: SN2 ~ 80 kJ/mol, radical H-abstraction ~ 30–40, Diels–Alder ~ 80–100.

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