ORG-01

Hammett equation

log(k/k0) = ρ σ. Substituent constant σ, reaction constant ρ.

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Physical organicHammett 1937

Governing equation

\log(k/k_0)=\rho\sigma

$\sigma \in \left[-0.8, 1.2\right]$

where

\rho: Reaction constant (—)
\sigma: Substituent σ (—)
k_0: Reference rate (1/s)
k: Rate (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

\log(k/k_0)=\rho\sigma

$\sigma \in \left[-0.8, 1.2\right]$

$\sigma = -0.8$ $k = 0.158$

Along the curve

②

Domain of the variable — blue

\sigma_{\min} = -0.8,\quad \sigma_{\max} = 1.2

$\sigma \in \left[-0.8, 1.2\right]$

$\sigma = -0.8$ $\sigma = -0.8$

Along the curve

③

Response curve — green

\log(k/k_0)=\rho\sigma

$\sigma \in \left[-0.8, 1.2\right]$

$\sigma = -0.8$ $k = 0.158$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}k}{\mathrm{d}\sigma}

$\sigma \in \left[-0.8, 1.2\right]$

$\sigma = -0.787$ $k^{\prime} = 0.376$

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-01 — Hammett equation) is the form associated with Hammett 1937. Working symbols: $\rho$ , $\sigma$ , $k_0$ $\rightarrow$ $k$ . σ > 0 for electron-withdrawing groups. ρ > 0 if negative charge builds at the centre.

Purpose

Purpose: compute

k

from

\rho

\sigma

k_0

in Organic chemistry via

\log(k/k_0)=\rho\sigma

log(k/k0) = ρ σ. Substituent constant σ, reaction constant ρ. 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

\rho = 1.000\,\mathrm{—}

\sigma = 0.200\,\mathrm{—}

k_0 = 1.000\,\mathrm{1/s}

, the governing relation

\log(k/k_0)=\rho\sigma

yields

k = 1.5849\,\mathrm{1/s}

. meta/para benzene, no steric overlay. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Reaction constant \rho1 —Substituent σ \sigma0.2 —Reference rate k_01 1/s

Outputs

Rate k1.5849 1/s

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Narration of this film

meta/para benzene, no steric overlay.

σ > 0 for electron-withdrawing groups. ρ > 0 if negative charge builds at the centre.

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