ORG-02

Taft polar equation

log(k/k0) = ρ* σ*. Polar aliphatic substituent effect.

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Physical organicTaft 1952

Governing equation

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

$\sigma^* \in \left[-0.4, 2.5\right]$

where

\rho^*: Polar reaction constant (—)
\sigma^*: Taft σ* (—)
k_0: Reference rate (1/s)
k: Rate (1/s)

The figure, part by part

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①

Governing law — red

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

$\sigma^* \in \left[-0.4, 2.5\right]$

$\sigma^* = -0.4$ $k = 0.251$

Along the curve

②

Domain of the variable — blue

\sigma^*_{\min} = -0.4,\quad \sigma^*_{\max} = 2.5

$\sigma^* \in \left[-0.4, 2.5\right]$

$\sigma^* = -0.4$ $\sigma^* = -0.4$

Along the curve

③

Response curve — green

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

$\sigma^* \in \left[-0.4, 2.5\right]$

$\sigma^* = -0.4$ $k = 0.251$

Along the curve

④

Rate of change — amber

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

$\sigma^* \in \left[-0.4, 2.5\right]$

$\sigma^* = -0.382$ $k^{\prime} = 0.925$

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-02 — Taft polar equation) is the form associated with Taft 1952. Working symbols: $\rho^*$ , $\sigma^*$ , $k_0$ $\rightarrow$ $k$ . Taft split polar (σ*) from steric (Es) using ester hydrolysis in acid vs base.

Purpose

Purpose: compute

k

from

\rho^*

\sigma^*

k_0

in Organic chemistry via

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

log(k/k0) = ρ* σ*. Polar aliphatic substituent effect. 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^* = 1.500\,\mathrm{—}

\sigma^* = 0.500\,\mathrm{—}

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

, the governing relation

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

yields

k = 5.6234\,\mathrm{1/s}

. Aliphatic series, polar part only. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Polar reaction constant \rho^*1.5 —Taft σ* \sigma^*0.5 —Reference rate k_01 1/s

Outputs

Rate k5.6234 1/s

Reading speed

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Narration of this film

Aliphatic series, polar part only.

Taft split polar (σ*) from steric (Es) using ester hydrolysis in acid vs base.

Reading speed

Watch on YouTube