ORG-23

Trouton's rule

ΔSvap ≈ ΔHvap / Tb ≈ 88 J/(mol·K). Boiling from enthalpy of vaporisation.

Reading speed

Physical organicTrouton

Governing equation

\Delta S_{\mathrm{vap}}=\Delta H_{\mathrm{vap}}/T_b\approx 88\,\mathrm{J\,mol^{-1}K^{-1}}

$T_b \in \left[200, 600\right]$

where

\Delta H_{vap}: Enthalpy of vaporisation (kJ/mol)
T_b: Boiling point (K)
\Delta S_{vap}: Entropy of vaporisation (J/(mol·K))
T_{Trouton}: Trouton Tb estimate (K)

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

\Delta S_{\mathrm{vap}}=\Delta H_{\mathrm{vap}}/T_b\approx 88\,\mathrm{J\,mol^{-1}K^{-1}}

$T_b \in \left[200, 600\right]$

$T_b = 200$ $\Delta S_{vap} = 154$

Along the curve

②

Domain of the variable — blue

T_b_{\min} = 200,\quad T_b_{\max} = 600

$T_b \in \left[200, 600\right]$

$T_b = 200$ $T_b = 200$

Along the curve

③

Response curve — green

\Delta S_{\mathrm{vap}}=\Delta H_{\mathrm{vap}}/T_b\approx 88\,\mathrm{J\,mol^{-1}K^{-1}}

$T_b \in \left[200, 600\right]$

$T_b = 200$ $\Delta S_{vap} = 154$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta S_{vap}}{\mathrm{d}T_b}

$T_b \in \left[200, 600\right]$

$T_b = 202.5$ $\Delta S_{vap}^{\prime} = -0.751$

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-23 — Trouton's rule) is the form associated with Trouton. Working symbols: $\Delta H_{vap}$ , $T_b$ $\rightarrow$ $\Delta S_{vap}$ , $T_{Trouton}$ . Nonpolar liquids share a similar entropy of vaporisation. H-bonded liquids (water, alcohols) exceed 88.

Purpose

Purpose: compute

\Delta S_{vap}

T_{Trouton}

from

\Delta H_{vap}

T_b

in Organic chemistry via

\Delta S_{\mathrm{vap}}=\Delta H_{\mathrm{vap}}/T_b\approx 88\,\mathrm{J\,mol^{-1}K^{-1}}

ΔSvap ≈ ΔHvap / Tb ≈ 88 J/(mol·K). Boiling from enthalpy of vaporisation. 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

\Delta H_{vap} = 30.800\,\mathrm{kJ/mol}

T_b = 350.000\,\mathrm{K}

, the governing relation

\Delta S_{\mathrm{vap}}=\Delta H_{\mathrm{vap}}/T_b\approx 88\,\mathrm{J\,mol^{-1}K^{-1}}

yields

\Delta S_{vap} = 88.0\,\mathrm{J/(mol·K)}

T_{Trouton} = 350.0\,\mathrm{K}

. Enter ΔHvap in kJ/mol and Tb, or read the Trouton estimate Tb = ΔHvap / 0.088. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Enthalpy of vaporisation \Delta H_{vap}30.8 kJ/molBoiling point T_b350 K

Outputs

Entropy of vaporisation \Delta S_{vap}88.0 J/(mol·K)
Trouton Tb estimate T_{Trouton}350.0 K

Reading speed

Watch on YouTube

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Narration of this film

Enter ΔHvap in kJ/mol and Tb, or read the Trouton estimate Tb = ΔHvap / 0.088.

Nonpolar liquids share a similar entropy of vaporisation. H-bonded liquids (water, alcohols) exceed 88.

Reading speed

Watch on YouTube