ORG-13

Atom economy

AE = m_desired / m_reactants × 100. How much of the reactants sits in the product.

Reading speed

Green chemistryTrost atom economy

Governing equation

\mathrm{AE}=100\,m_{\mathrm{des}}/\sum m_{\mathrm{reac}}

$m_{des} \in \left[10, 500\right]$

where

m_{des}: Desired molar mass (g/mol)
\sum m_{reac}: Reactant molar mass (g/mol)
AE: Atom economy (%)

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

\mathrm{AE}=100\,m_{\mathrm{des}}/\sum m_{\mathrm{reac}}

$m_{des} \in \left[10, 500\right]$

$m_{des} = 10$ $AE = 5.556$

Along the curve

②

Domain of the variable — blue

m_{des}_{\min} = 10,\quad m_{des}_{\max} = 500

$m_{des} \in \left[10, 500\right]$

$m_{des} = 10$ $m_{des} = 10$

Along the curve

③

Response curve — green

\mathrm{AE}=100\,m_{\mathrm{des}}/\sum m_{\mathrm{reac}}

$m_{des} \in \left[10, 500\right]$

$m_{des} = 10$ $AE = 5.556$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}AE}{\mathrm{d}m_{des}}

$m_{des} \in \left[10, 500\right]$

$m_{des} = 13.08$ $AE^{\prime} = 0.556$

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-13 — Atom economy) is the form associated with Trost atom economy. Working symbols: $m_{des}$ , $\sum m_{reac}$ $\rightarrow$ $AE$ . Trost: addition and rearrangement score 100%; substitutions and fragmentations leak mass.

Purpose

Purpose: compute

AE

from

m_{des}

\sum m_{reac}

in Organic chemistry via

\mathrm{AE}=100\,m_{\mathrm{des}}/\sum m_{\mathrm{reac}}

AE = m_desired / m_reactants × 100. How much of the reactants sits in the product. 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

m_{des} = 120.000\,\mathrm{g/mol}

\sum m_{reac} = 180.000\,\mathrm{g/mol}

, the governing relation

\mathrm{AE}=100\,m_{\mathrm{des}}/\sum m_{\mathrm{reac}}

yields

AE = 66.7\,\mathrm{%}

. Stoichiometric masses of the balanced equation. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Desired molar mass m_{des}120 g/molReactant molar mass \sum m_{reac}180 g/mol

Outputs

Atom economy AE66.7 %

Reading speed

Watch on YouTube

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Narration of this film

Stoichiometric masses of the balanced equation.

Trost: addition and rearrangement score 100%; substitutions and fragmentations leak mass.

Reading speed

Watch on YouTube