Atom Economy

Atom economy is the theoretical fraction of reactant mass incorporated into a specified desired product according to the balanced equation. The relation is useful for Compare reaction routes by theoretical incorporation of reactant atoms into the desired product.. For A+B→AB with molar masses 20 and 30 g/mol, atom economy is 50/50·100%=100%. If a 10 g/mol by-product C also forms, it is 50/60·100%=83.3%. Check: the value is at most 100%. The final check tests a balance, direction or magnitude relevant to this formula. First map each quantity to the actual experiment, then substitute values. The result describes the modelled relationship; it does not automatically establish every mechanism in the real sample.

The symbols mean: ν_P: stoichiometric coefficient of desired product (dimensionless); M_P: molar mass of desired product (g/mol); ν_R: reactant coefficients (dimensionless); M_R: molar masses of reactants (g/mol). Follow Molar masses in the same mass/mol unit · atom economy in %. Concentrations, activities, volumes and times must use compatible scales. A logarithm needs a dimensionless argument, and a balance must include all contributing species. State temperature and standard state whenever they are part of the definition; otherwise the result may refer to a different chemical condition. An amount is not a mass without molar mass, and activity is not an unnormalised concentration. Say whether inputs were measured or taken from a reference.

This stoichiometric metric depends on the balanced reaction and chosen desired product. It ignores conversion, selectivity, solvent, energy and work-up waste, so it is distinct from experimental yield and process efficiency. Check this assumption for the actual sample, temperature and phase. Nonideality, mass transport or side reactions can make a precise calculation systematically wrong. Compare the balanced reaction and the activity or concentration scale with the model, then state the assumption that most affects the result. Near model boundaries, check activities and phase state rather than extending a dilute-solution approximation. Different conditions require a fresh model check.

Recalculate the example: For A+B→AB with molar masses 20 and 30 g/mol, atom economy is 50/50·100%=100%. If a 10 g/mol by-product C also forms, it is 50/60·100%=83.3%. Check: the value is at most 100%. Check Molar masses in the same mass/mol unit · atom economy in % and substitute the value back into the relation. Also ask whether its sign, balance or magnitude is chemically plausible. If a check fails, inspect units, coefficients and reference values before blaming rounding. Substitution checks the algebra; comparing assumptions with the experiment checks whether the model is appropriate.

Atom Economy is related to Percent Reaction Yield, Stoichiometric Titration Balance, Mole Fraction, E-Factor in Green Chemistry, but answers a distinct question: Compare reaction routes by theoretical incorporation of reactant atoms into the desired product.. Do not confuse it with a relation for a neighboring quantity or a different standard state. Name the target quantity and sample conditions first, then choose the equation containing that quantity. Similar-looking equations may use different stoichiometric bases or validity ranges. The linked entries may supply inputs for another step, but they do not replace this distinction. This keeps the interpretation auditable.