Equation 1b 
(Click to enlarge Table 3)
Most chemists have measured the effectiveness a reaction by the percent yield, but this is only a part of history. Considering the above reaction in which they have used a total of 4.13 g of reagent (0.8 g of 1-butanol, 1.33 g of NaBr and 2.0 g of H2SO4), under the best conditions will only get 1.48 g of the desired product, the question we should ask is "What about the rest (4.13 g -1.48 g = 2.7 g) of the mass of the reactants?. The answer is that they end by-products (NaHSO4 and H2O) that can be waste, unused, non-toxic or recycled / reused. At most 36% (1.48 g g/4.13 X 100) of the mass of the reactive end in the desired product. And if percentage yield is 81% only 29% (.81 X .36 X 100) of the mass of the reactants actually end in the desired product!
In an effort to promote awareness of the atoms in the reactants that are incorporated into the desired product and those who are wasted (or entering into unwanted products), Barry Trost has developed the concept of atom economy. In 1998 Trost received the award for Presidential Green Chemistry Challenge Award for this item.
To illustrate, reconsider the nucleophilic substitution reaction in acid, green highlighting in Equation 1b all atoms that are incorporated into the desired product, while those shown in brown are wasted. Likewise, the desired product atoms are green and the atoms that make up the waste products of brown. Table 3 provides another view of the atom economy for this reaction. In columns 1 and 2 of this table shows the formulas and formula weights of reagents (PF). Green (columns 3 and 4) are the atoms and weights of the atoms in the reactants that are incorporated into the desired product (4), brown (columns 5 and 6) are the atoms and weights of the atoms reagents that end up in unwanted side products. Looking at the last column of this table we can see that all the atoms of the reactants (4C, 12H, 5O, 1Br, 1NA and 1S) only 4C, 9H, and 1Br used in the desired product while the rest ( 3H, 5O, 1NO, 1S) are wasted as part of waste products. This is an example of poor atom economy! . A logical application of the concept of atom economy Trost,
(Click to enlarge Table 3) is to calculate the percentage of the economy the atom. This is obtained by taking the ratio of the mass of the atoms used (137) and tota mass of the atoms of all reactants (275) by multiplying by 100. As shown below, this reaction only 50% of atom economy.
% Atom Economy = (FW of atoms utilized / FW of all reactants) X 100
= (137/275) X 100 = 50%
De Thus, in the best (if the reaction yield was 100%), only half the mass of the reactants are incorporated the desired product, while the rest would lead to unwanted side product.
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