What is the difference between "atom economy" and "percentage yield" ?

% atom economy =

# ("relative formula mass of useful product" )/("relative formula mass of the reactants used"# x 100

Pecentage yield = #("actual mass of product")/("theoretical mass of product")# x 100

So why do we have these two measurements?

A high percentage yield may not be efficient as it looks. It takes no account of the quantity of "waste product" obtained.

For example the "Wittig Synthesis" is a common synthesis used in the manufacture of many pharmaceuticals to convert ketones to alkenes.

A typical yield is 86% which looks good. To keep it simple I'll just give the word equation:

cyclohexanone (#M_r# 98) + phosphonium ylide (#M_r# 276.0) #rarr#

methylene cyclohexane (#M_r# 96) + phosphorine oxide (#M_r # 278)

The useful product is methylene cyclohexane. The waste product is phosphorine oxide.

A high % yield overlooks the quantity of phosphorine oxide waste product. If you look at the #M_r# values of the two products you can see that for every 96 tonnes of useful product there is 278 tonnes of waste generated. Now that doesn't look so good.

Atom economy takes into account how efficiently all the reactant atoms are used in a reaction and take account of the amount of reactant that actually ends up in the desired product.

#M_r# of reactants = 98.0 + 276.0 = 374.0
#M_r# of useful product = 96.0

So % atom economy #(96.0)/(374)# x 100 = 26%

So not so good after all!