Why equilibrium reactions can never have a 100% yield?

we are used to seeing

mA + nB ---> xC + yD

where m moles of A added to n moles of B react to become x moles of C and y moles of D

we commonly make the assumption that the reaction will 'run to completion' (100% yield)

for many reactions this is a fair assumption but not exactly true

however these many reactions run 'nearly' to completion (well over 99% yield)

the actual result is better expressed as

mA + nB <---> xC + yD

where the two way arrow indicates a reversible reaction

the balance between reactants and products depends upon the energy change for each direction

nature tends toward the lower energy state

another take on this is to say that as the amounts of C and D build up, the likelihood of them colliding in such a way as to reform A and B increases

this is summarized in the equilibrium expression

. . . . . [C]^x * [D]^y

Keq =----------------------

. . . . . [A]^m * [B]^n

and if Keq is very large the result will be almost all product

but a smaller Keq results in a significant amount of reactants still being present at equilibrium

some reactions have a super small Keq and you have almost all reactants left

your aspirin reaction has a fairly small (or not too big) Keq

so it comes to equilibrium at a point less than 100% yield

by the way Keq is empirically derived although some theoretical calculations may come close

Keq is dependent on conditions, also

one of the tricks a chemist might use is to manipulate conditions to maximize desired results

another trick is to continuously remove a product while continuing to add reactants

then it gets real messy when a set of reactants can produce more than one set of products

ouch!

happens a lot in organic chemistry