Saponification with limiting hydroxide

Consider a hypothetical closed, well mixed chemical solution initially containing $20\mathrm{mmol}$ of ethyl acetate, $12\mathrm{mmol}$ of hydroxide, and no acetate ions or ethanol. One millimole is $10^{-3}$ mole. Assume complete conversion as far as the one-to-one chemical equation allows, with no competing chemical reactions. This is an ideal stoichiometry calculation, not a measured yield.

Let the extent of reaction be $\xi$, expressed in millimoles. The four values of amount of substance, in the order ethyl acetate, hydroxide, acetate ion, ethanol, areThe upper bound follows because both reactant quantities must be nonnegative. Thus hydroxide is the limiting reagent, and the ideal endpoint $\xi =12$ leavesThe carboxylate formed equals the hydroxide consumed, while unreacted ester remains. Adding more hydroxide raises the stoichiometry bound; merely waiting longer does not change that bound. To convert these values of amount of substance into concentrations, a volume is also required. The endpoint does not specify the reaction rate or time needed to approach it.