= 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>, are
$$
\bigl(20-\xi,\;12-\xi,\;\xi,\;\xi\bigr)\,\mathrm{mmol},\qquad 0\leq\xi\leq12.
$$
The upper bound follows because both <reactant> quantities must be nonnegative. Thus <hydroxide> is the <limiting reagent>, and the ideal endpoint $\xi=12$ leaves
$$
8\,\mathrm{mmol}\ \text{ethyl acetate},\quad
0\,\mathrm{mmol}\ \text{hydroxide},\quad
12\,\mathrm{mmol}\ \text{acetate},\quad
12\,\mathrm{mmol}\ \text{ethanol}.
$$
The <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.
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