= Standardization endpoint and blank bias
Hold the known <primary standard inventory> fixed, and let $V$ be the correct blank-subtracted <titre>. In the following model, any remaining endpoint offset has been removed from this reference. If a <titration endpoint> overshoot adds $\delta V>0$, the inferred <titrant> <concentration> is too small:
$$
c=\frac{n_s}{V},\qquad \widehat c=\frac{n_s}{V+\delta V},\qquad
\frac{\widehat c-c}{c}=-\frac{\delta V}{V+\delta V}.
$$
The denominator grows while the numerator stays fixed. For $\delta V\ll V$, the relative effect is approximately $-\delta V/V$, but the displayed fraction is exact for this additive model. An unremoved positive <titration blank> $b$ has the same mathematical effect: replace $\delta V$ by $b$. If both remain, replace it by $\delta V+b$. This analogy concerns their effects on the denominator; it does not mean a blank measures endpoint overshoot.
For the chosen $24.80\,\mathrm{mL}$ reference <titre>, an extra $0.05\,\mathrm{mL}$ gives $\widehat c=0.1006036217\ldots\,\mathrm{mol\,L^{-1}}$ and relative error $-0.05/24.85=-0.201207\ldots\%$. Leaving both a $0.05\,\mathrm{mL}$ blank and a $0.05\,\mathrm{mL}$ overshoot gives denominator $24.90\,\mathrm{mL}$ and relative error $-0.10/24.90=-0.401606\ldots\%$.
\Image[/standardization-endpoint-and-blank-bias.png]
{title=Endpoint overshoot and an unremoved positive <titration blank> both lower the inferred <titrant> <concentration>}
{description=Original additive-error model, not measured data. The curves compare reference <titres> of $24.80\,\mathrm{mL}$ and $5.00\,\mathrm{mL}$. The table uses the selected $0.002500\,\mathrm{mol}$ inventory and $24.80\,\mathrm{mL}$ reference. Equal extra denominator <volumes> give equal bias, whether caused by overshoot or an unremoved blank.}
For comparison, the same extra $0.05\,\mathrm{mL}$ on a $5.00\,\mathrm{mL}$ reference <titre> gives $-0.05/5.05=-0.990099\ldots\%$. The ratio of these error magnitudes is $24.85/5.05=4.920792\ldots$, while the small-error approximation would give $24.80/5.00=4.96$. A larger <titre> reduces the fractional effect of a fixed extra <volume (thermodynamics)>; it does not fix unknown purity, incomplete transfer, or an incorrect <stoichiometry>.
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