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: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 $\hat{c}=0.1006036217\dots \mathrm{mol}{\mathrm{L}}^{-1}$ and relative error $-0.05/24.85=-0.201207\dots \%$. Leaving both a $0.05\mathrm{mL}$ blank and a $0.05\mathrm{mL}$ overshoot gives denominator $24.90\mathrm{mL}$ and relative error $-0.10/24.90=-0.401606\dots \%$.

For comparison, the same extra $0.05\mathrm{mL}$ on a $5.00\mathrm{mL}$ reference titre gives $-0.05/5.05=-0.990099\dots \%$. The ratio of these error magnitudes is $24.85/5.05=4.920792\dots$, 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; it does not fix unknown purity, incomplete transfer, or an incorrect stoichiometry.