= Permanganate-iron endpoint and blank model
The apparatus and motivating measurement are described in <permanganate-iron titration>; the following is an original account of its possible errors. Assume correct <titrant standardization>, the <acidic permanganate-iron balance>, quantitative conversion of the sampled $\mathrm{Fe}^{2+}$, and additive contributions expressed as equivalent <titrant> <volumes>. Write
$$
V=V_{\mathrm{Fe}}+B_s+D_s+A+I,\qquad
V_b=B_b+D_b,\qquad
V_{\mathrm{Fe}}=\frac{n_{\mathrm{Fe}}}{5c}.
$$
Here $V$ is the sample <titre>, $V_b$ the <titration blank>, $B_s,B_b$ background reagent consumption, and $D_s,D_b$ signed offsets of the observed <titration endpoints> from the respective <stoichiometry> conditions after background consumption. The subscripts distinguish sample and blank. $I$ is additional sample-specific <permanganate> demand, absent from the blank; $A$ is apparent delivery used to fill an initially air-containing <burette> tip rather than enter the flask. Assume the blank's tip is already filled; the sample should also have $A=0$ after proper preparation. These terms are a diagnostic model, not measured components of the stipulated $0.10\,\mathrm{mL}$ blank.
\Image[/redox-titration-endpoint-burette-and-blank.png]
{title=<Burette> delivery, <titration endpoint> and <titration blank> describe different parts of the inference}
{description=Original schematic and additive <volume (thermodynamics)> model, not a photograph or measured <titration curve>. The numerical decomposition $12.60=12.50+0.10\,\mathrm{mL}$ assumes matched background and endpoint contributions and no tip-air or sample-specific demand. Boxes are not to scale; the blank's reagent consumption and endpoint offset are not separately specified. The exact <equivalence point> has no guaranteed visible colour flag.}
Subtracting the two accounts proves the error relation
$$
\widehat n_{\mathrm{Fe}}=5c(V-V_b)=n_{\mathrm{Fe}}+5c\Delta V,\qquad
\Delta V=(B_s-B_b)+(D_s-D_b)+A+I.
$$
The simple inference is valid when this residual is negligible. Matching <water> and <sulfuric acid> tests the background terms, but does not by itself establish $D_s=D_b$: flask composition and viewing conditions can differ. A coloured sample can mask residual <permanganate>, changing the assigned <titration endpoint> without a corresponding <redox> consumption. A sample-specific <reducing agent> instead contributes positive $I$ by consuming <permanganate>. A reagent <titration blank> cannot measure either effect just by omitting the sample.
A transient purple streak before mixing is not the mixed-flask <titration endpoint>. Conversely, the <equivalence point> is the five-to-one inventory match, without a promised visible flag. In the ideal selective model, a persistent excess colour requires some <permanganate> beyond that match. No particular drop size, waiting time or endpoint offset is stipulated here; the same stated colour criterion must be applied to sample and blank, and its transferability checked.
The model also predicts error direction. If a tip bubble disappears during sample delivery, $A>0$ makes the inferred <amount of substance> too high because final minus initial <burette> reading includes liquid that stayed in the tip. Conditioning the tip before the first reading prevents this particular discrepancy; subtracting a separate <titration blank> is not an instrument repair. Repeated <aliquots> test scatter, a known added $\mathrm{Fe}^{2+}$ inventory tests the five-to-one response, and an independent <titrant standardization> tests $c$. These are the proposed controls from <permanganate-iron titration>, with distinct diagnostic roles; none alone proves absence of all sample interference.
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