= Permanganate-iron titration
A proposed modern teaching measurement puts a <pipette>-measured portion of an <iron> $\mathrm{Fe}^{2+}$ <chemical solution> in a <conical flask>, acidifies with excess dilute <sulfuric acid>, and adds standardized <potassium permanganate> from a clamped <burette> while swirling. The documented endpoint principle is that added purple <permanganate> is consumed until the first small excess leaves a pale purple colour; no separate colour indicator is required. Insufficient acidity can produce brown <manganese dioxide>, invalidating the assumed five-<electron> <half-reaction>.<Iron Tablet Determination Analytical Competition (Royal Society of Chemistry resource)>[“Setting the Scene”, final two paragraphs: burette, conical flask, decolourisation, endpoint and excess sulfuric acid]{ref}
Record initial and final <burette> readings; their difference is the delivered <volume (thermodynamics)> $V$. The following controls are proposed additions to test the inference. Run a reagent blank with the same <water>, <sulfuric acid> and endpoint criterion but no sample, obtaining $V_b$. Use a separately established <potassium permanganate> <concentration> $c$, clear the <burette> tip of air, and repeat sample portions. A known added <amount of substance> of $\mathrm{Fe}^{2+}$ should increase consumption by one fifth of that amount. A blank estimates reagent demand and the small endpoint excess; it cannot remove an interfering sample <reactant>.
Assuming complete, selective reaction according to the <acidic permanganate-iron balance>, the corrected inference is
$$
n(\mathrm{Fe}^{2+})=5c(V-V_b).
$$
With $c$ in $\mathrm{mol\,L^{-1}}$, use $V$ and $V_b$ in litres. As an original stipulated calculation, not an experimental result, take $c=0.02000\,\mathrm{mol\,L^{-1}}$, $V=12.60\,\mathrm{mL}$ and $V_b=0.10\,\mathrm{mL}$. Then the <permanganate> consumption is $0.2500\,\mathrm{mmol}$ and the inferred $\mathrm{Fe}^{2+}$ amount is $1.250\,\mathrm{mmol}$. In a $25.00\,\mathrm{mL}$ sample portion this corresponds to $0.05000\,\mathrm{mol\,L^{-1}}$.
\Image[/redox-titration-electron-and-amount-ledger.png]
{title=<Permanganate-iron titration>: corrected delivery becomes an <electron> and <amount of substance> ledger}
{description=Original calculation using the stipulated $0.02000\,\mathrm{mol\,L^{-1}}$ <titrant>, $12.60\,\mathrm{mL}$ <titre>, $0.10\,\mathrm{mL}$ <titration blank> and $25.00\,\mathrm{mL}$ <aliquot>. The two <half-reactions> exchange $1.250\,\mathrm{mmol}$ of formal <electrons>; this is not a free-<electron> inventory in the <chemical solution>. Values are constructed, not experimental data.}
In this example the corrected <volume (thermodynamics)> is $12.50\,\mathrm{mL}=0.01250\,\mathrm L$. The <acidic permanganate-iron balance> gives $z_A=1$ for $\mathrm{Fe}^{2+}$ and $z_T=5$ for <permanganate>. Thus $0.2500\,\mathrm{mmol}$ of <permanganate> accepts $1.250\,\mathrm{mmol}$ of formal <electrons>, exactly what $1.250\,\mathrm{mmol}$ of $\mathrm{Fe}^{2+}$ supplies. The <amount of substance> ratio is five to one, despite equality of the exchanged <electron> amounts.
The denominator is the original $25.00\,\mathrm{mL}$ <aliquot>, not its final <volume (thermodynamics)> after adding <sulfuric acid>, <water> and <titrant>. Such <dilution> changes <concentrations> in the flask without changing the initial sampled <amount of substance> of $\mathrm{Fe}^{2+}$. Omitting the $0.10\,\mathrm{mL}$ <titration blank> would instead give $1.260\,\mathrm{mmol}$ and $0.05040\,\mathrm{mol\,L^{-1}}$, an overestimate of $0.80\%$ relative to the corrected constructed value. The displayed digits express the stipulated calculation, rather than establish its <measurement uncertainty>.
The endpoint detects residual <permanganate>, not the <iron> identity directly. Other sample <reactants> that consume <permanganate> raise the apparent $\mathrm{Fe}^{2+}$ amount; prior <oxidation> of sample $\mathrm{Fe}^{2+}$ to $\mathrm{Fe}^{3+}$ lowers it. A recovery check probes response to the added <iron> but does not prove absence of every interference. The readout determines the reacting $\mathrm{Fe}^{2+}$ inventory under the stated conditions, rather than total <iron> in an arbitrary mixture. No measured titres are asserted here.
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