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.^[ref]

Record initial and final burette readings; their difference is the delivered volume $V$. 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 isWith $c$ in $\mathrm{mol}{\mathrm{L}}^{-1}$, use $V$ and $V_b$ in litres. As an original stipulated calculation, not an experimental result, take $c=0.02000\mathrm{mol}{\mathrm{L}}^{-1}$, $V=12.60\mathrm{mL}$ 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 $0.05000\mathrm{mol}{\mathrm{L}}^{-1}$.

In this example the corrected volume 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 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 $0.05040\mathrm{mol}{\mathrm{L}}^{-1}$, 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.

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. WriteHere $V$ 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.

Subtracting the two accounts proves the error relationThe 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.