= Acidic permanganate-iron balance
An increase in <oxidation state> records <oxidation>; a decrease records <reduction>. Thus $\mathrm{Fe}^{2+}\to\mathrm{Fe}^{3+}$ raises the <iron> <oxidation state> by one, while $\mathrm{MnO}_4^-\to\mathrm{Mn}^{2+}$ lowers the <manganese> <oxidation state> from $+7$ to $+2$. Five <iron> <ions> supply the five-<Electron> inventory required per <permanganate> <ion>.
In an acidic <chemical solution>, the complete <half-reactions> are
$$
\begin{aligned}
\mathrm{Fe}^{2+}&\longrightarrow\mathrm{Fe}^{3+}+e^-,\\
\mathrm{MnO}_4^-+8\mathrm H^++5e^-&\longrightarrow\mathrm{Mn}^{2+}+4\mathrm H_2\mathrm O.
\end{aligned}
$$
First balance <oxygen> with four <water> <molecules>, then <hydrogen> with eight <protons>, and finally <electric charge> with five <Electrons>. Multiply the <iron> <half-reaction> by five and add; the exchanged <Electrons> cancel:
$$
\boxed{\mathrm{MnO}_4^-+8\mathrm H^++5\mathrm{Fe}^{2+}\longrightarrow\mathrm{Mn}^{2+}+4\mathrm H_2\mathrm O+5\mathrm{Fe}^{3+}.}
$$
Both sides contain one <manganese>, four <oxygen>, eight <hydrogen> and five <iron> <chemical atoms>, with net <electric charge> $+17e$. The $\mathrm H^+$ notation represents the acidic aqueous <proton> inventory; it does not imply bare <protons> moving independently of <water>. These <half-reactions> and their sum are the acidic balance used in the documented <permanganate-iron titration>.<Iron Tablet Determination Analytical Competition (Royal Society of Chemistry resource)>[Iron Tablet Determination Analytical Competition, “Setting the Scene”: both half-reactions and the overall equation]{ref}
\Image[/permanganate-iron-electron-balanced-inventory.png]
{title=<Acidic permanganate-iron balance>: five exchanged <Electrons> and conserved <chemical atom> and <electric charge> inventories}
{id=image-permanganate-iron-electron-balanced-inventory}
{description=Original exact <stoichiometry> diagram. Matching five formal <Electron> slots is a bookkeeping operation, not a picture of free <Electrons> in the <chemical solution>. The lower table verifies the net <chemical equation>; its $+17$ is the net <electric charge> number of the written reacting species, not the bulk <chemical solution>.}
The coefficients predict amounts consumed, not a collision of five <ions> or an <elementary reaction>. Bulk <chemical solution> also contains compensating <counterions>, which are omitted from this net <chemical equation>. The <hydrogen> and <oxygen> <oxidation states> are unchanged; balancing their inventories remains essential even though they do not account for the exchanged <Electrons>.
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