Role of H₃PO₄ in Fe(II) Titration

In the titration of iron(II) ions, $\text{Fe}^{2+}$, with potassium dichromate, $\text{K}_2\text{Cr}_2\text{O}_7$, in an acidic medium, phosphoric acid, $\text{H}_3\text{PO}_4$, is typically added. This is a redox titration where $\text{Fe}^{2+}$ is oxidized to $\text{Fe}^{3+}$, and $\text{Cr}_2\text{O}_7^{2-}$ is reduced to $\text{Cr}^{3+}$.

The main reaction is:

\( \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{Fe}^{2+} \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O} + 6\text{Fe}^{3+} \)

When diphenylamine sulphonate is used as an indicator, its oxidation potential needs to be suitable for the titration. The indicator works by changing color when it is oxidized at the equivalence point. For a clear color change, the potential jump around the equivalence point should span the oxidation potential of the indicator.

Potential Reduction by H₃PO₄

The crucial role of $\text{H}_3\text{PO}_4$ is related to the $\text{Fe}^{3+}/\text{Fe}^{2+}$ redox couple. The standard electrode potential for this couple is:

\( \text{Fe}^{3+} + e^{-} \rightleftharpoons \text{Fe}^{2+} \quad E^{\circ} = +0.77 \text{ V} \)

Phosphoric acid forms stable complexes with $\text{Fe}^{3+}$ ions, such as $[\text{Fe(PO}_4\text{)}]$. This complex formation effectively reduces the concentration of free $\text{Fe}^{3+}$ ions in the solution. According to the Nernst equation, the potential of a redox couple depends on the concentration of the oxidized and reduced species. By significantly lowering the concentration of $\text{Fe}^{3+}$, the equilibrium of the $\text{Fe}^{3+}/\text{Fe}^{2+}$ couple is shifted, and its electrode potential is significantly reduced.

Why Potential Reduction is Important

The standard potential for the dichromate reduction is:

\( \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6e^{-} \rightleftharpoons 2\text{Cr}^{3+} + 7\text{H}_2\text{O} \quad E^{\circ} = +1.33 \text{ V} \)

The potential of the diphenylamine sulphonate indicator in acidic solution is around +0.85 V to +0.9 V. If the $\text{Fe}^{3+}/\text{Fe}^{2+}$ potential remains high (+0.77 V), the potential change at the equivalence point might not be sharp enough, or the potential range might not perfectly match the indicator's transition potential. By lowering the $\text{Fe}^{3+}/\text{Fe}^{2+}$ potential (e.g., down to approximately +0.4 V in the presence of $\text{H}_3\text{PO}_4$), $\text{H}_3\text{PO}_4$ increases the potential difference between the two reacting couples ($\text{Cr}_2\text{O}_7^{2-}/\text{Cr}^{3+}$ and the modified $\text{Fe}^{3+}/\text{Fe}^{2+}$). This results in a larger and sharper potential jump at the equivalence point, which allows the diphenylamine sulphonate indicator to give a distinct color change precisely at the equivalence point.

Therefore, the primary role of $\text{H}_3\text{PO}_4$ is to reduce the electrode potential of the $\text{Fe}^{3+}/\text{Fe}^{2+}$ couple by complexing $\text{Fe}^{3+}$ ions, ensuring a sharp endpoint with the chosen indicator.

Let's briefly consider the other options:

• Avoid aerial oxidation of Fe(II): While acidic conditions help, sulfuric acid is usually present and provides the necessary acidity. $\text{H}_3\text{PO}_4$'s main function is not preventing aerial oxidation.
• Stabilize the indicator: Although the reaction conditions can affect indicator stability, the primary reason for adding $\text{H}_3\text{PO}_4$ is its effect on the $\text{Fe}^{3+}/\text{Fe}^{2+}$ potential, which enables the indicator to function correctly.
• Stabilize K₂Cr₂O₇: Potassium dichromate is quite stable in acidic solutions; $\text{H}_3\text{PO}_4$ is not added for its stabilization.

Thus, the most significant role of $\text{H}_3\text{PO}_4$ is the reduction of the $\text{Fe}^{3+}/\text{Fe}^{2+}$ electrode potential.