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Q.Which is a stronger reducing agent Cr2+Cr^{2+} or Fe2+Fe^{2+} and why?

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The key idea is that the stability of the +3 oxidation state relative to the +2 state determines reducing strength. Cr2+Cr^{2+} is a stronger reducing agent than Fe2+Fe^{2+} because oxidation takes it from d4d^4 to d3d^3 — and in an aqueous medium the d3d^3 configuration (a half-filled t2gt_{2g} level) is especially stable — whereas the oxidation of Fe2+Fe^{2+} is a d6→d5d^6 \rightarrow d^5 change with a smaller stability gain.

Why this approach works

The question asks you to compare the reducing power of two transition metal ions. A reducing agent is a species that donates electrons and gets oxidized itself. So, the stronger the tendency of M2+M^{2+} to lose an electron and become M3+M^{3+}, the stronger the reducing agent.

This tendency depends on the stability of the +3 oxidation state relative to the +2 state. In transition metals, stability is heavily influenced by electronic configuration — particularly the achievement of half-filled (d5d^5) or fully-filled (d10d^{10}) subshells, which are extra stable due to exchange energy and symmetry.

Let’s examine each ion.


  1. Electronic configurations of the ions

    • Chromium (CrCr, atomic number 24): Cr2+Cr^{2+}: [Ar] 3d4[Ar]\,3d^4 Cr3+Cr^{3+}: [Ar] 3d3[Ar]\,3d^3
    • Iron (FeFe, atomic number 26): Fe2+Fe^{2+}: [Ar] 3d6[Ar]\,3d^6 Fe3+Fe^{3+}: [Ar] 3d5[Ar]\,3d^5

    Notice that oxidation is a d4→d3d^4 \rightarrow d^3 change for chromium but a d6→d5d^6 \rightarrow d^5 change for iron. In an aqueous (octahedral) medium, d3d^3 means a half-filled t2gt_{2g} level (t2g3t_{2g}^3) — an especially stable arrangement (see CFSE).

  2. Which ion wants to lose an electron more?

    • For Cr2+Cr^{2+} to become Cr3+Cr^{3+}, it loses one electron. The d4d^4 configuration of Cr2+Cr^{2+} (high-spin t2g3eg1t_{2g}^3e_g^1) is not particularly stable. The resulting Cr3+Cr^{3+} (d3d^3) has a half-filled t2gt_{2g} set (t2g3t_{2g}^3), which in an aqueous medium is an especially stable arrangement — so the d4→d3d^4 \rightarrow d^3 oxidation is strongly favoured. In fact, Cr2+Cr^{2+} is so eager to oxidize that it can even reduce water to hydrogen gas in acidic conditions.

    • For Fe2+Fe^{2+} to become Fe3+Fe^{3+}, it also loses one electron. But Fe2+Fe^{2+} (d6d^6) is reasonably stable — it has a paired electron in one t2gt_{2g} orbital, but the configuration is not as unstable as d4d^4. More importantly, Fe3+Fe^{3+} (d5d^5) is extremely stable due to the half-filled subshell. So while Fe2+Fe^{2+} can be oxidized, the d6→d5d^6 \rightarrow d^5 stability gain in water is smaller than chromium's d4→d3d^4 \rightarrow d^3 gain — NCERT's own answer notes that in a medium like water, d3d^3 is more stable than d5d^5 (see CFSE).

    The critical point: Cr2+Cr^{2+} is much more unstable than Fe2+Fe^{2+}, and its oxidation to Cr3+Cr^{3+} is highly favourable. This makes Cr2+Cr^{2+} a stronger reducing agent.

  3. Standard reduction potentials confirm this

    The standard reduction potentials for the M3+/M2+M^{3+}/M^{2+} couples are:

    • Cr3++e−→Cr2+Cr^{3+} + e^- \rightarrow Cr^{2+}: E∘=−0.41 VE^\circ = -0.41\ \text{V} …

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