Recall the definitions of oxidation and reduction.

• Oxidation is the loss of electrons, resulting in an increase in oxidation state.
• Reduction is the gain of electrons, resulting in a decrease in oxidation state.

• (i) $\text{Fe}^{3+} + 3\text{e}^- \longrightarrow \text{Fe}$

  • $\text{Fe}^{3+}$ gains 3 electrons to become $\text{Fe}$. The oxidation state changes from +3 to 0.
  • This is a gain of electrons, so it is reduction.

• (ii) $\text{Cr} \longrightarrow \text{Cr}^{3+} + 3\text{e}^-$

  • $\text{Cr}$ loses 3 electrons to become $\text{Cr}^{3+}$. The oxidation state changes from 0 to +3.
  • This is a loss of electrons, so it is oxidation.

• (iii) $\text{MnO}_4^{2-} \longrightarrow \text{MnO}_4^- + \text{e}^-$

  • In $\text{MnO}_4^{2-}$, the oxidation state of Mn is +6 ($x + 4(-2) = -2 \implies x = +6$).
  • In $\text{MnO}_4^-$, the oxidation state of Mn is +7 ($y + 4(-2) = -1 \implies y = +7$).
  • $\text{MnO}_4^{2-}$ loses 1 electron to become $\text{MnO}_4^-$. The oxidation state of Mn changes from +6 to +7.
  • This is a loss of electrons, so it is oxidation.

• (iv) $\text{Li}^+ + \text{e}^- \longrightarrow \text{Li}$

  • $\text{Li}^+$ gains 1 electron to become $\text{Li}$. The oxidation state changes from +1 to 0.
  • This is a gain of electrons, so it is reduction.

Here are the classifications:

• (i) $\text{Fe}^{3+} + 3\text{e}^- \longrightarrow \text{Fe}$: Reduction
• (ii) $\text{Cr} \longrightarrow \text{Cr}^{3+} + 3\text{e}^-$: Oxidation
• (iii) $\text{MnO}_4^{2-} \longrightarrow \text{MnO}_4^- + \text{e}^-$: Oxidation
• (iv) $\text{Li}^+ + \text{e}^- \longrightarrow \text{Li}$: Reduction