3.3 Oxidation States & Valence Electron Trends

Oxidation States & Valence Electron Trends

Quick Summary: An oxidation state is a formal charge bookkeeping tool that assigns shared bonding electrons entirely to the more electronegative atom. Main-group elements exhibit characteristic oxidation states governed by valence electron configurations, while transition metals display variable oxidation numbers by utilizing both $(n-1)d$ and $ns$ electrons. Moving across a period, metallic character decreases, shifting elemental oxides from basic to amphoteric and acidic.

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1. Principles of Oxidation States

Chemical bonding involves the redistribution of electron density between atoms. To monitor these electron shifts in reactions, chemists assign oxidation states (or oxidation numbers):

The oxidation state is the hypothetical charge an atom would bear if all bonds to different elements were 100% ionic, transferring shared electron pairs completely to the more electronegative partner.

Oxidation states differ fundamentally from related concepts:

• Actual Charges: While ions in binary salts (like $\text{Na}^+$ and $\text{Cl}^-$ in $\text{NaCl}$) carry real integral charges matching their oxidation numbers ($+1$ and $-1$), atoms in covalent molecules (such as $\text{H}_2\text{O}$) carry only fractional partial charges ($\delta^+, \delta^-$). Here, assigning $\text{H} = +1$ and $\text{O} = -2$ is a bookkeeping convention.
• Formal Charge: Formal charge divides shared electrons equally between bonded atoms, whereas oxidation states assign shared pairs to the more electronegative atom.
• Homonuclear Bonds: In bonds between identical atoms (e.g., $\text{O}-\text{O}$ in $\text{H}_2\text{O}_2$), shared electrons are divided equally, contributing zero charge shift.

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2. Main-Group Valence Trends and Group Oxidation States

For representative main-group elements, valence configurations define the boundary oxidation states:

• Maximum Positive State: Loss or sharing of all valence electrons, equaling the element's group valence (Group number $- 10$ for Groups 13–18).
• Minimum Negative State: Gain of electrons needed to reach a noble gas octet ($\text{Group Valence} - 8$).

The Inert-Pair Effect

In heavy post-transition elements (Period 6 elements $\text{Tl}, \text{Pb}, \text{Bi}$), the $6s^2$ electrons experience strong relativistic contraction and penetrate close to the nucleus. These electrons resist chemical participation, stabilizing the oxidation state 2 units lower than the group maximum: thallium favors $\text{Tl}^+$ over $\text{Tl}^{3+}$, and lead favors $\text{Pb}^{2+}$ over $\text{Pb}^{4+}$.

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3. Transition Metal Oxidation States and $d$-Orbital Chemistry

Transition metals exhibit variable oxidation states due to the close energy proximity of $(n-1)d$ and $ns$ subshells.

Ionization Sequence

When transition metals ionize, they lose their outermost $ns$ electrons before any $(n-1)d$ electrons:

$\text{Fe}: [\text{Ar}] 3d^6 4s^2 \xrightarrow{-2e^-} \text{Fe}^{2+}: [\text{Ar}] 3d^6 \xrightarrow{-1e^-} \text{Fe}^{3+}: [\text{Ar}] 3d^5$

Trends Across the $3d$ Series

• Early/Middle Elements (Sc to Mn): Can involve all $4s$ and unpaired $3d$ electrons in bonding. Maximum oxidation states increase progressively: Sc reaches $+3$ (all three electrons of $3d^1 4s^2$), Ti $+4$ ($3d^2 4s^2$), V $+5$ ($3d^3 4s^2$), Cr $+6$ ($3d^5 4s^1$), and Mn $+7$ ($3d^5 4s^2$, as in $\text{MnO}_4^-$). These are formal oxidation states in covalent oxo species such as $\text{CrO}_4^{2-}$ and $\text{MnO}_4^-$, not free $\text{Cr}^{6+}$ or $\text{Mn}^{7+}$ ions.
• Late Elements (Fe to Zn): Beyond manganese, $3d$ electrons begin pairing up and $Z_{\text{eff}}$ increases sharply. Higher oxidation states become energetically unfavorable: Iron forms $+2$ and $+3$; Copper forms $+1$ and $+2$; Zinc forms exclusively $+2$ ($3d^{10}$ remains intact).

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4. Priority Rules for Assigning Oxidation Numbers

Assign oxidation numbers using this hierarchical sequence (earlier rules override later rules):

1. Free Elements: Uncombined atoms have an oxidation number of $0$ ($\text{Na}, \text{O}_2, \text{P}_4, \text{S}_8, \text{Fe} = 0$).
2. Monatomic Ions: Oxidation number equals ionic charge ($\text{K}^+ = +1, \text{Al}^{3+} = +3, \text{Cl}^- = -1, \text{S}^{2-} = -2$).
3. Fluorine: Always $-1$ in all chemical compounds.
4. Group 1 & 2 Metals: Group 1 metals are always $+1$; Group 2 metals are always $+2$; Aluminum is always $+3$.
5. Hydrogen: Assigned $+1$ with nonmetals ($\text{H}_2\text{O}, \text{HCl}$); assigned $-1$ in metal hydrides ($\text{NaH}, \text{CaH}_2$).
6. Oxygen: Assigned $-2$ in most compounds. Exceptions: peroxides ($\text{H}_2\text{O}_2$, $-1$), superoxides ($\text{KO}_2$, $-1/2$), and oxygen difluoride ($\text{OF}_2$, $+2$).
7. Halogens: Assigned $-1$, unless bonded to oxygen or a more electronegative halogen.
8. Sum Rule: Sum of oxidation numbers equals $0$ for neutral molecules, or equals the net charge for polyatomic ions.

Step-by-Step Examples

• Dichromate ion ($\text{Cr}_2\text{O}_7^{2-}$): $2(\text{Cr}) + 7(-2) = -2 \implies 2(\text{Cr}) - 14 = -2 \implies \text{Cr} = +6$.
• Permanganate ion ($\text{MnO}_4^-$): $1(\text{Mn}) + 4(-2) = -1 \implies \text{Mn} - 8 = -1 \implies \text{Mn} = +7$.
• Chlorine trifluoride ($\text{ClF}_3$): Fluorine is $-1$, so $1(\text{Cl}) + 3(-1) = 0 \implies \text{Cl} = +3$.

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5. Metallic Character and Oxide Acid-Base Chemistry

Metallic character (the tendency to lose valence electrons) increases down a group and decreases across a period. This trend dictates the chemical behavior of elemental oxides:

Amphoteric Behavior of Aluminum Oxide

Aluminum oxide ($\text{Al}_2\text{O}_3$) illustrates dual reactivity:

• As a Base: $\text{Al}_2\text{O}_3(s) + 6\text{HCl}(aq) \longrightarrow 2\text{AlCl}_3(aq) + 3\text{H}_2\text{O}(l)$
• As an Acid: $\text{Al}_2\text{O}_3(s) + 2\text{NaOH}(aq) + 3\text{H}_2\text{O}(l) \longrightarrow 2\text{Na}[\text{Al(OH)}_4](aq)$