DAT General Chemistry: Assigning Oxidation Numbers

DAT High-Yield Concept

Oxidation State Rules Follow a Strict Hierarchy: Free elements are always 0, Group 1 metals are +1, Group 2 metals are +2, fluorine is always -1, hydrogen is usually +1, and oxygen is usually -2.
Sum Principle: The sum of oxidation states across all atoms must equal 0 for neutral compounds or equal the net charge for polyatomic ions.
Peroxide Exception: Oxygen carries a -1 oxidation state in peroxides (e.g., $\ce{H2O2}$ ) because of the homonuclear $\ce{O-O}$ single bond.
Metal Hydride Exception: Hydrogen carries a -1 oxidation state when bonded directly to electropositive metals (e.g., $\ce{NaH}$ , $\ce{CaH2}$ ).

Oxidation Number (Oxidation State): A hypothetical charge assigned to an atom assuming that all bonds to different elements are 100% ionic. Tracking changes in oxidation states enables chemists to identify which species undergo oxidation or reduction in a chemical process (covered in depth in its own lesson).

1. Hierarchical Rules for Assigning Oxidation Numbers

To assign oxidation numbers correctly on the DAT, you must apply rules in strict priority order. Higher-ranking rules take precedence over lower-ranking rules whenever a conflict arises.

Free Elements: Any element in its uncombined elemental state has an oxidation number of 0 (e.g., $\ce{Na}$ , $\ce{O2}$ , $\ce{P4}$ , $\ce{S8}$ ).
Monatomic Ions: The oxidation state equals the charge on the ion (e.g., $\ce{Na^+}$ is +1, $\ce{S^{2-}}$ is -2).
Group 1 & Group 2 Metals: Group 1 metals are always +1; Group 2 metals are always +2 in compounds.
Fluorine: Fluorine is the most electronegative element and is always assigned -1 in all compounds.
Hydrogen: Hydrogen is assigned +1 when bonded to nonmetals and -1 when bonded to metals (metal hydrides).
Oxygen: Oxygen is assigned -2 in most compounds, with exceptions for peroxides (-1), superoxides ( $-1/2$ ), and bonded to fluorine (e.g., +2 in $\ce{OF2}$ ).
Group 17 (Halogens): Halogens are assigned -1, except when combined with oxygen or a more electronegative halogen.

DAT Priority Mnemonic: "Free Ions Metals First, Hydrogen Oxygen Halogens Follow" (Free elements → Monatomic Ions → Group 1/2 Metals → Fluorine → Hydrogen → Oxygen → Halogens). Higher priority rules override lower priority rules!

Assigning oxidation numbers: the rules are ranked, and the ranking makes the exceptions — An oxidation number is a bookkeeping charge: it is what an atom's charge would be if every bond's electrons were handed entirely to the more electronegative partner. Work through the rules in rank order and let the last unknown fall out of the sum, which must equal zero for a neutral formula and the ion's charge for a polyatomic ion. The two famous exceptions are not separate facts. Because group 1 metals are fixed at plus one before hydrogen is considered, hydrogen is forced to minus one in a metal hydride such as NaH. Because hydrogen is fixed at plus one before oxygen is considered, each oxygen is forced to minus one in the peroxide H2O2. Oxidation numbers are not real charges; sulfur in sulfuric acid is not carrying six units of positive charge.

2. Assigning Oxidation States in Neutral Compounds and Polyatomic Ions

For neutral compounds, the algebraic sum of oxidation numbers for all constituent atoms equals zero. For polyatomic ions, the sum equals the ion charge. You set up a simple algebraic equation to solve for an unassigned atom.

Mathematical Sum Rule:

\sum \text{Oxidation States} = \text{Net Charge of Species}

Worked Example 1: Polyatomic Ion Assignment

Problem: Determine the oxidation state of chromium in the dichromate ion, $\ce{Cr2O7^{2-}}$ .

Reasoning:

According to rule priority, oxygen takes precedence over chromium and is assigned -2.
Set up the sum equation where $x$ represents the oxidation state of chromium:

2(x) + 7(-2) = -2

2x - 14 = -2

2x = +12 \implies x = +6

Answer: Each chromium atom has an oxidation state of +6.

Common DAT Exam Trap: Students often set the sum to zero instead of the ion's charge (-2), leading to an incorrect result of +7.

Element	Standard Oxidation State	Exceptional Oxidation State	Trigger Condition
Oxygen ( $\ce{O}$ )	-2	-1	Peroxides ( $\ce{O2^{2-}}$ ) containing $\ce{O-O}$ single bonds
Oxygen ( $\ce{O}$ )	-2	+2	Bonded to fluorine (e.g., $\ce{OF2}$ )
Hydrogen ( $\ce{H}$ )	+1	-1	Metal hydrides (bonded to Group 1 or 2 metals)
Chlorine ( $\ce{Cl}$ )	-1	Positive (+1 to +7)	Bonded to oxygen or fluorine in oxoanions/interhalogens

3. Key DAT Exceptions: Peroxides and Metal Hydrides

The Peroxide Exception

In peroxides, two oxygen atoms are linked via a covalent single bond ( $\ce{-O-O-}$ ). Because homonuclear bonds share valence electrons equally, each oxygen atom receives an oxidation state of -1 rather than the standard -2.

Worked Example 2: Hydrogen Peroxide Assignment

Problem: Assign oxidation states to each element in hydrogen peroxide, $\ce{H2O2}$ .

Reasoning:

Hydrogen bonded to nonmetals ranks higher in priority than oxygen and is assigned +1.
Set the sum equal to 0 for a neutral molecule:

2(+1) + 2(\text{OS}_{\ce{O}}) = 0

+2 + 2(\text{OS}_{\ce{O}}) = 0 \implies 2(\text{OS}_{\ce{O}}) = -2 \implies \text{OS}_{\ce{O}} = -1

Answer: Hydrogen is +1 and oxygen is -1.

Common DAT Exam Trap: Force-assigning oxygen to -2 in peroxides would yield a incorrect hydrogen oxidation state of +2, which violates hydrogen's valence capacity.

The Metal Hydride Exception

Electronegativity determines electron allocation. Hydrogen (electronegativity 2.2) is more electronegative than alkali metals (e.g., $\ce{Na}$ , 0.9) and alkaline earth metals (e.g., $\ce{Ca}$ , 1.0). Therefore, in binary metal hydrides, hydrogen pulls electron density toward itself and adopts an oxidation state of -1.

Worked Example 3: Calcium Hydride Assignment

Problem: Assign oxidation states to all atoms in calcium hydride, $\ce{CaH2}$ .

Reasoning:

Group 2 metals take precedence over hydrogen and are fixed at +2 in compounds.
Solve for hydrogen in the neutral compound:

1(+2) + 2(\text{OS}_{\ce{H}}) = 0

+2 + 2(\text{OS}_{\ce{H}}) = 0 \implies 2(\text{OS}_{\ce{H}}) = -2 \implies \text{OS}_{\ce{H}} = -1

Answer: Calcium is +2 and hydrogen is -1.

Common DAT Exam Trap: Defaulting hydrogen to +1 when bonded to metals, which incorrectly yields a -2 state for an electropositive metal.

Structures of acetic acid , illustrating how to partition the valence electrons for purposes of determining the oxidation state of each atom. (Source: DMacks ( talk ) · Public domain · Wikimedia Commons)

Critical Thinking Questions

Why does oxygen exhibit a positive oxidation state in $\ce{OF2}$ (+2), but a negative oxidation state in $\ce{H2O2}$ (-1)?
In organic molecules such as acetic acid ( $\ce{CH3COOH}$ ), why do individual carbon atoms have different oxidation states despite belonging to the same molecule?
How does the priority rule system automatically handle the peroxide exception without needing to memorize every specific compound structure?

References

Sources returned by Google Search grounding during lesson verification.

Chemistry LibreTexts: Oxidation States (Oxidation Numbers) — chem.libretexts.org
Chad's Prep: How to Assign Oxidation Numbers — chadsprep.com

Assigning Oxidation Numbers

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