Q.In which of the following compounds, an element exhibits two different oxidation states.
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Oxidation Number Calculation
Oxidation Number Calculation: From Intuition to Precision
Imagine you're watching a tug-of-war between two atoms in a molecule. Each atom has a certain "pull" on the shared electrons — chemists call this electronegativity. The oxidation number is like a scorecard that tells us: If the more electronegative atom took all the shared electrons, what charge would each atom end up with?
This isn't a real charge — it's a bookkeeping tool. Real molecules don't have these exact charges. But this imaginary scorecard helps us track where electrons go during chemical reactions, especially in redox (reduction-oxidation) processes.
The Core Idea
Oxidation number (also called oxidation state) is the hypothetical charge an atom would have if all bonds to atoms of different elements were 100% ionic — meaning the more electronegative atom keeps all the shared electrons.
For an atom bonded to another atom of the same element (like O₂ or N₂), the electrons are shared equally. So the oxidation number is zero — no one "wins" the tug-of-war.
The Rules (Your Toolkit)
These rules are applied in order — rule 1 overrides rule 2, and so on. Memorise them in this sequence:
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Free elements (uncombined, like Fe, O₂, H₂, S₈) have oxidation number = 0.
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Monatomic ions have oxidation number = their charge.
Example: Na⁺ = +1, Cl⁻ = −1, Mg²⁺ = +2.
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Fluorine is always −1 in compounds (it's the most electronegative element — it always "wins").
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Oxygen is usually −2, except:
- In peroxides (like H₂O₂) it's −1
- In OF₂ (with fluorine) it's +2 (fluorine wins)
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Hydrogen is usually +1 when bonded to non-metals, −1 when bonded to metals (like NaH, CaH₂).
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The sum of oxidation numbers in a neutral compound = 0.
In a polyatomic ion, the sum = the ion's charge.
Never apply rule 6 before rules 1–5. The sum rule is your check, not your starting point.
How to Calculate: A Step-by-Step Example
Let's find the oxidation number of sulphur in H₂SO₄ (sulphuric acid).
Step 1: Write the known oxidation numbers.
Hydrogen: +1 (rule 5, bonded to non-metal oxygen)
Oxygen: −2 (rule 4, not a peroxide)
Step 2: Let the unknown be x (for sulphur).
Step 3: Apply the sum rule (rule 6). The compound is neutral, so:
2(+1)+x+4(−2)=0
Step 4: Solve:
2+x−8=0
x−6=0
x=+6
Sulphur in H₂SO₄ has oxidation number +6.
Another Example: A Polyatomic Ion
Find the oxidation number of chromium in Cr₂O₇²⁻ (dichromate ion).
Oxygen: −2 (rule 4)
Let chromium = x
Sum of oxidation numbers = charge of ion (−2):
2x+7(−2)=−2
2x−14=−2
2x=12
x=+6
When you get a fractional oxidation number (like +2.5 in Fe₃O₄), it means the compound has two different oxidation states for the same element. Fe₃O₄ actually contains Fe²⁺ and Fe³⁺ in a 1:2 ratio.
Common Traps to Avoid
| Mistake | Why it's wrong |
|---------|----------------| …
The key idea is Oxidation Number Calculation — we assign oxidation numbers to each atom using standard rules (O is usually -2, H is +1, and the sum equals the charge of the species).
Step 1: For NH₂OH (hydroxylamine), N is bonded to two H atoms and one OH group. Let N’s oxidation state be x:
x+2(+1)+(−2)+(+1)=0⇒x+2−2+1=0⇒x=−1. Only one oxidation state for N.
Step 2: For NH₄NO₃ (ammonium nitrate), it contains two distinct ions: NH₄⁺ and NO₃⁻.
In NH₄⁺: x+4(+1)=+1⇒x=−3.
In NO₃⁻: y+3(−2)=−1⇒y=+5.
Here, nitrogen appears in two different oxidation states: -3 and +5.
Step 3: For N₂H₄ (hydrazine), each N: 2x+4(+1)=0⇒x=−2 (both N same). …
The key is to compute the oxidation number of each element in the given compounds. Only in NH₄NO₃ does nitrogen appear in two different oxidation states: –3 in the ammonium ion and +5 in the nitrate ion. The correct option is (ii).
Oxidation numbers are a bookkeeping tool that helps us track electron distribution in compounds. They are assigned based on a set of rules: the oxidation number of an atom in its elemental form is zero; for a monatomic ion, it equals the charge; oxygen is usually –2 (except in peroxides), hydrogen is usually +1 (except in metal hydrides), and the sum of oxidation numbers in a neutral compound is zero, while in a polyatomic ion it equals the ion's charge.
The trick in this question is that a single element can have different oxidation states in the same compound if the compound contains that element in two different structural environments. That happens when the compound is an ionic salt made of two different polyatomic ions, each containing the same element. Let's check each option.
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NH₂OH (hydroxylamine)
This is a neutral molecule. Let the oxidation number of N be x.
H is +1 (three H atoms: two bonded to N, one to O).
O is –2.
Sum: x+3(+1)+(−2)=0⇒x+3−2=0⇒x=−1.
So nitrogen has a single oxidation state: –1. No two different states here.
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NH₄NO₃ (ammonium nitrate)
This is an ionic compound: NH₄⁺ and NO₃⁻.
In NH₄⁺: let N be x. H is +1 each, four H atoms.
x+4(+1)=+1⇒x+4=+1⇒x=−3.
In NO₃⁻: let N be y. O is –2 each, three O atoms.
y+3(−2)=−1⇒y−6=−1⇒y=+5.
Nitrogen appears as –3 in the ammonium ion and +5 in the nitrate ion — two different oxidation states in the same compound. This is the answer.
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N₂H₄ (hydrazine)
Neutral molecule. Let N be x. H is +1 each, four H atoms.
2x+4(+1)=0⇒2x+4=0⇒x=−2.
Both nitrogens have the same oxidation state: –2.
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N₃H (hydrogen azide, HN₃)
HN₃ is a single neutral covalent molecule (H–N=N⁺=N⁻, a resonance hybrid), not a salt built from two separate ions. Treating the three nitrogens as equivalent gives an average oxidation number: …
Showing the 12 most recent of 15 on this concept.
- AP EAPCET 2026Set eng-2026-05-12-AN1 markMCQQ.Hydrolysis of chlorine nitrate gives oxoacid of chlorine X and oxoacid of nitrogen Y. The oxidation states of Cl in X, N in Y are respectively (A) +1, +3 (B) -1, +3 (C) +1, +5 (D) +3, +5
›Reveal solutionSolution
Hydrolysis of ClONO2 cleaves the Cl–O–N linkage at the O–N bond, giving HOCl (Cl = +1) and HNO3 (N = +5).
Concept and Intuition
Chlorine nitrate has the connectivity Cl−O−NO2. Hydrolysis (reaction with water) breaks the weaker O−N bond, inserting an −OH onto each fragment: the Cl−O− portion picks up an H to become Cl−OH (hypochlorous acid), and the −NO2 portion picks up an −OH to become HO−NO2 (nitric acid).
ClONO2+H2O→HOCl+HNO3
Step-by-Step Solution
- Write the hydrolysis: ClONO2+H2O→HOCl(X)+HNO3(Y).
- Oxidation state of Cl in HOCl: let it be x. (+1)+(−2)+x=0⇒x=+1.
- Oxidation state of N in HNO3: let it be y. (+1)+y+3(−2)=0⇒y=+5. …
- AP EAPCET 2025Set eng-2025-05-21-AN1 markMCQQ.The oxides of nitrogen obtained by the reaction of nitric acid with(i) P4O10,(ii) P4 respectively are (A) NO, N2O (B) N2O3, NO (C) N2O5, NO2 (D) NO2, N2O
›Reveal solutionSolution
P₄O₁₀ dehydrates HNO₃ to its anhydride N₂O₅, while concentrated HNO₃ oxidising P₄ is itself reduced to NO₂. Answer: (C).
Concept and Intuition
This question tests two distinct roles nitric acid can play: (i) as a substrate being dehydrated by a strong desiccant (P₄O₁₀), which simply removes water to leave nitric acid's anhydride, versus (ii) as a concentrated oxidising agent reacting with a reducing element (P₄), where HNO₃ itself gets reduced, typically to NO₂ when concentrated.
Step-by-Step Solution
- Reaction (i): HNO3 with P4O10. P4O10 is one of the strongest dehydrating agents known. It removes water from nitric acid molecules: 4HNO3+P4O10→2N2O5+4HPO3. This is purely a dehydration (not redox) — nitric acid's acid anhydride, N2O5, is formed.
- Reaction (ii): HNO3 with P4. Here HNO₃ acts as an oxidising agent on elemental phosphorus. Concentrated nitric acid oxidises P4 to phosphoric acid (H3PO4), while HNO₃ itself is reduced. Since it is the concentrated acid reacting with a reducing agent, the reduction product is NO2 (concentrated HNO₃ is reduced to NO₂, whereas dilute HNO₃ typically gives NO). …
- AP EAPCET 2025Set eng-2025-05-23-FN1 markMCQQ.The composition of a sample of wustite is Fe0.93O1.00. Percentage of iron in the form of Fe3+ ion is nearly (A) 85 (B) 15 (C) 93 (D) 7
›Reveal solutionSolution
This is a non-stoichiometric defect (metal-deficiency) calculation for wustite Fe0.93O1.00; charge balance gives about 15% of the iron as Fe3+.
Concept and Intuition
Wustite is a classic example of a metal-deficient non-stoichiometric compound: some Fe2+ sites are vacant, and to keep the crystal electrically neutral, an equivalent number of the remaining Fe ions are oxidised to Fe3+ (each Fe2+ vacancy is compensated by 2 Fe3+ ions). We solve this by simple charge balance.
Step-by-Step Solution
- Let the moles of Fe3+ be x and Fe2+ be y, per formula unit. Total iron: x+y=0.93.
- Total negative charge from oxide ions: O2− present = 1.00, contributing charge =2×1.00=2.
- For electrical neutrality, total positive charge from iron must equal 2: 3x+2y=2. …
- AP EAPCET 2025Set eng-2025-05-23-FN1 markMCQQ.The amphoteric oxide of Vanadium (V) reacts with alkali and forms an oxoion 'X' and with acid forms an oxoion Y. The oxidation states of 'V' in X and Y are respectively (A) +2,+5 (B) +3,+3 (C) +5,+5 (D) +5,+2
›Reveal solutionSolution
This tests the amphoteric behaviour of V2O5: it dissolves in both alkali and acid without any change in the oxidation state of vanadium, which stays +5 in both product ions.
Concept and Intuition
V2O5 sits at the acidic-to-amphoteric borderline among the transition-metal oxides because vanadium is in its highest (+5) oxidation state. An oxide being amphoteric means it can react as a base (with acid) or as an acid (with alkali) — but in both cases here, vanadium's oxidation number doesn't change, because these are acid–base (ligand/oxo-exchange) reactions, not redox reactions.
Step-by-Step Solution
- With alkali (e.g. NaOH), V2O5 behaves as an acidic oxide and dissolves to form the orthovanadate ion:
V2O5+6OH−→2VO43−+3H2O
Oxidation state of V in VO43−: x+4(−2)=−3⇒x=+5.
2. With acid (e.g. dilute H2SO4 or HCl), V2O5 behaves as a basic oxide and dissolves to form the dioxovanadium(V) cation:
V2O5+2H+→2VO2++H2O
Oxidation state of V in VO2+: x+2(−2)=+1⇒x=+5. …
- AP EAPCET 2024Set ap-2024-05-16-AN1 markMCQQ.The number of mixed oxides from the following is Al2O3, Pb3O4, Mn2O7, Fe3O4, V2O5, Sb2O3 (A) 2 (B) 3 (C) 4 (D) 1
›Reveal solutionSolution
Tests recognising mixed oxides among a list of common oxides; only Pb3O4 and
Fe3O4 qualify, giving a count of 2.
Concept and Intuition
A mixed oxide is one that can be regarded as a combination (in a fixed ratio) of two simple
oxides of the same element in different oxidation states. The two classic textbook examples are
red lead, Pb3O4=2PbO⋅PbO2 (lead in +2 and +4 states), and
magnetite, Fe3O4=FeO⋅Fe2O3 (iron in +2 and +3 states).
Step-by-Step Solution
- Al2O3: aluminium is only in the +3 state here — a simple, amphoteric oxide. Not mixed.
- Pb3O4: lead present as both Pb(II) and Pb(IV); a genuine mixed oxide.
- Mn2O7: manganese only in the +7 state — a simple, strongly acidic covalent oxide. Not mixed.
- Fe3O4: iron present as both Fe(II) and Fe(III); a genuine mixed oxide.
- V2O5: vanadium only in the +5 state — a simple acidic oxide. Not mixed. …
- AP EAPCET 2024Set eng-2024-05-23-FN1 markMCQQ.Acidification of chromate gives 'Z'. The oxidation state of chromium in 'Z' is (A) +3 (B) +6 (C) +7 (D) +2
›Reveal solutionSolution
This tests the chromate–dichromate equilibrium; acidifying chromate gives dichromate (Z), and chromium's oxidation state remains +6 throughout (it's a structural/pH-driven change, not a redox change).
Concept and Intuition
Chromate (CrO42−) and dichromate (Cr2O72−) are interconvertible depending on the pH of the solution: chromate (yellow) is the stable form in basic/neutral solution, while dichromate (orange) is the stable form in acidic solution. This is a classic condensation equilibrium (two tetrahedral CrO42− units joining via a shared oxygen to form Cr2O72−) — not an oxidation-reduction reaction, so the oxidation state of Cr doesn't change.
Step-by-Step Solution
- Write the pH-dependent equilibrium: 2CrO42−+2H+⇌Cr2O72−+H2O.
- "Acidification of chromate gives Z" means Z = dichromate ion, Cr2O72−.
- Calculate the oxidation state of Cr in CrO42−: let Cr = x. Then x+4(−2)=−2⇒x=+6.
- Calculate the oxidation state of Cr in Cr2O72−: let Cr = x. Then 2x+7(−2)=−2⇒2x−14=−2⇒x=+6. …
- AP EAPCET 2023Set ap-2023-05-23-FN1 markMCQQ.One mole of aqueous S2O32− is completely reacted with 2 moles of Br2(l). What is the oxidation state (s) of S in the product formed? (A) 0, +5 (B) +6 (C) -2, +4 (D) +4
›Reveal solutionSolution
S2O32−+2Br2+H2O→2SO2+4Br−+2H+; sulphur is oxidised to +4.
Concept and Intuition
In thiosulphate S2O32− the two sulphur atoms have an average oxidation state of +2. Each mole of Br2 is reduced, Br2+2e−→2Br−, accepting 2 electrons. The amount of oxidant therefore fixes how many electrons leave the sulphur and hence its final oxidation state.
Step-by-Step Solution
- Electrons removed =2 mol Br2×2=4 per mole of S2O32−.
- The two S atoms start at a total oxidation number of 2×(+2)=+4.
- Removing 4 electrons raises the total to +8, i.e. an average of +4 per sulphur.
- Balancing confirms one product: S2O32−+2Br2+H2O→2SO2+4Br−+2H+ (charge −2=−2, O =4=4).
- In SO2 sulphur is +4.
Common Mistakes …
- AP EAPCET 2023Set eng-2023-05-16-FN1 markMCQQ.X+Y→ oleum The sum of oxidation states of central atom in X and Y is (A) 12 (B) 10 (C) 06 (D) 08
›Reveal solutionSolution
Oleum is made by dissolving SO₃ in H₂SO₄; sulfur is in the +6 oxidation state in both, so the sum is 12.
Concept and Intuition
Oleum (fuming sulfuric acid, H2S2O7, also called pyrosulfuric acid) is industrially made by absorbing sulfur trioxide gas into concentrated sulfuric acid: SO3+H2SO4→H2S2O7. Both starting materials have sulfur as the central atom.
Step-by-Step Solution
- Identify X and Y from the reaction that forms oleum: X=SO3, Y=H2SO4.
- Oxidation state of S in SO3: let x be S's oxidation state; x+3(−2)=0⇒x=+6. …
- AP EAPCET 2023Set eng-2023-05-17-AN1 markMCQQ.The formula of nickel oxide is Ni0.98O1.00. What is the approximate percentage of Ni+2 in it? (A) 92 (B) 94 (C) 96 (D) 98
›Reveal solutionSolution
This tests using charge balance in a non-stoichiometric metal oxide to find the fraction of metal in each oxidation state. Answer: ≈96% Ni2+.
Concept and Intuition
In Ni0.98O1.00, nickel is metal-deficient relative to oxygen, so some nickel must be present as Ni3+ to balance the extra negative charge from oxide ions (charge neutrality of the overall compound).
Step-by-Step Solution
- Let moles of Ni2+=a and moles of Ni3+=b. Total Ni: a+b=0.98.
- Total negative charge from O: 1.00×2=2.00. This must equal total positive charge from Ni: 2a+3b=2.00.
- Substitute a=0.98−b: 2(0.98−b)+3b=2.00⇒1.96+b=2.00⇒b=0.04.
- So a=0.98−0.04=0.94. …
- AP EAPCET 2022Set ap-2022-07-12-AN1 markMCQQ.The common oxidation states of elements of 15th group elements are (A) -3, +3, +5 (B) -3, +2, +5 (C) -1, +3, +5 (D) -2, +3, +5
›Reveal solutionSolution
Group 15 (pnictogens) elements commonly show oxidation states −3, +3 and +5.
Concept and Intuition
With 5 valence electrons (ns2np3), these elements can gain 3 electrons to reach the stable octet (−3), or lose/share the 3 unpaired p-electrons (+3), or lose/share all 5 valence electrons (+5, using both s and p electrons — favoured more for lighter members due to the inert pair effect being weaker there).
Step-by-Step Solution
- Write the valence configuration: ns2np3.
- Gaining 3 electrons completes the octet → oxidation state −3 (e.g., NH3, PH3). …
- AP EAPCET 2022Set ap-2022-07-12-FN1 markMCQQ.Match the following List-I (Reactions) / List-II (Equivalent weights) A KMnO4H+Mn2+ i) M/8 B C2O42−→CO2 ii) M/6 C K2Cr2O7→Cr3+ iii) M/5 D NH3→NO3− iv) M/2 (A) A – (iv); B- (iii); C – (ii); D-(i) (B) A – (iii); B- (iv); C – (i); D-(ii) (C) A – (iii); B- (iv); C – (ii); D-(i) (D) A – (ii); B- (iv); C – (iii); D- (i)
›Reveal solutionSolution
Equivalent weight = molar mass / n-factor, where n-factor is the number of electrons transferred per formula unit in each redox change; working these out gives A–iii, B–iv, C–ii, D–i.
Concept and Intuition
For a redox reagent, the equivalent weight is M/n where n is the number of electrons gained or lost per formula unit as it converts from the given species to the given product. This is found from the oxidation-state change of the atom(s) being oxidised/reduced.
Step-by-Step Solution
- A. KMnO4H+Mn2+: Mn goes from +7 to +2, a change of 5 electrons. n = 5 → equivalent weight = M/5 = (iii).
- B. C2O42−→CO2: each carbon goes from +3 to +4 (loses 1 electron), and there are 2 carbons, so 2 electrons total. n = 2 → equivalent weight = M/2 = (iv).
- C. K2Cr2O7→Cr3+: each Cr goes from +6 to +3 (gains 3 electrons), and there are 2 Cr atoms, so 6 electrons total. n = 6 → equivalent weight = M/6 = (ii). …
- AP EAPCET 2022Set ap-2022-07-12-FN1 markMCQQ.Identify the element that can exhibit negative oxidation states. (A) C (B) Ge (C) Sn (D) Pb
›Reveal solutionSolution
Only carbon, among C, Ge, Sn, Pb, readily shows negative oxidation states, since the group becomes progressively more metallic (and hence more inclined to positive states) going down.
Concept and Intuition
Group 14 elements range from the clearly non-metallic carbon at the top to the metallic lead at the bottom. Non-metallic character favours forming compounds where the element gains electrons (negative oxidation state), while metallic character favours losing electrons (positive oxidation state). This trend, combined with the inert-pair effect strengthening the +2 state for the heavier members, means Ge, Sn, and Pb are essentially never seen in negative oxidation states, while carbon commonly is (e.g. −4 in methane, CH4, or in ionic carbides like CaC2/Al4C3).
Step-by-Step Solution
- Carbon (C): highly electronegative for its group, non-metallic, forms −4 states (e.g. CH4) and other negative states in hydrides/carbides.
- Germanium (Ge): a metalloid, predominantly shows +2/+4, essentially no negative oxidation states in ordinary chemistry.
- Tin (Sn): metallic, shows +2/+4 only. …
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