MPSC 2026 Prelims Paper-I · Question 69 of 100

Correct — option (3), Zero. The very first rule for assigning oxidation numbers says that an atom of an element in the free or uncombined state has an oxidation number of zero. An allotrope is nothing but a free element wearing a different structural arrangement: diamond and graphite are both pure carbon, dioxygen and ozone are both pure oxygen, white and red phosphorus are both pure phosphorus, rhombic and monoclinic sulphur are both pure sulphur. In every one of these the only bonds present are between atoms of the same element. Oxidation number is a bookkeeping device that asks which atom would take the shared electrons if the bond were broken unequally; between two identical atoms there is no reason to give the pair to one rather than the other, so the electrons are split evenly and nothing is gained or lost. Each atom is therefore assigned zero — every carbon in diamond and in graphite, every oxygen in O2 and in O3, every phosphorus in P4, every sulphur in S8. This is also consistent with the rule that the oxidation numbers in a neutral molecule must add up to zero: since all the atoms are identical and must carry the same value, that value can only be zero. The allotropic form makes no difference at all, which is exactly the point the question is testing. Note that the stem as printed reads 'The oxidation states ... is', a number disagreement in the English column; the sense is not in doubt.

• (1)+2 — An oxidation number of +2 belongs to an element that has been combined with something more electronegative than itself — the alkaline earth metals magnesium and calcium in their compounds, iron in the ferrous state, or, unusually, oxygen in oxygen difluoride, where fluorine is the only element electronegative enough to make oxygen positive. All of these require a second element to be present. An allotrope contains only one element, so there is nothing for it to be oxidised by, and no positive value can arise. Any positive option in this question fails for the same structural reason before its particular value is even considered.
• (2)+1 — The value +1 is the standard oxidation number of hydrogen when it is bonded to a non-metal and of the alkali metals in their compounds — sodium in sodium chloride, hydrogen in water and in hydrochloric acid. It always describes an atom that has lost the tug of war for a shared pair to a more electronegative partner. In an allotrope there is no partner: hydrogen in H2 is not +1 but zero, because both atoms are hydrogen. The number describes the atom's situation in a compound, not any fixed property of the element itself, and that is the distinction the question is built on.
• (4)−1 — A value of −1 belongs to an atom that has won the shared pair from a less electronegative partner — chlorine in sodium chloride, hydrogen in a metal hydride such as sodium hydride, or oxygen in a peroxide such as hydrogen peroxide, where the O-O bond is shared evenly and each oxygen carries only −1 rather than the usual −2. Every one of those cases is a compound. In an allotrope the only bonds are between identical atoms, so no atom can be reduced relative to another, and the value stays at zero however elaborate the structure — including the S8 ring and the P4 tetrahedron.

Allotropy is the existence of an element in two or more distinct forms in the same physical state, differing in how the atoms are joined rather than in what they are. Carbon is the richest example: diamond, in which every carbon is bonded tetrahedrally to four others in a rigid three-dimensional network, giving extreme hardness and no electrical conduction; graphite, in which the atoms lie in flat hexagonal sheets held to each other only weakly, giving softness, lubricating properties and electrical conduction; and the fullerenes, the closed cage molecules of which buckminsterfullerene, C60, is the best known. Oxygen exists as ordinary dioxygen, O2, and as ozone, O3. Phosphorus has white, red and black forms of sharply different reactivity. Sulphur has rhombic and monoclinic crystalline forms, both built of S8 rings. Because the difference between allotropes is structural and not compositional, no chemical bookkeeping quantity that depends on which elements are combined can distinguish them.

Oxidation number is the accounting system on which the whole of redox chemistry rests, and it runs on a short set of rules. An atom of a free element is zero. A monatomic ion carries the oxidation number equal to its charge. Oxygen is normally −2, but −1 in peroxides and positive in its compounds with fluorine. Hydrogen is +1 with non-metals and −1 in metal hydrides. Fluorine, being the most electronegative element, is always −1. The sum over a neutral molecule is zero and over an ion equals the ion's charge. With these, oxidation and reduction can be defined without any reference to oxygen at all: oxidation is an increase in oxidation number and reduction a decrease, which is why a reaction between two metals and their ions, with no oxygen anywhere, still counts as a redox reaction. One distinction worth keeping separate is formal charge, a different bookkeeping device used in drawing Lewis structures; the resonance structures of ozone carry formal charges of +1 and −1 on oxygen atoms even though every oxidation number in ozone is zero.

• Rule one of oxidation numbers: every atom of an element in the free or uncombined state has an oxidation number of zero — in H2, O2, O3, Cl2, P4, S8, Na, Mg and Al alike.
• Allotropy is the existence of an element in two or more forms in the same physical state, differing in structure and not in composition. An allotrope is still the pure element, so its oxidation number is zero whatever the form.
• Allotropes of carbon: diamond (three-dimensional tetrahedral network, hardest natural substance, non-conducting), graphite (hexagonal sheets, soft, a lubricant, conducts electricity) and the fullerenes, of which C60 is best known.
• Other standard allotropes: dioxygen and ozone for oxygen; white, red and black phosphorus; rhombic and monoclinic sulphur, both built of S8 rings.
• The remaining oxidation-number rules: a monatomic ion takes the charge on the ion; oxygen is usually −2 but −1 in peroxides; hydrogen is +1 with non-metals and −1 in metal hydrides; fluorine is always −1; the sum is zero for a neutral molecule and equals the charge for an ion.

• Assuming a structurally elaborate allotrope such as S8 or P4 must carry some charge. Complexity of structure is irrelevant; what matters is that only one element is present.
• Confusing oxidation number with formal charge. Ozone's resonance structures show formal charges of +1 and −1 on oxygen, yet every oxidation number in ozone is zero.
• Treating an oxidation number as a fixed property of an element. It describes an atom's situation in a particular species — hydrogen is +1 in water, −1 in sodium hydride and zero in H2.

Two shapes dominate. The rule question, as here, which asks for the oxidation number of an element in a free or allotropic form, or of oxygen in a peroxide, or of hydrogen in a hydride — each of them a single rule applied once. The calculation question gives a compound or an ion, most often a manganese, chromium or sulphur species such as permanganate, dichromate or thiosulphate, and asks for the oxidation number of the central atom, which is solved by setting the known values against the total charge. A third, lighter shape asks about allotropy itself: name the allotropes of carbon, or ask which pair of substances are allotropes rather than isotopes. Learning the seven assignment rules once, and keeping allotropes and isotopes distinct, covers all three.

No directly related past PYQ was found.

• practice — not a real PYQ

  Diamond, graphite and fullerene differ from one another in structure although each consists of carbon atoms only. Such forms of an element are called :

  • (a)Isotopes
  • (b)Isomers
  • (c)Allotropes
  • (d)Isobars

  Answer(c) Allotropes — different structural forms of the same element in the same physical state. Isotopes are atoms of one element differing in the number of neutrons; isobars are atoms of different elements with the same mass number; isomers are compounds sharing a molecular formula but differing in structure.

• practice — not a real PYQ

  The oxidation number of oxygen in hydrogen peroxide (H2O2) is :

  • (a)−2
  • (b)−1
  • (c)0
  • (d)+2

  Answer(b) −1 — the standard exception to the rule that oxygen is −2. In a peroxide the two oxygen atoms are bonded to each other, and that bond is shared evenly between identical atoms, so each oxygen draws only the electrons of its bond with hydrogen and carries −1. In oxygen difluoride, by contrast, oxygen is positive, because fluorine is more electronegative still.