MPSC 2022 Prelims Paper-I · Question 50 of 100

Correct — option (2), tetrahedrally. A carbon atom has four electrons in its outermost shell, and in diamond every one of them is used to form a covalent bond with a neighbouring carbon atom. Four bonds means four neighbours, and the four repel one another, so they arrange themselves as far apart as they can get — pointing towards the four corners of a regular tetrahedron with the central atom at its centre, the angle between any two bonds being about 109 and a half degrees. In the language of bonding this is the sp3 hybridised state of carbon, in which the one s orbital and the three p orbitals of the valence shell are mixed to give four identical orbitals directed towards the corners of a tetrahedron. What makes diamond diamond is that this arrangement is repeated without interruption. Each of the four neighbours is itself surrounded tetrahedrally by four more, and those by four more again, so the whole crystal is a single continuous three-dimensional network of covalent bonds rather than a collection of molecules held together by weaker forces. There is no such thing as a molecule of diamond; the crystal is the molecule. Every property of diamond follows from that structure and is worth deriving rather than memorising. Because breaking the crystal means breaking strong covalent bonds in every direction, diamond is the hardest naturally occurring substance and is used for cutting, drilling and grinding, and as an abrasive. Because those bonds must be broken to melt it, its melting point is extremely high. Because all four valence electrons are locked into bonds, there are no free electrons to carry current, so diamond does not conduct electricity, although it conducts heat exceptionally well through the vibration of its rigid lattice. Its high refractive index and strong dispersion are what give a cut stone its brilliance. The contrast with graphite, the other familiar allotrope of carbon, makes the point sharply: in graphite each carbon atom bonds to only three others in flat hexagonal sheets, the fourth electron is left free to move, and the sheets are held to one another by weak forces, which is why graphite is soft enough to write with, slippery enough to lubricate, and able to conduct electricity — everything that diamond is not, from the same element, because the atoms are arranged differently. Option (2) is the answer.

• (1)linearly — A linear arrangement means an atom with two neighbours placed on opposite sides of it, at an angle of 180 degrees, and it belongs to carbon in a quite different bonding state. Carbon is linear where it is sp hybridised and forms two sigma bonds, as in acetylene, where each carbon is bonded to one hydrogen and to the other carbon through a triple bond, or in carbon dioxide, where the carbon sits between two oxygen atoms. Neither situation arises in diamond, where every carbon atom uses all four of its valence electrons on four separate single bonds and therefore has four neighbours, not two. The option is worth a moment only as a reminder that the geometry around an atom is decided by the number of things attached to it: two gives linear, three gives trigonal planar, four gives tetrahedral, and six gives octahedral.
• (3)tetragonally — This is the most dangerous of the three wrong options, because it begins with the same syllable as the right answer and a candidate reading quickly under time pressure may take it for the word wanted. The two words belong to different vocabularies. Tetrahedral describes the shape made by four neighbours around a central atom, with bond angles of about 109 and a half degrees. Tetragonal is a term from crystallography, naming one of the seven crystal systems, in which the unit cell has two edges of equal length and a third of different length with all the angles right angles; diamond does not belong to that system at all but crystallises in the cubic system. Where the word tetragonal is used of the arrangement around an atom, in the form tetragonal planar, it means four neighbours lying in one plane at the corners of a square, which is the geometry of a complex such as the tetrachloroplatinate ion, and it is not the geometry of carbon in diamond, whose four neighbours are emphatically not coplanar. Reading the option to its end, rather than recognising its first four letters, is what separates the two.
• (4)octahedrally — An octahedral arrangement means six neighbours placed at the corners of a regular octahedron, one above, one below and four around the middle, with bond angles of 90 degrees. Carbon cannot adopt it, and the reason is simply arithmetic: carbon has four valence electrons and belongs to the second period of the periodic table, where the valence shell can hold no more than eight electrons, so it can form four covalent bonds and no more. Six-coordination is common enough elsewhere — sulphur hexafluoride is a molecular example, and in the sodium chloride crystal every sodium ion has six chloride ions as nearest neighbours and every chloride ion six sodium ions — but those involve either an element that can expand its valence shell or an ionic lattice rather than a covalent one. A useful cross-check is that six bonds from each carbon would also make diamond's formula and its measured density impossible.

Allotropy is the existence of an element in more than one physical form in the same physical state, the forms differing in the way the atoms are joined rather than in what the atoms are, and carbon is its standard illustration. In diamond each carbon atom is sp3 hybridised and forms four single covalent bonds directed towards the corners of a tetrahedron, so the crystal is a giant covalent network extending in three dimensions; it is very hard, has a very high melting point, does not conduct electricity, and is prized as a gemstone for its refraction of light. In graphite each carbon atom is sp2 hybridised and forms three covalent bonds in a plane, producing flat sheets of linked hexagons; the fourth electron of each atom is delocalised over the sheet, which makes graphite a conductor, and the sheets are held together only by weak forces, which lets them slide over one another and makes graphite soft, greasy to the touch and useful both as a pencil lead and as a dry lubricant. The fullerenes are a third family, of which the best known is the sixty-atom molecule made of twenty hexagons and twelve pentagons arranged like a football, and graphene is a single isolated sheet of the graphite structure. The general principle that these forms illustrate is the one examiners are really testing: in a solid, the properties follow from the structure and the bonding, so hardness, melting point and electrical conductivity can all be predicted once the arrangement of the atoms is known.

This is a one-line recall question with a substantial idea behind it, and MPSC uses such items to test whether a candidate can connect a structure to the properties that follow from it. The Commission's favourite version of the theme is the comparison between diamond and graphite, asked either directly — why is graphite a conductor and diamond an insulator, why is graphite soft when both are pure carbon — or through a statement list in which properties of the two are mixed. A candidate who has learnt only the phrase associated with diamond will answer this question but not those. The option set here also demonstrates a technique that the paper uses repeatedly: two of the four options begin with the same letters, so that a candidate who recognises a word by its opening rather than reading it whole is led into the wrong one. The counter-measure is mechanical and costs almost nothing — read every option to its last syllable before marking, particularly in a paper where more than two thirds of the options are under twenty characters long and are therefore read very fast.

• In diamond each carbon atom forms four single covalent bonds to four neighbouring carbon atoms directed towards the corners of a regular tetrahedron, with bond angles of about 109 and a half degrees, the carbon being sp3 hybridised.
• The tetrahedral arrangement repeats throughout the crystal, so diamond is a giant covalent network in three dimensions rather than a substance made of separate molecules.
• Diamond is the hardest naturally occurring substance and has a very high melting point because breaking or melting it requires covalent bonds to be broken in every direction.
• Diamond does not conduct electricity because all four valence electrons of every carbon atom are locked into covalent bonds, leaving none free to move, although it conducts heat very well.
• In graphite each carbon atom bonds to only three others in flat hexagonal sheets, the fourth electron is delocalised and carries current, and the weakly held sheets slide over one another, which makes graphite soft, conducting and useful as a lubricant.

• Mistaking tetragonal for tetrahedral because the two words begin alike, which is the specific confusion this option set is built to produce
• Assuming that a carbon atom could have six neighbours, when a second-period element cannot form more than four covalent bonds
• Learning the properties of diamond as a list to be memorised rather than deriving them from the three-dimensional covalent network, which leaves the comparison with graphite unanswerable
• Forgetting that diamond conducts heat well even though it does not conduct electricity, since the two forms of conduction depend on different mechanisms

Carbon and its allotropes are among the most frequently set topics in the chemistry portion of MPSC papers, because a single well-understood structure supports many different questions. The Commission asks the coordination of the carbon atom, as here; it asks why one allotrope conducts and the other does not; it asks which is the hardest substance, which is used as a lubricant, which form the fullerenes take; and it sets statement lists mixing the properties of diamond and graphite so that they have to be separated. Structure-and-property reasoning of this kind extends beyond carbon to the comparison of ionic, covalent, molecular and metallic solids, which the Commission tests in the same way. Preparing the diamond and graphite pair as a two-column comparison — bonding, coordination, structure, hardness, conductivity, uses — covers nearly everything that can be asked from this corner of the syllabus.

No directly related past PYQ was found.

• practice — not a real PYQ

  Graphite conducts electricity while diamond does not. The reason is that

  • (a)graphite contains metallic impurities that carry the current
  • (b)each carbon atom in graphite uses only three of its four valence electrons in bonding, leaving one free to move
  • (c)graphite is softer than diamond and therefore allows electrons to pass
  • (d)graphite has ionic bonds while diamond has covalent bonds

  Answer(b) Each carbon atom in graphite uses only three of its four valence electrons in bonding, leaving one free to move — the three bonded electrons form a flat sheet of hexagons, and the fourth is delocalised over the sheet and can carry an electric current along it. In diamond all four valence electrons of every carbon atom are committed to covalent bonds in a rigid three-dimensional network, so no electron is free and the crystal is an insulator. Both substances are pure carbon and neither has ionic bonds, so the difference lies entirely in the arrangement.

• practice — not a real PYQ

  The bond angle between any two carbon-carbon bonds in the diamond structure is approximately

  • (a)90 degrees
  • (b)109 degrees 28 minutes
  • (c)120 degrees
  • (d)180 degrees

  Answer(b) 109 degrees 28 minutes — this is the angle at the centre of a regular tetrahedron between lines drawn to any two of its corners, and it is the arrangement that four identical bonds adopt when they repel one another as far apart as possible in three dimensions. An angle of 120 degrees belongs to the trigonal planar arrangement of three bonds, as in a sheet of graphite, and 180 degrees to the linear arrangement of two, as in carbon dioxide.