MPSC 2022 Prelims Paper-I · Question 54 of 100

Correct — option (4), 10 g of hydrogen gas. The number of molecules in a sample is not decided by how much the sample weighs but by how many moles of substance the weight represents, because one mole of any substance contains the same number of molecules — Avogadro's number, about six point zero two two multiplied by ten to the twenty-third. The number of moles is the mass divided by the molar mass, so a given mass yields the most molecules when it is made of the lightest molecules. Work the four options out with the atomic masses supplied in the square-bracketed line of the question. Iodine crystals consist of diatomic molecules, so the molar mass is twice 127, that is 254 grams; 250 grams therefore comes to 250 divided by 254, a little under one mole. Carbon dioxide has a molar mass of 12 plus twice 16, that is 44 grams; 22 grams is exactly half of that, so half a mole. Water has a molar mass of twice 1 plus 16, that is 18 grams; 45 grams divided by 18 gives two and a half moles. Hydrogen gas is diatomic with a molar mass of 2 grams; 10 grams divided by 2 gives five moles. The four quantities therefore stand at five moles, two and a half moles, about zero point nine eight of a mole and half a mole, and the largest of them by a clear margin is the hydrogen. Five moles of hydrogen contains five times Avogadro's number of molecules, roughly three multiplied by ten to the twenty-fourth, which is more than twice the count in any of the other three samples and ten times the count in the carbon dioxide. Option (4) is the answer. The lesson the question is built to teach is that mass is a misleading guide to molecular count. The heaviest sample offered here, the 250 grams of iodine, contains fewer molecules than the 45 grams of water and far fewer than the 10 grams of hydrogen, because an iodine molecule is 127 times as heavy as a hydrogen molecule; and the lightest sample offered, the 10 grams of hydrogen, contains the most. Since hydrogen is the lightest element there is, an option naming hydrogen in a question of this type deserves to be checked first, and once its value of five moles is in hand the other three can be dismissed as soon as each is seen to fall below it. The atomic masses printed in the bracketed line are supplied precisely because the calculation cannot be done without them, and their presence in the question is itself a signal that arithmetic rather than recall is being asked for.

• (1)250 g of iodine crystals — This is the trap the question is designed around, and it works on the instinct that the biggest number must give the biggest answer. Two hundred and fifty grams is by far the largest mass offered, but iodine is also by far the heaviest substance offered: its atoms have a mass of 127 units each and the molecule is diatomic, giving a molar mass of 254 grams, so the whole 250 grams amounts to slightly less than a single mole. That is under one fifth of the five moles in the hydrogen sample. The comparison is worth doing once in full, because it fixes the idea: a molecule of iodine is 127 times as heavy as a molecule of hydrogen, so to hold the same number of molecules as ten grams of hydrogen an iodine sample would have to weigh about 1,270 grams. Note also that iodine must be treated as a diatomic molecule here, as the halogens are; taking its molar mass as 127 rather than 254 would give about two moles, still short of the hydrogen but enough to disturb the ranking of the middle options.
• (2)22 g of carbon dioxide — This sample contains the fewest molecules of the four, not the most. The molar mass of carbon dioxide is 44 grams, made up of 12 for the carbon and 32 for the two oxygen atoms, so 22 grams is exactly half a mole and contains about three multiplied by ten to the twenty-third molecules — one tenth of the number in the hydrogen sample. The figure of 22 grams is chosen to be tempting, since it sits close to the familiar 22.4 litres that one mole of a gas occupies at standard temperature and pressure, and a candidate who half-remembers that constant may associate the number with a full mole rather than with half of one. The two quantities are unrelated: 22.4 litres is a volume and applies to any gas, whereas 22 grams is a mass and its meaning depends entirely on which gas it is. Confusing a molar volume with a molar mass is one of the commonest errors in mole calculations and is worth guarding against explicitly.
• (3)45 g of water — This is the strongest of the three wrong options and the one a careful candidate has to compute rather than dismiss. Water has a molar mass of 18 grams, so 45 grams is two and a half moles, which is a substantial quantity — more than the iodine and five times the carbon dioxide — and it would be the answer if the hydrogen were not in the set. It is nevertheless only half the five moles that ten grams of hydrogen provides, because a water molecule is nine times as heavy as a hydrogen molecule while the water sample is only four and a half times as heavy as the hydrogen sample. The general point is that in a question of this kind every option has to be reduced to moles before any comparison is made; ranking by mass, or by how familiar the substance is, gives the wrong order. Working all four out takes under a minute with the atomic masses supplied, and the four values here are five, two and a half, about zero point nine eight, and half a mole.

The mole is the chemist's unit for counting particles, and it is defined so that one mole of any substance contains the same number of elementary entities, Avogadro's number, approximately six point zero two two multiplied by ten to the twenty-third. The mass of one mole of a substance in grams is numerically equal to its relative molecular mass, which is obtained by adding up the atomic masses of the atoms in its formula, so one mole of water weighs 18 grams, one mole of carbon dioxide 44 grams and one mole of hydrogen gas 2 grams. Three relations follow and between them they answer nearly every question in this area: the number of moles equals the mass divided by the molar mass; the number of particles equals the number of moles multiplied by Avogadro's number; and, for a gas at standard temperature and pressure, the volume equals the number of moles multiplied by 22.4 litres. The last of these is Avogadro's law in practical form, the statement that equal volumes of gases under the same conditions contain equal numbers of molecules, and it is the reason gas volumes can be compared directly while gas masses cannot. Care is needed with the elements that exist as diatomic molecules — hydrogen, nitrogen, oxygen, fluorine, chlorine, bromine and iodine — because a question asking for molecules requires the molar mass of the molecule and not the atomic mass of the element, and the difference is a factor of two.

This is a calculation question, and MPSC includes a small number of them in every paper to separate candidates who can work quickly and accurately under pressure from those who rely on recall alone. The atomic masses are supplied in a bracketed line, which is a clear signal that the item is meant to be computed rather than recognised, and the whole calculation takes well under a minute once the method is fixed: convert each option to moles, then compare. The trap is psychological as much as chemical, since the largest mass in the list belongs to the heaviest substance and the smallest mass to the lightest, so answering on the appearance of the numbers gives precisely the wrong answer. A useful shortcut for this family is to look first at the option naming the lightest substance, because hydrogen, with a molar mass of two, will almost always yield the most moles for any comparable mass; having found its value, the rest can be checked against it and abandoned as soon as they fall short. The same technique applies to the neighbouring family of questions asking which sample contains the most atoms, where the count must be multiplied further by the number of atoms in each formula unit.

• One mole of any substance contains Avogadro's number of molecules, approximately six point zero two two multiplied by ten to the twenty-third, so the sample with the most moles is the sample with the most molecules.
• The number of moles in a sample is its mass divided by its molar mass, which means that for a given mass the lightest molecules give the largest number of molecules.
• In this question the four samples work out at five moles of hydrogen, two and a half moles of water, about zero point nine eight of a mole of iodine and half a mole of carbon dioxide, so the ten grams of hydrogen contains the most molecules.
• Hydrogen, nitrogen, oxygen and the halogens exist as diatomic molecules, so the molar mass of iodine as a molecule is 254 grams and not 127, and the molar mass of hydrogen gas is 2 grams and not 1.
• One mole of any gas occupies about 22.4 litres at standard temperature and pressure, which is a statement about volume and must not be confused with any figure expressed in grams.

• Ranking the options by mass instead of by moles, which puts the heaviest sample first when it in fact contains among the fewest molecules
• Using the atomic mass in place of the molecular mass for an element that exists as a diatomic molecule, which halves or doubles the answer
• Confusing the molar volume of 22.4 litres with a mass in grams, a confusion the figure of 22 grams in this option set is chosen to provoke
• Answering a question about the number of atoms as though it were about the number of molecules, when the two differ by the number of atoms in the formula unit

Mole calculations reach MPSC papers as direct conversions between mass, moles and number of particles; as comparison questions of the kind asked here, in which four samples must be ranked; as gas volume questions using the molar volume; and as simple stoichiometry, in which the mass of a product is wanted from the mass of a reactant. The Commission supplies atomic masses when they are needed, which makes such items self-contained and therefore reliable marks for a candidate who has the method ready. The method is worth rehearsing until it is automatic, because the arithmetic is easy but the setting up is where errors occur — deciding whether the species is atomic or diatomic, deciding whether molecules or atoms are wanted, and keeping mass and volume apart. Practising a dozen such conversions is enough to make the family secure.

No directly related past PYQ was found.

• practice — not a real PYQ

  Which of the following samples contains the largest number of molecules ? [H = 1, N = 14, O = 16, S = 32]

  • (a)16 g of oxygen gas
  • (b)16 g of sulphur dioxide
  • (c)16 g of ammonia
  • (d)16 g of water

  Answer(c) 16 g of ammonia — when the masses are equal the sample with the smallest molar mass contains the most molecules. Ammonia has a molar mass of 17 grams, water 18, oxygen gas 32 and sulphur dioxide 64, so the four samples come to about 0.94, 0.89, 0.5 and 0.25 moles respectively. The ammonia therefore holds the largest number of molecules, and the comparison shows that molar mass alone decides the ranking once the masses are the same.

• practice — not a real PYQ

  How many molecules are present in 11 g of carbon dioxide ? [C = 12, O = 16, Avogadro's number = 6.022 × 10^23]

  • (a)6.022 × 10^23
  • (b)3.011 × 10^23
  • (c)1.5055 × 10^23
  • (d)12.044 × 10^23

  Answer(c) 1.5055 × 10^23 — the molar mass of carbon dioxide is 44 grams, so 11 grams is one quarter of a mole, and one quarter of Avogadro's number is 1.5055 × 10^23 molecules. The steps are always the same: divide the mass by the molar mass to get the number of moles, then multiply the number of moles by Avogadro's number to get the number of molecules.