CDS (I) 2022 General Knowledge · Question 10 of 120

Correct — B, 26. The number of moles is the mass in grams divided by the molar mass in grams per mole. Helium is a noble gas and exists as separate single atoms rather than as diatomic molecules, so its molar mass is simply its atomic mass, 4 g per mole. Dividing 104 g by 4 g per mole gives 26 moles. As a check, 26 moles is 26 × 6·022 × 10²³ atoms, about 1·57 × 10²⁵ helium atoms. The one decision the question is testing is whether you write 4 or 8 in the denominator, and the answer turns on remembering that helium, like the other noble gases, does not pair up into molecules.

• (a)52 — What comes out if 2 is used as the molar mass. Two grams per mole belongs to hydrogen gas, H₂, not to helium, and helium is four times heavier per particle.
• (c)13 — The trap this item is built around. Thirteen is 104 divided by 8, which is what you get by treating helium as diatomic, He₂, and doubling its atomic mass. Helium is monatomic and never forms He₂.
• (d)6.5 — 104 divided by 16, the molar mass of atomic oxygen. It has no connection to helium at all, and is four times too small.

One mole is the amount of a substance containing 6·022 × 10²³ particles, Avogadro's number, and the mass of one mole in grams is numerically equal to the atomic or molecular mass in unified atomic mass units. The step that decides most mole calculations is choosing the right particle. For a diatomic gas such as hydrogen, oxygen or nitrogen the molar mass is twice the atomic mass, because the particle is a molecule of two atoms. For a noble gas — helium, neon, argon, krypton, xenon or radon — the outer shell is already full, the atom has no tendency to bond, and the particle is a single atom, so the molar mass equals the atomic mass.

Write down the molar mass before touching the division and this item takes ten seconds. Helium's atomic mass is 4, and because it is monatomic that is also its molar mass, so 104 ÷ 4 = 26. Three of the four options are what appears when the denominator is chosen wrongly, which tells you where the examiner expects the error. It is worth noticing that a full outer shell is a chemical fact with a physical consequence: the same unwillingness to bond is why helium stays a gas down to the lowest temperatures of any element and is used to cool superconducting magnets, including those in an MRI scanner.

• Number of moles = given mass ÷ molar mass.
• Helium is monatomic, so its molar mass is 4 g per mole, the same as its atomic mass.
• 104 g ÷ 4 g per mole = 26 moles, which is about 1·57 × 10²⁵ atoms.
• Avogadro's number is 6·022 × 10²³ particles per mole.
• Hydrogen, nitrogen, oxygen, fluorine, chlorine, bromine and iodine occur as diatomic molecules; the noble gases do not.

• Doubling the atomic mass out of habit and treating helium as diatomic.
• Confusing atomic mass with atomic number, which for helium are 4 and 2.
• Reporting the number of atoms when the question asks for the number of moles.

As a one-step mass-to-moles conversion, with the difficulty hidden in whether the gas named is monatomic or diatomic.

• practice — not a real PYQ

  The number of moles present in 64 g of oxygen gas is

  • (a)1
  • (b)2
  • (c)4
  • (d)32

  Answer(b) 2 — oxygen gas is diatomic, so its molar mass is 32 g per mole, and 64 ÷ 32 = 2.

• practice — not a real PYQ

  Which one of the following gases exists as single atoms rather than as diatomic molecules under ordinary conditions?

  • (a)Nitrogen
  • (b)Chlorine
  • (c)Argon
  • (d)Hydrogen

  Answer(c) Argon — it is a noble gas with a complete outer shell, so it has no tendency to bond with a second atom of its own kind.