Questions: The Mole and Molar Mass

Question 1

A student compares one mole of helium atoms (atomic mass ≈ 4 g/mol) to one mole of iron atoms (atomic mass ≈ 56 g/mol). Which statement is correct?

• A. The mole of iron contains more atoms because iron atoms are heavier
• B. The mole of helium contains more atoms because helium is a lighter element
• C. Both moles contain exactly the same number of atoms (6.022 × 10²³), but the iron sample is much heavier
• D. The number of atoms depends on the sample volume, not the mole quantity

Answer: (C)

The mole is a *count*, not a mass. One mole of anything — helium, iron, water, or elephants — contains exactly 6.022 × 10²³ entities. The masses differ because the atoms themselves have different masses: 1 mol of He weighs 4 g while 1 mol of Fe weighs 56 g. The most common misconception is equating 'heavier element' with 'more atoms per mole,' which confuses molar mass (mass per mole) with amount (number of moles).

Question 2

A chemist has 44.0 g of carbon dioxide (CO₂, molar mass = 44.0 g/mol). How many molecules of CO₂ are present?

• A. 44.0 molecules — one molecule per gram
• B. 6.022 × 10²³ molecules — exactly one mole
• C. 2 × 6.022 × 10²³ molecules — because CO₂ has two oxygen atoms
• D. 3 × 6.022 × 10²³ molecules — because CO₂ has three atoms total

Answer: (B)

44.0 g ÷ 44.0 g/mol = 1.00 mol of CO₂. One mole of molecules = 6.022 × 10²³ molecules. The number of *atoms per molecule* (3 in CO₂) is irrelevant here — the question asks for molecules, not atoms. The conversion is always: grams → moles (÷ molar mass) → particles (× Avogadro's number). This is the core three-step chain.

Question 3

One mole of water (H₂O) and one mole of iron (Fe) contain the same number of particles but have very different masses.

• T. True
• F. False

Answer: True

This is the central conceptual point: a mole is a count like a 'dozen.' One mole of any substance contains 6.022 × 10²³ formula units regardless of what the substance is. The masses differ because the particles themselves have different masses — water molecules weigh about 18 amu each, iron atoms about 56 amu each. So 1 mol of water weighs 18 g and 1 mol of iron weighs 56 g, but both contain exactly Avogadro's number of particles.

Question 4

Avogadro's number (6.022 × 10²³) is an arbitrary large number chosen for convenience, similar to how a 'dozen' = 12 was chosen arbitrarily.

• T. True
• F. False

Answer: False

Unlike 'dozen' (which is arbitrary), Avogadro's number is specifically defined to create an exact correspondence between atomic mass units and grams: one mole of carbon-12 atoms weighs exactly 12 grams. This makes the molar mass of any element numerically equal to its atomic mass in amu, which you read from the periodic table. The non-arbitrariness is what makes the mole useful — it is the bridge constant that converts the atomic scale to the laboratory scale with no additional conversion factor.

Question 5

Why does chemistry need the mole concept at all? What problem does it solve, and why can't chemists just work in grams directly?

Model answer: Chemical reactions occur between individual atoms and molecules in fixed whole-number ratios (e.g., 2 H₂ + O₂ → 2 H₂O). To use these ratios, you need to count particles, not weigh mass — but individual atoms are too small and too numerous to count directly. The mole provides a conversion factor that links countable amounts (moles) to weighable amounts (grams). Without the mole, there would be no way to translate a balanced equation into laboratory measurements.

Working in grams alone fails because the ratio of grams needed depends on atomic mass, not on the reaction stoichiometry. For the reaction 2H₂ + O₂ → 2H₂O, you need 2 moles of H₂ for every 1 mole of O₂ — but that is 4 g of H₂ for every 32 g of O₂, which is a 1:8 mass ratio, not 2:1. Without the mole as an intermediary, every stoichiometry calculation would require knowing and accounting for atomic masses from scratch. The mole bundles that conversion into a single, universal unit.