Questions: The Mole: Avogadro's Number and Counting Atoms

Question 1

A chemist needs exactly 3.011 × 10²³ molecules of glucose (C₆H₁₂O₆, molar mass = 180 g/mol). How many grams should she weigh out?

• A. 180 g — one full mole of glucose
• B. 90 g — one-half mole of glucose
• C. 540 g — three moles of glucose
• D. 60 g — one-third mole of glucose

Answer: (B)

3.011 × 10²³ molecules is exactly half of Avogadro's number (6.022 × 10²³), so the chemist needs 0.5 mol. Mass = moles × molar mass = 0.5 mol × 180 g/mol = 90 g. The key step is converting the particle count to moles using Avogadro's number before converting to grams using molar mass. Students who answer 180 g are forgetting to halve the mole count — they confuse 'one Avogadro's number of particles' with '3.011 × 10²³ particles.'

Question 2

Why is Avogadro's number 6.022 × 10²³ specifically, rather than some convenient round number like 1 × 10²³?

• A. It equals the number of atoms in exactly 1 cm³ of an ideal gas at standard conditions
• B. It is defined so that one mole of carbon-12 atoms has a mass of exactly 12 grams, linking particle count to measurable mass
• C. It is the number of atoms per gram for hydrogen, the lightest element
• D. It was set by international convention as a convenient large number, with no deeper physical significance

Answer: (B)

The definition of the mole is built around carbon-12: one mole is the number of atoms in exactly 12 grams of carbon-12. That count turns out to be 6.022 × 10²³. The magic is that this makes the molar mass of any element (in g/mol) numerically equal to its atomic mass (in amu) — 12.01 amu per carbon atom becomes 12.01 g/mol for a mole of carbon. The number is not arbitrary; it is the specific value that creates this correspondence between the atomic and macroscopic scales.

Question 3

One mole of iron contains the same number of atoms as one mole of uranium, even though iron atoms are much lighter than uranium atoms.

• T. True
• F. False

Answer: True

The mole is a counting unit — it specifies a number of particles (6.022 × 10²³), not a mass. One mole of any substance, regardless of what it is, contains Avogadro's number of particles. One mole of iron contains 6.022 × 10²³ iron atoms; one mole of uranium also contains 6.022 × 10²³ uranium atoms. They differ in mass (55.85 g vs. 238.03 g) but are identical in particle count. This is precisely what makes the mole useful — it lets chemists count particles by weighing.

Question 4

The mole concept applies mainly to atoms and molecules; it can seldom meaningfully be used for ions or electrons.

• T. True
• F. False

Answer: False

The mole is a general-purpose counting unit applicable to any specified particle: atoms, molecules, ions, electrons, photons, or anything else. Chemists routinely speak of moles of electrons in electrochemistry (Faraday's constant is 96,485 C/mol of electrons), moles of ions in solution chemistry, and moles of photons in spectroscopy. The particle must be specified (one mole of what?), but the concept is not restricted to neutral atoms and molecules.

Question 5

Explain why the mole is described as a 'bridge' between the macroscopic and microscopic worlds. What problem does it solve that could not be solved by measuring in grams alone?

Model answer: Grams measure mass, but chemical reactions happen between particles — atoms and molecules react in fixed whole-number ratios. If a reaction requires two hydrogen atoms for every oxygen atom, you need to know particle counts, not masses. The mole bridges this gap: because molar mass in g/mol equals atomic mass in amu, you can weigh out a substance, divide by its molar mass, and instantly know how many particles (in units of Avogadro's number) you have. Grams alone tell you nothing about particle ratios; moles convert macroscopic measurements into particle counts and back again.

The deeper insight is that Avogadro's number was chosen precisely to make this bridge exact. By defining the mole so that 12 g of C-12 = 1 mole, chemists ensured that the periodic table's atomic masses (measured in amu relative to C-12) translate directly into grams-per-mole. A student who thinks the mole is 'just a big number' is missing this design: it is a carefully chosen big number that makes the atomic and macroscopic scales commensurable.