Explain how Avogadro's constant links the macroscopic quantity 'one mole' to the particulate scale, and justify why its numerical value cannot be derived theoretically but must be determined experimentally.

IB DP Chemistry Higher Level (2023 syllabus) — S1.4 Counting particles by mass: The mole · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (4 marks)

Avogadro's constant, Nₐ, is the number of elementary entities in exactly one mole of a substance.

It serves as a conversion factor that links the microscopic scale (individual atoms or molecules, measured in atomic mass units) to the macroscopic laboratory scale (grams). By fixing Nₐ at 6.022 140 76 × 10²³ mol⁻¹, one mole of a substance has a mass that is directly proportional to the number of particles it contains.

The numerical value of Nₐ is not derived from theory; it is defined by convention. The 2019 SI redefinition fixes Nₐ to the stated value so that one mole of carbon‑12 has a mass of exactly 12 g. This choice is arbitrary and serves as a convenient macroscopic standard.

Because the value is tied to a defined, but conventionally chosen, macroscopic standard, it must be determined experimentally. Methods such as X‑ray crystallography, electrolysis using the Faraday constant, or Millikan‑type oil‑drop experiments are used to measure Nₐ rather than calculating it from first principles.

Examiner tips

  • Define Nₐ and state its fixed value. Explain its role as a bridge between atomic mass units and grams. Mention the 2019 SI redefinition and the arbitrary choice of 12 g C‑12. State that experimental methods are required to determine the value.
  • common_mistakes
  • :
  • Confusing Nₐ with the Avogadro number per mole of a specific element. Claiming the value can be derived from quantum theory. Omitting the 2019 SI redefinition or the 12 g C‑12 convention.

Mark scheme (4 marks)

  1. Avogadro's constant (Nₐ) is defined as the number of elementary entities (atoms, molecules, ions, etc.) in exactly one mole of a substance
  2. It acts as a conversion factor / bridge between the atomic/molecular scale (individual particles, measured in atomic mass units) and the macroscopic laboratory scale (grams), allowing chemists to count particles by weighing
  3. The mole is defined by fixing Nₐ at exactly 6.022 140 76 × 10²³ mol⁻¹ (2019 SI redefinition), but the numerical value itself reflects the historical choice to relate one mole to 12 g of carbon-12, which is an arbitrary/conventional macroscopic standard
  4. Because the value is tied to a defined (but conventionally chosen) macroscopic standard, it must be measured experimentally using physical methods (e.g. X-ray crystallography, electrolysis using the Faraday constant, or Millikan-type oil-drop experiments) rather than derived from theory alone

Key terms in this question

Avogadro's constant · mole · particulate scale

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