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AS & A-Level Physics 15 — Ideal Gases and Molecular Motion

AS & A-Level Physics 15 — Ideal Gases and Molecular Motion

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Independent Deckloop revision aligned with the Cambridge International AS & A Level Physics (9702) syllabus, 2025–2027. Not affiliated with or endorsed by Cambridge International Education. Chapter 15 of 26: Ideal gases and molecular motion. Concepts, worked applications and misconception checks.

Physics EN A-Level
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Avogadro Constant and Molar Calculations

One mole of any substance contains a specific, fixed number of elementary entities (atoms, molecules, ions, or electrons), known as the Avogadro constant, NAN_A. Its value is approximately 6.02×1023 mol−16.02 \times 10^{23} \text{ mol}^{-1}. This constant provides the conversion factor between the amount of substance (in moles) and the actual number of particles. The mass of one mole of a substance is called its molar mass, typically expressed in grams per mole (g mol−1g \text{ mol}^{-1}) or kilograms per mole (kg mol−1kg \text{ mol}^{-1}). By knowing the molar mass and Avogadro's constant, we can determine the number of particles in a given mass of substance, or the mass of a single particle.

Key points

  • One mole of any substance contains NAN_A particles, where NA≈6.02×1023 mol−1N_A \approx 6.02 \times 10^{23} \text{ mol}^{-1}.
  • The number of particles N=nNAN = n N_A, where nn is the amount of substance in moles.
  • Molar mass is the mass of one mole of a substance.
  • The mass of a single particle can be found by dividing the molar mass by NAN_A (ensuring consistent units).

Worked example

Question

A sample of pure methane (CH4CH_4) has a mass of 160 g160 \text{ g}. The molar mass of methane is 16.0 g mol−116.0 \text{ g mol}^{-1}. Calculate: (a) the amount of methane in moles, and (b) the total number of methane molecules in the sample. (NA=6.02×1023 mol−1N_A = 6.02 \times 10^{23} \text{ mol}^{-1})

Solution

1. (a) To find the amount of substance (moles), divide the total mass by the molar mass:
2. n=massmolar mass=160 g16.0 g mol−1=10.0 moln = \frac{\text{mass}}{\text{molar mass}} = \frac{160 \text{ g}}{16.0 \text{ g mol}^{-1}} = 10.0 \text{ mol}
3. (b) To find the total number of molecules, multiply the amount of substance by the Avogadro constant:
4. N=nNA=10.0 mol×6.02×1023 mol−1=6.02×1024N = n N_A = 10.0 \text{ mol} \times 6.02 \times 10^{23} \text{ mol}^{-1} = 6.02 \times 10^{24} molecules

(a) 10.0 mol10.0 \text{ mol} (b) 6.02×10246.02 \times 10^{24} molecules

Common pitfalls

  • Incorrectly using units for molar mass (e.g., using kg mol−1kg \text{ mol}^{-1} when mass is in grams, or vice versa). Always ensure consistency.
  • Confusing the Avogadro constant (NAN_A) with the number of moles (nn). NAN_A is a constant, while nn is a variable for a specific sample.

Prerequisites

  • Understanding of amount of substance and the mole.
  • Ability to perform calculations involving division and multiplication with large numbers and scientific notation.
  • Familiarity with prefixes for unit conversion (e.g., grams to kilograms).
Further resources