The mole
Section: Ideal Gases | Syllabus: Cambridge AS Level Physics 9702
Amount of Substance The pressure, volume, and temperature of a gas are dependent on the number and behaviour of gas molecules. We use the SI base quantity amount of substance (n) to relate macroscopic properties to the number of molecules present.
1 mole is the amount of substance containing 6.02214076 × 10^23 elementary entities. Elemantary entities can be atoms, molecules, ions, or electrons. Avogadro Constant (N_A) The number 6.02 × 10^23 mol^-1 (to 3 s.f.) is the Avogadro constant.
It represents the number of particles in one mole of any substance. Key Relationships 1. Moles and Particles: n = N/N_A, where N is the total number of particles. 2. Total Mass: The mass of the gas M_total = Nm, where m is the mass of one molecule.
3. Density: ρ = Nm/V. 4. Molar Mass (M): The mass of 1 mole of substance is M = N_A m. The relative molecular mass of a substance in grams is equal to the mass of one mole. mass(g) = molar mass (g mol^-1) × amount (mol) Note: In this specific formula, mass is in grams , not kg.
Worked Examples Worked Example 1: Atoms in Argon Question: The molar mass of argon is 39.9 g. Determine the number of atoms in 10.0 g of argon. Solution 1. Find moles: n = mass / molar mass = 10.0 / 39.9 = 0.2506 mol.
2. Find atoms: N = n × N_A = 0.2506 × 6.02 × 10^23 = 1.51 × 10^23 atoms. Worked Example 2: Molecules in a Room Question: A room has dimensions 4.0 m × 4.0 m × 3.0 m. The density of air is 1.2 kg m^-3 and the average mass of a gas molecule is 4.8 × 10^-26 kg.
Determine the number of gas molecules in the room. Solution 1. Volume V = 4 × 4 × 3 = 48 m^3. 2. Total mass M = ρ V = 1.2 × 48 = 57.6 kg. 3. Number of molecules N = M / m = 57.6 / (4.8 × 10^-26) = 1.2 × 10^27 molecules.
Figure 15.1: The Mole Concept Illustration showing different substances (e.g., Helium atoms vs. Oxygen molecules) where 1 mole of each contains exactly N_A particles, emphasizing that elementary entities are identical for a given sample.
Figure 15.2: Triangle of Molar Relationships Formula triangle showing the relationships between Number of particles (N), Amount in moles (n), and Avogadro constant (N_A) [N = n × N_A]; and between Mass (m), Moles (n), and Molar Mass (M) [m = n × M].
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