Derive the ideal gas equation. What is the universal gas constant?
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Define an ideal gas. A gas whose atoms or molecules do not attract or repel one another; real gases act like it at low pressure and high temperature.
2 · Write the three gas laws.
Boyle: V ∝ 1/P (T and n constant)
Charles: V ∝ T (P and n constant)
Avogadro: V ∝ n (P and T constant)
3 · Combine them. V ∝ nT/P, so PV = nkT, where k = 1.381 × 10⁻²³ J K⁻¹ is the Boltzmann constant.
4 · Change to moles. n = μN, where N is the Avogadro number, so PV = μNkT. With R = Nk: PV = μRT.
5 · Explain R. R = 8.31 J mol⁻¹ K⁻¹. It is universal because it is the same for all gases. For 1 mole, PV = RT.
6 · Work a quick example. 1 mole at 273 K and 1.013 × 10⁵ Pa: V = 8.31 × 273 ÷ (1.013 × 10⁵) ≈ 0.0224 m³ (22.4 L).
7 · Real-life link. Oxygen cylinders are kept away from heat, because P rises with T at a fixed volume.
8 · Close in one line. The ideal gas equation PV = μRT joins all three gas laws in one.
Scoring tip: Show each proportionality before combining them. Box PV = μRT and write R with its unit.
