The volume of a gas varies with changes in pressure and temperature. In order to compare the volumes occupied by different gases, we must adopt a set of standard conditions of temperature and pressure called room temperature and pressure (RTP). Accordingly, 25°C (298.15K) and one atmosphere (760 torr) are used as standard conditions for measurement of volumes of gases at room temperature.
It has been found that one mole of all gases occupies a volume of 24 dm³ at RTP. This is called molar volume. It is worth noting that one mole of each gas contains the same number of molecules, occupies the same volume and at the same time has different mass. In other words the masses and the sizes of the molecules of gases do not change the volume occupied by them. The concept of molar volume is useful because it enables us to calculate the number of moles or masses of the gases if we know their volumes.
📐 Worked examples
Calculate the number of moles of nitrogen gas present when it occupies a volume of 2.5 dm³ at RTP.
Solution: 24 dm³ → 1 mole
1 dm³ → 1/24 mole
2.5 dm³ → (1/24) × 2.5 = 0.10 mole
No. of moles = Volume at RTP / Molar volume
Calculate the volume of 0.5 mol of hydrogen at RTP.
Solution: 0.5 = Volume / 24 → Volume = 0.5 × 24 = 12 dm³
Calculate the volume occupied by 200 g carbon dioxide at RTP.
Solution: No. of moles = mass / molar mass = 200/44 = 4.545 mol.
Volume = moles × molar volume = 4.545 × 24 = 109 dm³ (approx.)
⚡ 15.1 Quick Check!
Calculate the amount of CO₂ in 100 dm³ at RTP. (Answer: 100/24 = 4.17 mol)
🧪 15.2 Concentration of a solution
(this section intentionally extended from molar volume concepts — molarity uses similar thinking) Concentration = amount of solute (mol) / volume (dm³).
• “24 at RTP” – think 2+4=6 and 6 moles? no! Just remember 24 as the magic number for room temp.
• Molar mass doesn’t affect volume – all gases are equal at RTP (like free seats!).
• Quick check: Volume (dm³) ÷ 24 = moles; Moles × 24 = volume.
• CO₂ molar mass 44 ~ 4/10 of 100? use 200/44 ~ 4.5 then ×24 = 109.
📅 35‑minute professional lesson planner
- 00:00–05:00 : Hook – Show different gas cylinders; ask “Why same volume for different gases?”
- 05:00–10:00 : Direct instruction – Define RTP (25°C, 1 atm), molar volume = 24 dm³/mol.
- 10:00–18:00 : Guided examples – Solve 15.1, 15.2, 15.3 on board. Emphasize factor label.
- 18:00–23:00 : Quick check & pair activity – “100 dm³ CO₂ → ? moles” and “0.25 mol Cl₂ → ? volume”.
- 23:00–30:00 : Concentration connection – Introduce 15.2 (concentration), use molar volume logic.
- 30:00–35:00 : Quiz warm‑up & exit ticket – Two MCQs similar to below, discuss misconceptions.
✨ Activity: “Gas volume domino” – each student gets a card with moles or volume, find matching partner.
📝 10 MCQs · molar volume at RTP
Click on the correct option – correct turns green, others red. Use submit to see score.