Imagine you have one mole of golf balls and one mole of beach balls. They both contain the same number of objects — but they take up very different amounts of space. Now imagine the opposite: one mole of hydrogen gas and one mole of oxygen gas. At the same temperature and pressure, they take up exactly the same volume. This is one of the most surprising facts in chemistry — and it's the foundation of all gas calculations.
📚 Core Content
At the same temperature and pressure, one mole of any ideal gas occupies the same volume. This is Avogadro's law. It seems strange at first — surely a mole of large CO₂ molecules takes more space than a mole of tiny He atoms?
The key insight is that in a gas, the molecules are so far apart that the actual size of the molecule barely matters. The volume of a gas is almost entirely empty space between particles. What determines the volume is the number of particles (which determines how hard they collectively push on the container walls) and the temperature and pressure. Since one mole always means the same number of particles (NA), one mole of any gas at the same conditions occupies the same volume.
Molar volume only has a fixed value at a defined temperature and pressure. Two standard conditions are used in HSC Chemistry:
This formula works exactly like n = m ÷ MM from Lesson 2, but for gases. Instead of converting between mass and moles using molar mass, you convert between volume and moles using molar volume.
🧮 Worked Examples
🧪 Activities
1 Calculate the volume occupied by 2.50 mol of oxygen gas (O₂) at SATP.
2 A 11.2 L sample of hydrogen gas (H₂) is collected at STP. How many moles does it contain?
3 A balloon contains 8.40 g of methane gas (CH₄) at SATP. Calculate the volume of the balloon. (C = 12.011, H = 1.008)
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| Gas | Formula | Molar Mass (g mol⁻¹) | Amount (mol) | Measured Volume (L) |
|---|---|---|---|---|
| Helium | He | 4.003 | 1.00 | 24.8 |
| Nitrogen | N₂ | 28.014 | 1.00 | 24.8 |
| Carbon dioxide | CO₂ | 44.009 | 1.00 | 24.8 |
| Sulfur dioxide | SO₂ | 64.058 | 1.00 | 24.8 |
| Xenon | Xe | 131.29 | 1.00 | 24.8 |
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Answer A, B, and C in your workbook.
❓ Multiple Choice
1. What is the molar volume of an ideal gas at SATP (25°C, 100 kPa)?
2. How many moles of gas are in a 49.6 L sample collected at SATP?
3. Which statement about molar volume is correct?
4. A sample of chlorine gas (Cl₂) has a mass of 35.45 g. What volume does it occupy at SATP? (Cl = 35.45 g mol⁻¹)
5. A gas sample occupies 620 mL at SATP. How many moles does it contain?
✍️ Short Answer
6. State Avogadro's law and use it to explain why one mole of helium gas (M = 4.003 g mol⁻¹) and one mole of sulfur hexafluoride gas (SF₆, M = 146.06 g mol⁻¹) occupy the same volume at the same temperature and pressure. 3 MARKS
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7. A laboratory produces 4.40 g of carbon dioxide gas (CO₂) during a reaction at SATP. Calculate: (a) the number of moles of CO₂ produced, and (b) the volume this gas occupies at SATP. (C = 12.011, O = 15.999) 4 MARKS
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Answer in your workbook.
8. A student collects 3.72 L of an unknown gas at STP and determines it has a mass of 7.44 g. Calculate the molar mass of the gas and suggest what the gas might be. Show all working. 4 MARKS
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Answer in your workbook.
A. Avogadro's law states that equal amounts (moles) of any ideal gas at the same temperature and pressure occupy the same volume. All five samples contain exactly NA particles, so they exert the same pressure on their container at the same temperature, and thus occupy the same volume. The mass (and thus the molar mass) of each molecule is irrelevant because gas volume is dominated by empty space between particles, not the size of the molecules themselves.
B. All gases would occupy 2 × 24.8 = 49.6 L. For example, for N₂: V = 2.00 × 24.8 = 49.6 L.
C. The student is incorrect. The molar volume of 24.8 L mol⁻¹ applies only to gases. Liquid water at 25°C has a density of 1.00 g mL⁻¹, so 1.00 mol (18.015 g) of water occupies only 18.015 mL = 0.018 L — nearly 1400 times less than 24.8 L. In liquids, molecules are densely packed with no significant empty space between them.
1. B — 24.8 L mol⁻¹ at SATP (25°C, 100 kPa). 22.4 L mol⁻¹ is for STP (0°C).
2. C — n = 49.6 ÷ 24.8 = 2.00 mol.
3. A — Avogadro's law: equal moles of ideal gases → equal volumes at same T and P.
4. D — MM(Cl₂) = 2 × 35.45 = 70.90 g mol⁻¹. n = 35.45 ÷ 70.90 = 0.500 mol. V = 0.500 × 24.8 = 12.4 L.
5. C — Convert: 620 mL = 0.620 L. n = 0.620 ÷ 24.8 = 0.025 mol.
Q6 (3 marks): Avogadro's law states that equal volumes of all ideal gases at the same temperature and pressure contain the same number of molecules [1]. Both 1 mol He and 1 mol SF₆ contain exactly 6.022 × 10²³ molecules [1]. Gas volume is determined by the number of particle–wall collisions per second (pressure) and temperature, not by the mass of individual molecules — so despite SF₆ being ~36× heavier, both samples occupy the same volume at the same T and P [1].
Q7 (4 marks):
(a) MM(CO₂) = 12.011 + 2(15.999) = 44.009 g mol⁻¹ n = m ÷ MM = 4.40 ÷ 44.009 = 0.100 mol (b) V = n × Vm = 0.100 × 24.8 = 2.48 LQ8 (4 marks):
STP → Vm = 22.4 L mol⁻¹ n = V ÷ Vm = 3.72 ÷ 22.4 = 0.1661 mol MM = m ÷ n = 7.44 ÷ 0.1661 = 44.8 g mol⁻¹ ≈ 44 g mol⁻¹A molar mass of ~44 g mol⁻¹ is consistent with carbon dioxide (CO₂, MM = 44.009 g mol⁻¹) or propane (C₃H₈, MM = 44.097 g mol⁻¹). At STP, CO₂ is the more likely candidate in a typical lab context.
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