Gases & Molar Volume
One mole of hydrogen gas and one mole of oxygen gas at the same temperature and pressure take up exactly the same volume. One of the most surprising facts in chemistry — and the foundation of all gas calculations.
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Four printable worksheets that build from the foundations up to exam-style questions — start at whatever level suits you.
One mole of helium gas (mass ≈ 4 g) and one mole of carbon dioxide gas (mass ≈ 44 g) are both placed in separate containers at room temperature and pressure. Would you expect them to take up the same volume of space or different volumes? Justify your answer before you begin this lesson.
$$V = n \times V_m$$
Key facts
- Molar volume at STP = 22.71 L mol⁻¹ (0°C, 100 kPa — NESA standard)
- Molar volume at SATP = 24.8 L mol⁻¹
- The formula V = n × Vm
Concepts
- Why all ideal gases have the same molar volume
- The difference between STP and SATP
- When to use each molar volume value
Skills
- Calculate V from n using V = n × Vm
- Calculate n from V by rearranging
- Select the correct Vm value for given conditions
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.
Standard conditions
Molar volume only has a fixed value at a defined temperature and pressure. Two standard conditions are used in HSC Chemistry:
Avogadro's law: equal volumes of all ideal gases at the same temperature and pressure contain equal numbers of molecules, because gas volume is mostly empty space. Molar volume: STP (0 °C, 100 kPa) = 22.71 L mol⁻¹; SATP (25 °C, 100 kPa) = 24.8 L mol⁻¹ — default for NSW HSC.
Pause — copy the highlighted definition into your book before moving on.
Did you get this? True or false: at the same temperature and pressure, 1 mol of H₂ and 1 mol of CO₂ occupy the same volume — even though CO₂ molecules are much larger.
Quick check: A question states the conditions are 25 °C and 100 kPa. Which Vₘ should you use?
We just saw that one mole of any ideal gas at the same conditions occupies the same volume — the molar volume. That raises a question: how do you use molar volume to calculate volume or moles in a problem? This card answers it → with the formula V = n × Vm.
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.
V = n × Vm gives: mol × L mol⁻¹ = L ✓
For gases: V = n × Vm; rearranged n = V ÷ Vm. Always convert mL to L (÷ 1000) before substituting. State which Vm you used (22.71 or 24.8 L mol⁻¹) in every answer — this formula applies to gases only.
Add the highlighted equation to your notes before the check below.
Fill the blanks: drag each token into the matching blank.
V must be in ___ before substituting; if given in mL, divide by ___. At STP, Vₘ = ___ L mol⁻¹. At SATP, Vₘ = ___ L mol⁻¹.
Match each gas-law term to its definition.
- STP
- SATP
- Vₘ
- Avogadro's law
- Volume occupied by one mole of any gas at specified conditions (L mol⁻¹).
- 0 °C and 100 kPa; Vₘ = 22.71 L mol⁻¹.
- Equal volumes of ideal gases at the same T and P contain equal numbers of molecules.
- 25 °C and 100 kPa; Vₘ = 24.8 L mol⁻¹.
Did you get this? True or false: the formula V = n × Vₘ also works for 1 mole of liquid water.
Worked examples · reveal as you go
What volume does 3.5 mol of nitrogen gas (N₂) occupy at SATP?
A 4.96 L sample of carbon dioxide gas is collected. How many moles does it contain — and does the answer change depending on the conditions?
Common errors · the 3 traps that cost marks
Using the wrong molar volume value
Using 22.4 L mol⁻¹ for SATP conditions (or vice versa) gives a completely wrong answer. A student who correctly sets up n = V ÷ Vm but uses 22.4 instead of 24.8 will lose marks even though their method is right.
Fix: Underline the conditions stated in the question before picking a Vm value. Default to 24.8 L mol⁻¹ for NSW HSC unless told otherwise.
Applying molar volume to liquids or solids
V = n × Vm only works for gases. One mole of liquid water does NOT occupy 24.8 L — it occupies about 18 mL. The huge molar volume of gases is a result of their widely spaced particles.
Fix: Check the state of matter in the question. Gas → use V = n × Vm. Solid or liquid → use n = m ÷ MM.
Not converting units before substituting
Vm is in litres per mole (L mol⁻¹). If a question gives volume in mL or cm³, convert to litres first (divide by 1000). Substituting mL directly into the formula gives an answer 1000× too large.
Fix: Convert volume to litres before substituting. 500 mL = 0.500 L; 2400 cm³ = 2.400 L.
A student calculates the moles in 496 mL of CO₂ at SATP. One line contains an error — click it.
- SATP conditions → Vₘ = 24.8 L mol⁻¹
- V = 496 mL → substitute as V = 496 L
- Apply n = V ÷ Vₘ
- n = 0.496 ÷ 24.8 = 0.0200 mol
Quick-fire practice · 5 reps +2 XP per reveal
Calculate the volume occupied by 2.50 mol of oxygen gas (O₂) at SATP.
A 11.2 L sample of hydrogen gas (H₂) is collected at STP. How many moles does it contain?
A balloon contains 8.40 g of methane gas (CH₄) at SATP. Calculate the volume of the balloon. (C = 12.011, H = 1.008)
A gas syringe collects 620 mL of CO₂ at SATP. Calculate the amount in moles.
A 3.72 L sample of an unknown gas at STP has mass 7.44 g. Calculate the molar mass of the gas.
At the start of this lesson, you predicted whether one mole of helium and one mole of carbon dioxide would take up the same volume or different volumes.
The answer: they occupy exactly the same volume — 24.8 L at SATP. This is Avogadro's law in action. Gas volume depends on the number of molecules (moles), not their mass. At the same temperature and pressure, all ideal gases have the same molar volume because gas is mostly empty space — the tiny size difference between a helium atom and a CO₂ molecule is negligible compared to the distances between them.
Pick your answer, then rate your confidence — that tells the system what to drill next.
Q1. 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.
Q2. 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)
Q3. 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.
Q4. A chemist needs to prepare exactly 0.500 mol of nitrogen gas (N₂) in the lab at SATP. Two students propose different methods: Student A says "Measure out 14.014 g of N₂ and collect it." Student B says "Collect 12.4 L of N₂ gas at SATP." Evaluate both proposals — identify any errors and determine which, if any, is correct. (N = 14.007 g mol⁻¹)
Q5. A research team needs to identify an unknown gas that is produced during a chemical reaction. They have access to: a gas syringe (to collect a known volume), a balance (to measure mass), and a periodic table. Design a step-by-step procedure to identify the gas using molar volume concepts, and explain how you would use the data collected to calculate the molar mass and identify the gas.
📖 Comprehensive answers (click to reveal)
Multiple choice — drill bank
1. B — 24.8 L mol⁻¹ at SATP. 22.71 L mol⁻¹ is for NESA STP.
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) = 70.90 g mol⁻¹. n = 35.45 ÷ 70.90 = 0.500 mol. V = 0.500 × 24.8 = 12.4 L.
5. C — 620 mL = 0.620 L. n = 0.620 ÷ 24.8 = 0.025 mol.
Short answer model answers
Q1 (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].
Q2 (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 L
Q3 (4 marks): STP → Vₘ = 22.71 L mol⁻¹. n = V ÷ Vₘ = 3.72 ÷ 22.71 = 0.164 mol. MM = m ÷ n = 7.44 ÷ 0.164 ≈ 45 g mol⁻¹ — consistent with CO₂ (44.0) or propane (44.1).
Q4 (5 marks): Student A: MM(N₂) = 28.014 g mol⁻¹; mass for 0.500 mol = 0.500 × 28.014 = 14.007 g, not 14.014 g. Student A's mass is incorrect (used a single nitrogen atom mass) [1]. Student B: V = n × Vₘ = 0.500 × 24.8 = 12.4 L — Student B is correct [1].
Q5 (6 marks): (1) Weigh empty gas syringe (m₁). (2) Collect a known V of gas at SATP. (3) Weigh syringe + gas (m₂). (4) Mass of gas: m = m₂ − m₁. (5) Calculate n = V ÷ 24.8. (6) MM = m ÷ n. Compare to periodic table — e.g. ~32 → O₂; ~44 → CO₂.
Five timed questions on gases and molar volume. Beat the boss to bank a tier — gold (perfect + fast), silver (80%+), or bronze (cleared).
⚔ Enter the arenaClimb platforms, hit checkpoints, and answer gas-law questions. Quick recall, lighter than the boss.
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