F. Gases and Atmospheric Chemistry · Gases and Atmospheric Chemistry

Inquiry: Finding the Molar Volume and Molar Mass of a Gas

F2.5 F2.3 A1.4 A1.5 A1.8 A1.13About 70 minutes

Learning goals

I can describe how to determine the molar volume of hydrogen and the molar mass of a gas by experiment.
I can follow safe lab practice and identify WHMIS hazards.
I can process gas data, including correcting for water vapour pressure and converting to STP.
I can calculate percentage error and explain the direction of specific sources of error.

Words to know

gas measuring tube (eudiometer)
A graduated tube, closed at one end, used to collect and measure the volume of a gas over water.

meniscus
The curved surface of a liquid in a narrow tube; volume is read at its bottom.

WHMIS
Workplace Hazardous Materials Information System: Canada's system of hazard labels, pictograms and Safety Data Sheets.

Safety Data Sheet (SDS)
A document giving a chemical's hazards and safe handling, storage and disposal.

analytical balance
A precise balance that measures mass to 0.0001 g or 0.001 g.

Measuring a "constant" yourself

In the lesson on Avogadro's hypothesis you were told that one mole of any gas occupies 22.4 L at STP. Could you measure that yourself? Yes, with a strip of magnesium, some acid and a gas measuring tube. You can also run the idea backwards: if you know the volume and the mass of a gas, you can find its molar mass, and so identify it. This lesson walks through both classic Grade 11 investigations, with real-style data, and has you try a version at home.

Lab safety and WHMIS

These investigations are done in a school lab with a teacher.

Hydrochloric acid carries the WHMIS corrosion pictogram: it can burn skin and eyes. Wear safety goggles and gloves, and rinse any splash with lots of water.
Hydrogen and butane are flammable gases (WHMIS flame pictogram). Keep all flames and sparks away, and ventilate the room.
Read the Safety Data Sheet (SDS) for each chemical before you start, and dispose of solutions the way your teacher directs.

Never try the acid or butane experiments at home.

Investigation A: The molar volume of hydrogen

Question: What is the molar volume of hydrogen gas at STP?

Method: A short piece of magnesium ribbon is cleaned with steel wool (to remove the oxide coating), weighed on an analytical balance and wrapped in a small cage of copper wire. A gas measuring tube is partly filled with dilute hydrochloric acid, then topped up carefully with water. The cage is put in the mouth of the tube, which is turned upside down into a beaker of water. The denser acid sinks, reaches the magnesium, and hydrogen bubbles up:

Mg(s) + 2 HCl(aq) → MgCl₂(aq) + H₂(g)

When the reaction is finished, the tube is moved to a tall cylinder of water and raised or lowered until the water level inside equals the level outside, so the gas is at atmospheric pressure. The volume, water temperature and barometric pressure are recorded.

Collecting hydrogen from magnesium and hydrochloric acid in an inverted gas measuring tube. The gas collected is hydrogen mixed with water vapour. Not to scale.

Measurement	Value
mass of Mg	0.0412 g
volume of gas collected	42.3 mL
water (and gas) temperature	21 °C
barometric pressure	100.8 kPa
vapour pressure of water at 21 °C	2.49 kPa

Sample data for Investigation A.

The calculation path for Investigation A.

Worked example

Example 1: Calculating the molar volume

Use the sample data to find the molar volume of hydrogen at STP and the percentage error.

Moles of H₂: n(Mg) = 0.0412 g ÷ 24.31 g/mol = 1.695 × 10⁻³ mol; the mole ratio is 1 : 1, so n(H₂) = 1.695 × 10⁻³ mol.
Pressure of dry H₂: P = 100.8 − 2.49 = 98.31 kPa
Volume at STP (combined gas law): V = 42.3 mL × (98.31 ÷ 101.325) × (273 ÷ 294) = 38.1 mL = 0.0381 L
Molar volume: Vₘ = 0.0381 L ÷ 1.695 × 10⁻³ mol = 22.5 L/mol
Percentage error = |22.5 − 22.4| ÷ 22.4 × 100 % = 0.4 %

22.5 L/mol at STP, a 0.4 % error. Excellent agreement.

Investigation B: The molar mass of butane

Question: What is the molar mass of the gas in a disposable lighter?

Method: A butane lighter is weighed. Its valve is held open under water so the gas bubbles into an inverted, water-filled graduated cylinder (no flame, ventilated room). After about 60 mL is collected, the water levels are equalized and the volume, temperature and pressure recorded. The lighter is dried very thoroughly and weighed again; its loss in mass is the mass of gas released.

Sample data: mass lost = 0.152 g; volume = 65.0 mL; temperature = 20 °C; pressure = 99.6 kPa; vapour pressure of water at 20 °C = 2.34 kPa.

Worked example

Example 2: Calculating the molar mass of butane

Use the sample data to find the molar mass and compare it with butane, C₄H₁₀ (58.12 g/mol).

P(butane) = 99.6 − 2.34 = 97.26 kPa
n = PV ÷ RT = (97.26)(0.0650) ÷ [(8.314)(293)] = 2.595 × 10⁻³ mol
M = m ÷ n = 0.152 g ÷ 2.595 × 10⁻³ mol = 58.6 g/mol
Percentage error = |58.6 − 58.12| ÷ 58.12 × 100 % = 0.8 %

58.6 g/mol, within 1 % of butane.

Sources of error and which way they push

Thinking about the direction of each error lets you judge which ones could explain your result:

Oxide coating on the Mg: some of the mass is MgO, which makes no H₂. Fewer moles of gas than calculated → measured volume too small → Vₘ too low.
Gas escaping before the tube is sealed, or bubbles missing the tube → volume too small → Vₘ (or n) too low.
Not subtracting water vapour → pressure of the dry gas taken as too high → Vₘ too high.
Water levels not equalized: if the inside level is higher, the gas is below atmospheric pressure.
Water left on the lighter when it's reweighed → mass loss seems smaller → molar mass too low.
Lighter gas is not pure butane: many lighters contain isobutane (same molar mass) and some contain propane (44.11 g/mol), which would lower the result.
Some gas dissolves in the water (more of a problem for CO₂ than for H₂ or butane).

Hands-on activity

Molar volume at home: baking soda and vinegar

You need: a grown-up, a clean, dry 500 mL plastic bottle, a large round balloon, a funnel (or a rolled paper cone), baking soda, white vinegar, a kitchen scale, a measuring cup, string and a ruler, a thermometer or weather app, eye protection.

Safety: wear eye protection. Point the bottle away from faces. Keep balloons and balloon pieces away from young children; check for latex allergies.

Weigh 10 g of baking soda (NaHCO₃) and use the funnel to put it into the balloon.
Pour 250 mL of vinegar into the bottle (more than enough: the baking soda will be the limiting reactant).
Stretch the balloon's neck over the bottle mouth without letting the powder fall in. Then lift the balloon so all the powder drops in.
When the fizzing stops (swirl gently), measure the balloon's circumference with the string. Record the room temperature and pressure (from a weather app).
Calculate: n(CO₂) = n(NaHCO₃) = 10 g ÷ 84.01 g/mol. Balloon volume V = C³ ÷ (6π²). Experimental molar volume = V ÷ n. Compare it with the theoretical value at your conditions, Vₘ = RT ÷ P (about 24.3 L/mol at 22 °C and 101 kPa).

What to look for: n ≈ 0.119 mol, so you'd expect about 2.9 L of CO₂. Your balloon will usually be smaller, giving a molar volume that is too low. Why? Some CO₂ dissolves in the liquid; the air already in the bottle (about 250 mL) also ends up partly in the balloon, which pushes the other way; the balloon is not a perfect sphere; the rubber squeezes the gas to slightly above atmospheric pressure. Write each of these as a source of error with its direction, just like the examples.

Just for fun

Lab magnesium ribbon has a mass of roughly 1 g per metre. To make a whole mole of hydrogen (22.4 L at STP) you would need 24.3 g of magnesium: over 20 m of ribbon, about the length of two city buses. In class, 4 cm is plenty. That's the beauty of ratios.

Your turn

Why must the vapour pressure of water be subtracted in both investigations?

Why are the water levels inside and outside the tube made equal before reading the volume?

0.0350 g of Mg produces 35.6 mL of H₂ collected over water at 22 °C and 99.9 kPa. Calculate the molar volume at STP.

Calculate the percentage error for a molar volume of 22.0 L/mol.

Name the WHMIS hazard for hydrochloric acid and for butane.

Why is the magnesium ribbon cleaned with steel wool before weighing?

More practice: warm-up

What gas is produced when magnesium reacts with hydrochloric acid?

What is the accepted molar volume at STP?

Which instrument measures atmospheric pressure in the lab?

How do you read the volume in a gas measuring tube?

What does SDS stand for?

More practice: on your own

A lighter loses 0.110 g. The gas fills 48.0 mL over water at 23 °C and 100.2 kPa. Find the molar mass of the gas.

A student forgets to dry the lighter before reweighing it. Will her molar mass be too high or too low? Explain.

A student's Mg ribbon was not cleaned. Predict the effect on her molar volume.

A student forgets to subtract the water vapour pressure in Investigation A. Is her molar volume too high or too low?

In the home activity, why is the vinegar used in excess?

Challenge

A student reports a molar volume at STP of 26.0 L/mol. Calculate the percentage error and suggest the most likely single cause.

In a trial at 24 °C and 101.1 kPa, 0.0280 g of Mg gives 28.9 mL of H₂ over water. Find the molar volume at the room conditions (no conversion to STP), and compare it with the ideal value RT/P for the dry gas.

Design an improvement to the home baking-soda activity that would reduce the effect of CO₂ dissolving in the vinegar.

Check your understanding

Quiz

In the magnesium–hydrochloric acid investigation, the moles of H₂ are found from:

Gas is collected over water at 22 °C and 100.0 kPa. The pressure of the dry gas is:

A student's molar volume is 21.8 L/mol. The percentage error is about:

Which error would make an experimental molar mass of butane too LOW?

Which WHMIS pictogram belongs on hydrochloric acid?

Why must the water levels inside and outside the gas tube be equal when the volume is read?

For parents and teachers

Big idea (F2.5 with A1.4, A1.5, A1.8, A1.13): students determine the molar volume of a gas (Mg + HCl) or the molar mass of a gas (butane lighter) by experiment, correct for water vapour, and analyse error with direction and size.

How to help: for any experimental result, ask "Is it too high or too low? Which error could push it that way? Is that error big enough?"

Common difficulties:

Forgetting water vapour or the STP conversion.
Listing errors without directions. Each error should come with "this makes the result too high/low because...".
Significant figures: the masses here are small, so careful rounding matters.

Safety at home: the home activity uses only baking soda, vinegar and a balloon. The acid and butane investigations are school-lab only: hydrochloric acid is corrosive and butane and hydrogen are flammable.