F2.5 Determine gas molar volume or molar mass through inquiry

Ontario Grade 11 Chemistry

Gases and Atmospheric Chemistry

Plan a measurement, connect it to particle amounts, and use the results carefully

A fixed amount of gas can fill a large or small space as conditions change. For example, a balloon expands when its gas is warmed. At the particle level, gas particles move freely and spread through the space available to them. A mole is a counting unit for particles. Molar volume is the volume occupied by one mole of gas at stated conditions. Molar mass is the mass of one mole of a substance. In an inquiry, you measure quantities and use a model to find one of these values. The result belongs to the conditions measured; do not report a gas volume without also giving its temperature and pressure.

What you will learn

Describe an inquiry that uses measured gas volume and a known amount of gas to determine molar volume.
Use a balanced reaction and measured reactant amount to find the amount of gas produced.
Explain how measured gas pressure, temperature, volume, and mass can be used to determine a gas molar mass.
Report results with suitable units and significant digits, and identify important sources of uncertainty.

1. Bridge from measurements to gas amount

You already use mass, volume, and temperature as measured quantities. A balance measures mass in grams. A gas syringe or graduated container can measure gas volume, often in millilitres or litres. A thermometer measures temperature. Pressure describes how strongly gas particles push on a surface. In gas calculations, temperature must be written in kelvins. Convert from Celsius by adding 273.15.

The amount of a substance is measured in moles. When a gas is made in a chemical reaction, a balanced equation gives the mole relationship between reactants and products. A balanced equation has the same number of each kind of atom on both sides. Its coefficients show the relative amounts in moles.

A gas sample is a collection of moving particles. If the sample contains more particles, it will generally take up more space when temperature and pressure are held the same. This link lets an investigator compare the measured gas volume with the amount of gas.

T(\mathrm{K})=T(^{\circ}\mathrm{C})+273.15

Keep units with measurements and calculations.
Use kelvins for gas-law calculations.
A balanced equation is needed when reaction amounts are used to find gas amount.

2. Inquiry for gas molar volume

Molar volume is the volume per mole of gas. It changes with temperature and pressure, so always state the conditions for the result. An inquiry can produce a gas, measure its volume, and determine the amount produced from a known reactant amount.

For example, a small measured amount of magnesium can react with excess hydrochloric acid to produce hydrogen gas. The gas can be collected in a suitable gas syringe. The balanced reaction is shown below. The coefficient relationship says that one mole of magnesium produces one mole of hydrogen, if the reaction goes to completion and the acid is in excess.

Before collecting data, plan how to measure the reactant mass, gas volume, room temperature, and pressure. Use appropriate eye protection and follow teacher instructions for handling acid and glassware. Hydrogen is flammable, so keep it away from flames and sparks. Do not assume a proposed procedure has produced valid results: collect and record your own observations.

Determine the reactant amount from its mass and molar mass. Use the balanced equation to find the amount of gas. Then divide gas volume by gas amount. Record the temperature and pressure beside the result. The value is an experimental molar volume under those conditions, not a universal constant.

Sources of uncertainty include gas escaping before collection, reading the syringe incorrectly, or an incomplete reaction. Repeating measurements can help show whether results are consistent. A result that differs from another group’s result does not by itself show which measurement is wrong; compare conditions and methods.

\mathrm{Mg(s)}+2\,\mathrm{HCl(aq)}\rightarrow\mathrm{MgCl_2(aq)}+\mathrm{H_2(g)}

Measure gas volume and establish gas amount independently.
Use the balanced reaction to connect reactant amount to gas amount.
State temperature and pressure with an experimental molar volume.

3. Inquiry for gas molar mass

Molar mass is mass divided by amount. For a gas, an inquiry can measure the mass of a known gas sample and determine its amount from the measured pressure, volume, and temperature. The course-level gas relationship connects these three conditions with the amount of gas.

A suitable plan needs a sealed container or gas-sampling device with a known volume, a way to measure gas pressure and temperature, and a way to determine the mass of the gas sample. In practice, the container’s mass is measured with and without the gas under an appropriate procedure. The difference is the gas mass. The exact method depends on the equipment and gas chosen.

First determine the gas amount using the gas relationship. Then divide the measured gas mass by that amount. Use a gas constant whose units match the pressure and volume units. For pressure in kilopascals and volume in litres, a suitable value is

8.31\ \mathrm{kPa\,L\,mol^{-1}\,K^{-1}}

. The calculated molar mass has units of grams per mole.

Careful measurement matters. A leak changes the sample. A warm container can affect the measured gas conditions. A balance reading near its limit may make the mass difference uncertain. Record the instrument precision and avoid reporting more digits than the measurements support.

PV=nRT,\quad M=\frac{m}{n}

Find gas amount from measured pressure, volume, and kelvin temperature.
Find molar mass by dividing gas mass by gas amount.
Match gas-constant units to pressure, volume, and temperature units.

4. Units, significant digits, and interpretation

A calculation is only useful if its units make sense. In the molar-volume method, litres divided by moles gives litres per mole. In the molar-mass method, grams divided by moles gives grams per mole. Convert millilitres to litres before using a gas constant written for litres.

Significant digits show the precision supported by measurements. Do not report a calculated result with more meaningful digits than the least precise measurement supports. Keep extra digits while calculating, then round the final result. Include the conditions and units so another reader can interpret it.

A measured value may differ from a reference value because of measurement limits, gas loss, or differences in conditions. Explain what was measured and how the amount was determined. Do not silently adjust data to match an expected value.

V_m=\frac{V}{n}

Check the final unit before accepting a result.
Round only after calculating.
Report the actual measurement conditions and method.

Worked example

Finding an experimental molar volume

In a hypothetical classroom inquiry, 0.0243 g of magnesium reacts completely with excess hydrochloric acid. A gas syringe collects 24.0 mL of hydrogen at 22.0 °C and 101 kPa. Use a magnesium molar mass of 24.3 g/mol. Determine the experimental molar volume. These sample values illustrate the method; they are not reported laboratory evidence.

Connect reactant and gas
The balanced reaction has a one-to-one mole relationship between magnesium and hydrogen. Therefore, the amount of hydrogen equals the amount of magnesium that reacted.
$n(\mathrm{H_2})=n(\mathrm{Mg})$
Find the amount of magnesium
Divide magnesium mass by its molar mass. The grams cancel, leaving moles. This gives the hydrogen amount because of the equation’s one-to-one relationship.
$n(\mathrm{Mg})=\frac{0.0243\ \mathrm{g}}{24.3\ \mathrm{g\,mol^{-1}}}=0.00100\ \mathrm{mol}$
Convert the gas volume
Convert millilitres to litres before calculating molar volume. The temperature and pressure are retained as the conditions of this result.
$24.0\ \mathrm{mL}=0.0240\ \mathrm{L}$
Calculate volume per mole
Divide the measured gas volume by the hydrogen amount. The units reduce to litres per mole.
$V_m=\frac{0.0240\ \mathrm{L}}{0.00100\ \mathrm{mol}}=24.0\ \mathrm{L\,mol^{-1}}$

Answer: The experimental molar volume is

24.0\ \mathrm{L\,mol^{-1}}

at

22.0\ ^{\circ}\mathrm{C}

and

101\ \mathrm{kPa}

.

Check: The answer has volume-per-amount units, and its three significant digits match the measured quantities. The conditions are included because gas volume depends on conditions.

Common mistakes and how to avoid them

Reporting a molar volume without temperature or pressure.

Correction: State the measured conditions because a gas sample’s volume changes when conditions change.

Using the mass of magnesium as though it were the amount of hydrogen.

Correction: Convert mass to moles using molar mass, then use the balanced reaction to determine gas moles.

Putting millilitres into an equation while using a gas constant based on litres.

Correction: Convert the volume to litres first, and check that all units match.

Rounding intermediate values too early or reporting many unsupported digits.

Correction: Keep extra digits during the calculation and round the final result to match measurement precision.

Lesson summary

Molar volume is measured gas volume divided by gas amount, with temperature and pressure stated.
A balanced reaction can connect a measured reactant amount to the amount of gas produced.
For a gas molar-mass inquiry, determine gas amount from pressure, volume, and temperature, then divide gas mass by amount.
Use consistent units, record actual observations, and report only justified significant digits.

Check your understanding

Question 1

A gas occupies 0.0360 L and its amount is 0.00150 mol. What is its molar volume?

$24.0\ \mathrm{L\,mol^{-1}}$
$0.0417\ \mathrm{L\,mol^{-1}}$
$54.0\ \mathrm{L\,mol^{-1}}$
correctIndex

Show answer and explanation

24.0\ \mathrm{L\,mol^{-1}}

Divide volume by amount:

0.0360\ \mathrm{L}\div0.00150\ \mathrm{mol}=24.0\ \mathrm{L\,mol^{-1}}

.

Question 2

Which information must be recorded to interpret an experimental gas molar volume?

Gas temperature and pressure
The colour of the container only
The mass of the container only
correctIndex

Show answer and explanation

Gas temperature and pressure

Gas volume depends on temperature and pressure, so both conditions should accompany the result.

Key terms

Amount of substance: A measure of how many particles are present, expressed in moles.
Molar volume: The volume occupied per mole of a gas at stated conditions.
Molar mass: The mass of one mole of a substance, commonly expressed in grams per mole.
Inquiry: An investigation that uses planned measurements and evidence to answer a question.
Significant digits: The digits in a measurement that communicate its recorded precision.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Chemistry (SCH3U), expectation F2.5. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

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F2.5 · Determine gas molar volume or molar mass through inquiry