F3.5 Explain Boyle’s, Charles’s, Gay-Lussac’s, combined, Dalton’s, and ideal gas laws

Ontario Grade 11 Chemistry

Gases and Atmospheric Chemistry

Ontario Grade 11 Chemistry — study topic F3.5

A sealed, flexible package can expand when warmed and contract when cooled. A gas in a syringe becomes harder to compress as its volume gets smaller. These familiar effects can be explained by moving gas particles. This lesson connects those particle ideas to six gas laws. You will need to recognize pressure, volume, temperature, and amount of gas. Temperature in gas-law calculations must be in kelvins, not degrees Celsius.

What you will learn

Describe how gas particles help explain changes in pressure, volume, and temperature.
Explain Boyle’s, Charles’s, and Gay-Lussac’s laws and identify what stays constant in each.
Use the combined gas law to relate changes in pressure, volume, and temperature.
Explain Dalton’s law of partial pressures and the ideal gas law.

1. Start with the particles and the measurements

A gas has no fixed shape or volume. Its particles move throughout the space available to them. They collide with each other and with the walls of their container. Pressure is the force of these collisions spread over an area. If particles hit the walls more often or with greater effect, the pressure can rise.

Volume is the space occupied by the gas. Temperature measures how hot or cold a substance is. At the particle level, a higher gas temperature means the particles have greater average kinetic energy. Kinetic energy is energy of motion. The amount of gas is often measured in moles, written as

n

. A mole is a counting unit for particles.

Before using a gas law, identify which quantities are changing and which are held constant. A quantity held constant does not change during the comparison. For example, a fixed amount of gas means no gas enters or leaves. The gas laws describe relationships under these stated conditions.

Gas-law temperature must be absolute temperature, measured in kelvins. Convert a Celsius temperature by adding

273.15

. Kelvin values do not use a degree sign. Pressure and volume units can vary, but use consistent units within an equation. Common units include kilopascals (

\mathrm{kPa}

), atmospheres (

\mathrm{atm}

), and litres (

\mathrm{L}

).

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

Pressure comes from gas particles colliding with container walls.
For gas laws, use kelvins: $T(\mathrm{K})=t(^{\circ}\mathrm{C})+273.15$ .
Check which quantities and amount of gas remain constant.

2. Three laws with one changing pair

Boyle’s law applies when temperature and amount of gas stay constant. If a gas is squeezed into a smaller volume, its particles have less space to move through. They strike the walls more often, so pressure rises. Pressure and volume change in opposite directions: when one increases, the other decreases. This is an inverse relationship.

Charles’s law applies when pressure and amount stay constant. Heating the gas makes its particles move faster. The gas expands until its pressure matches the constant external pressure. Volume and absolute temperature change in the same direction. This is a direct relationship. Doubling the kelvin temperature doubles the volume if the stated conditions hold.

Gay-Lussac’s law applies when volume and amount stay constant. Heating the gas makes its particles move faster and collide with the walls more strongly. Because the container cannot expand, pressure rises. Pressure and absolute temperature change in the same direction.

The equations show each relationship for an initial state and a final state. The subscript 1 means initial; 2 means final. Use kelvins for every temperature in these equations. These laws are useful only when their constant conditions are met.

P_1V_1=P_2V_2,\quad \frac{V_1}{T_1}=\frac{V_2}{T_2},\quad \frac{P_1}{T_1}=\frac{P_2}{T_2}

Boyle’s law: constant temperature and amount; pressure and volume change oppositely.
Charles’s law: constant pressure and amount; volume and kelvin temperature change together.
Gay-Lussac’s law: constant volume and amount; pressure and kelvin temperature change together.

3. Combined gas law: three changing measurements

Sometimes pressure, volume, and temperature all change, while the amount of gas stays fixed. The combined gas law links all three. It brings together the pressure–volume, volume–temperature, and pressure–temperature relationships. Use it when the initial and final states contain the same amount of gas.

Choose the unknown quantity and arrange the equation to solve for it. Convert each temperature to kelvins before substituting. Keep the pressure units the same on both sides and the volume units the same on both sides. When one pressure unit is used in both numerator and denominator, it cancels in the calculation.

The combined law does not apply if gas is added or removed. In that case, the amount is not constant, so this relationship is not the correct model. The ideal gas law, introduced below, includes the amount of gas.

\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}

Use the combined gas law when the amount of gas is fixed and pressure, volume, and temperature may change.
Convert Celsius temperatures before calculating.
Keep matching pressure and volume units consistent.

4. Gas mixtures and the ideal gas law

A gas mixture contains more than one gas in the same container. Dalton’s law states that the total pressure equals the sum of the partial pressures. A partial pressure is the pressure contributed by one gas in the mixture. For example, if two gases contribute pressures of

35\ \mathrm{kPa}

and

52\ \mathrm{kPa}

, their total pressure is

87\ \mathrm{kPa}

. All pressure values must use the same unit.

The ideal gas law links pressure, volume, amount, and absolute temperature for a gas. The constant

R

is the ideal gas constant. An ideal gas is a model in which gas particles are treated as very small and their interactions are neglected. Real gases can differ from this model, but the ideal gas law is the course-level relationship used to connect these four quantities.

Choose an

R

value that matches the units in the problem. For example,

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

works with pressure in kilopascals, volume in litres, amount in moles, and temperature in kelvins. Do not combine this value of

R

with pressure in atmospheres unless you first convert units or use a matching value of

R

.

P_{\mathrm{total}}=P_1+P_2+\cdots,\quad PV=nRT

Dalton’s law adds the partial pressures of gases in one mixture.
The ideal gas law includes $P$ , $V$ , $n$ , and $T$ .
Match the units of pressure and volume to the chosen gas constant.

Which gas law fits?

Law	Constant quantities	Relationship
Boyle’s	Temperature and amount	Pressure and volume change oppositely
Charles’s	Pressure and amount	Volume and kelvin temperature change together
Gay-Lussac’s	Volume and amount	Pressure and kelvin temperature change together
Combined	Amount	Pressure, volume, and temperature are linked
Dalton’s	Gas mixture in one container	Total pressure is the sum of partial pressures
Ideal gas	No fixed quantity required	Links pressure, volume, amount, and temperature

Worked example

Find the final volume with the combined gas law

A fixed amount of gas occupies

2.40\ \mathrm{L}

at

96.0\ \mathrm{kPa}

and

18.0\ ^\circ\mathrm{C}

. It is changed to

110.0\ \mathrm{kPa}

and

62.0\ ^\circ\mathrm{C}

. Find its final volume.

Choose the model
The amount of gas is fixed, while pressure, volume, and temperature may change. The combined gas law fits these conditions.
$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$
Convert temperatures
Add $273.15$ to each Celsius temperature. Gas-law temperature must be in kelvins.
$T_1=18.0+273.15=291.15\ \mathrm{K},\quad T_2=62.0+273.15=335.15\ \mathrm{K}$
Isolate the final volume
Rearrange the combined law to make $V_2$ the subject. Substitute the given values with pressure in kilopascals, volume in litres, and temperature in kelvins.
$V_2=\frac{P_1V_1T_2}{T_1P_2}=\frac{(96.0\ \mathrm{kPa})(2.40\ \mathrm{L})(335.15\ \mathrm{K})}{(291.15\ \mathrm{K})(110.0\ \mathrm{kPa})}$
Calculate and round
The units of pressure and temperature cancel, leaving litres. The given measurements support three significant figures, so report the volume to three significant figures.
$V_2=2.41\ \mathrm{L}$

Answer: The final volume is

2.41\ \mathrm{L}

.

Check: The pressure increases while the temperature also increases. The higher pressure tends to reduce volume, while the higher temperature tends to increase it. The calculated volume is close to the initial volume, which is reasonable because these effects partly offset.

Common mistakes and how to avoid them

Using Celsius directly in a gas-law equation.

Correction: Convert every gas-law temperature to kelvins first.

Treating Boyle’s law as a direct relationship between pressure and volume.

Correction: At constant temperature and amount, pressure rises when volume falls.

Using the combined gas law when gas enters or leaves.

Correction: The combined gas law requires a fixed amount of gas.

Adding pressure values that use different units.

Correction: Convert all partial pressures to the same unit before applying Dalton’s law.

Lesson summary

Gas particles create pressure by colliding with container walls.
Boyle’s, Charles’s, and Gay-Lussac’s laws each describe a pair of changing quantities while other quantities remain constant.
The combined gas law links pressure, volume, and temperature for a fixed amount of gas.
Dalton’s law adds partial pressures; the ideal gas law connects pressure, volume, amount, and kelvin temperature.
Use consistent units and kelvins in gas-law calculations.

Check your understanding

Question 1

A gas is compressed at constant temperature and amount. What happens to its pressure?

It decreases.
It increases.
It stays constant.
It becomes zero.

Show answer and explanation

It increases.

Boyle’s law describes an inverse pressure–volume relationship. A smaller volume gives higher pressure when temperature and amount stay constant.

Question 2

Which temperature belongs in a gas-law calculation for a sample at

25.0\ ^\circ\mathrm{C}

?

$25.0\ \mathrm{K}$
$248.2\ \mathrm{K}$
$298.2\ \mathrm{K}$
$273.2\ \mathrm{K}$

Show answer and explanation

298.2\ \mathrm{K}

Convert by adding

273.15

:

25.0+273.15=298.15\ \mathrm{K}

, which rounds to

298.2\ \mathrm{K}

.

Question 3

Two gases in one container have partial pressures of

40\ \mathrm{kPa}

and

25\ \mathrm{kPa}

. What is their total pressure?

$15\ \mathrm{kPa}$
$40\ \mathrm{kPa}$
$65\ \mathrm{kPa}$
$1000\ \mathrm{kPa}$

Show answer and explanation

65\ \mathrm{kPa}

Dalton’s law says to add the partial pressures:

40\ \mathrm{kPa}+25\ \mathrm{kPa}=65\ \mathrm{kPa}

.

Key terms

Absolute temperature: Temperature measured in kelvins, used in gas-law equations.
Partial pressure: The pressure contributed by one gas in a mixture.
Ideal gas: A gas represented by a simple model that treats particles as very small and neglects their interactions.
Mole: A unit used to count particles; the amount symbol is $n$ .

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Chemistry (SCH3U), expectation F3.5. 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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F3.5 · Explain Boyle’s, Charles’s, Gay-Lussac’s, combined, Dalton’s, and ideal gas laws

Ontario Grade 11 Chemistry

Ontario Grade 11 Chemistry — study topic F3.5

What you will learn

1. Start with the particles and the measurements

2. Three laws with one changing pair

3. Combined gas law: three changing measurements

4. Gas mixtures and the ideal gas law

Which gas law fits?

Find the final volume with the combined gas law

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through SCH3U

About this lesson and its review