F2.3 Solve problems with major gas laws and the ideal gas law

Ontario Grade 11 Chemistry

Gases and Atmospheric Chemistry

Ontario Grade 11 Chemistry — F2.3

A sealed syringe becomes harder to push as its plunger moves inward. A balloon can expand when warmed. These familiar changes involve gases, which can change volume and pressure as their conditions change. In this lesson, you will connect those observations to a simple particle model and use gas-law equations to solve problems. Before calculating, recall that a ratio compares two quantities and that an equation stays balanced when the same operation is applied to both sides.

What you will learn

Describe how gas particles help explain changes in pressure, volume, and temperature.
Choose and use a major gas law to solve for an unknown quantity.
Convert temperature to kelvins and use consistent units in gas-law calculations.
Use the ideal gas law to find one unknown when the other quantities are known.

1. What gas particles help explain

A gas fills the space available to it. Its particles are far apart compared with particles in a liquid or solid. They move in many directions and collide with the walls of their container. A collision is a contact between moving particles or between a particle and a surface.

Pressure is the force of gas particles pushing on a unit of surface area. In a sealed container, more frequent or harder particle collisions mean greater pressure. Volume is the space occupied by the gas. Temperature in gas-law calculations is measured in kelvins, a temperature scale that begins at absolute zero.

The particle model helps explain gas laws. If particles have less space, they hit the container walls more often. If particles move faster, their collisions tend to be harder. Gas-law relationships describe how measurable quantities change when other conditions are held steady.

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

Pressure, volume, temperature, and amount of gas are the quantities used in common gas-law problems.
A gas-law relationship applies under specified conditions, such as a fixed amount of gas or constant pressure.
Use kelvins for temperature in gas-law equations.

2. The major relationships

Boyle’s law applies when the temperature and amount of gas stay constant. Pressure and volume change in opposite directions: compressing a gas into a smaller volume raises its pressure. The product of pressure and volume stays constant.

Charles’s law applies when pressure and amount stay constant. Volume increases as kelvin temperature increases. For example, a flexible balloon can expand as the gas inside it warms, provided its pressure remains about the same.

Gay-Lussac’s law applies when volume and amount stay constant. Pressure increases as kelvin temperature increases. In a rigid sealed container, warming the gas raises the pressure because the particles move faster and collide harder.

Avogadro’s law applies when pressure and temperature stay constant. Volume increases as the amount of gas increases. Amount is measured in moles, the chemistry unit for counting particles. The combined gas law brings pressure, volume, and temperature together for a fixed amount of gas. Use the ideal gas law when pressure, volume, temperature, and amount are related in one situation.

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},\quad \frac{V_1}{n_1}=\frac{V_2}{n_2}

Boyle’s law: pressure and volume vary inversely when temperature and amount are fixed.
Charles’s law: volume and kelvin temperature vary directly when pressure and amount are fixed.
Gay-Lussac’s law: pressure and kelvin temperature vary directly when volume and amount are fixed.
Avogadro’s law: volume and amount vary directly when pressure and temperature are fixed.

3. Choosing an equation and using units

Start by listing the known values and the unknown. Identify what is fixed. If the problem says the gas amount and temperature are constant, Boyle’s law is a suitable choice. If pressure and amount are constant, use Charles’s law. The combined gas law is useful when a fixed amount of gas changes pressure, volume, and temperature.

For the combined gas law, the subscripts 1 and 2 mean the initial and final conditions. Match each pressure, volume, and temperature to the same condition. Do not mix an initial pressure with a final volume.

Convert a Celsius temperature to kelvins before using it. Do not use a Celsius value in a gas-law ratio. Use matching pressure units on both sides of an equation. For example, if one pressure is in kilopascals, express the other in kilopascals too. Keep volume units consistent as well.

The ideal gas law relates pressure, volume, amount, and kelvin temperature. The gas constant, represented by

R

, has a value that depends on the units chosen. With pressure in kilopascals and volume in litres, use the value shown here. Rearrange the equation using ordinary algebra to isolate the requested quantity.

Include units in the working so that you can see whether values are compatible. Report the final result with a sensible number of significant digits, based on the precision of the supplied measurements. Significant digits are the digits that show a measurement’s precision.

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

Select the law from the quantities that change and the conditions that stay constant.
For a fixed amount of gas, use the combined gas law when all three state variables may change.
Use kelvins and consistent pressure and volume units.
The ideal gas law can be rearranged to solve for pressure, volume, amount, or temperature.

4. A reliable problem-solving routine

Read the question once for the situation, then again to identify the initial and final conditions. Write down the value and unit for each quantity. Mark any stated constant conditions. Convert temperatures before substituting.

Choose a law that matches those conditions. Substitute values with their units, then rearrange to isolate the unknown. Check that the result makes sense. For example, Boyle’s law predicts that a decrease in volume at constant temperature will be accompanied by an increase in pressure.

A result that is far outside the expected scale can point to a missed temperature conversion, inconsistent units, or a misplaced value. Keep enough digits during the calculation and round the final answer appropriately.

List knowns, unknown, and constant conditions before selecting a law.
Convert temperature and check unit consistency before calculating.
Use the direction of the particle-level change as a reasonableness check.

Worked example

Finding the final pressure

A fixed amount of gas occupies

2.40\ \mathrm{L}

at

100.\ \mathrm{kPa}

and

20.0\ ^{\circ}\mathrm{C}

. It is compressed to

1.80\ \mathrm{L}

while its temperature remains constant. Find its final pressure.

Identify the conditions
The amount and temperature stay constant while pressure and volume change. Boyle’s law matches these conditions. Since the final volume is smaller, the final pressure should be larger.
Set up the relationship
Use the initial and final pressure-volume products. The two volumes are in litres, and both pressures use kilopascals.
$P_1V_1=P_2V_2$
Isolate the unknown
Divide both sides by the final volume to find the final pressure. Substitute the known values with their units.
$P_2=\frac{P_1V_1}{V_2}=\frac{(100.\ \mathrm{kPa})(2.40\ \mathrm{L})}{1.80\ \mathrm{L}}=133.\overline{3}\ \mathrm{kPa}$
Round and check
The given pressure has three significant digits, so report three significant digits. The pressure increased as the volume decreased, which agrees with Boyle’s law.
$P_2=133\ \mathrm{kPa}$

Answer: The final pressure is

133\ \mathrm{kPa}

.

Check: The volume fell to three-quarters of its initial value, so the pressure rose to four-thirds of its initial value. This agrees with the calculated result.

Common mistakes and how to avoid them

Using a Celsius temperature in a gas-law ratio.

Correction: Convert Celsius to kelvins first. Gas-law temperature ratios use the kelvin scale.

Choosing a law because its equation looks familiar, without checking the conditions.

Correction: Identify which quantities are constant and which change. Then choose the relationship that matches.

Mixing pressure or volume units in one equation.

Correction: Convert to matching units before substituting, and keep units visible through the calculation.

Assuming pressure and volume both rise together in a fixed-temperature situation.

Correction: For a fixed amount of gas at constant temperature, pressure and volume change in opposite directions.

Lesson summary

Gas particles collide with container walls, producing pressure.
Boyle’s, Charles’s, Gay-Lussac’s, and Avogadro’s laws each describe a relationship when specified conditions are fixed.
The combined gas law connects pressure, volume, and temperature for a fixed amount of gas.
The ideal gas law connects pressure, volume, amount, and kelvin temperature.
Convert temperatures to kelvins, use consistent units, and check whether the direction of change makes sense.

Check your understanding

Question 1

A sealed syringe contains a fixed amount of gas at constant temperature. If its volume is reduced, what happens to its pressure?

It increases.
It decreases.
It stays the same.
correctIndex: 0

Show answer and explanation

It increases.

Boyle’s law says pressure and volume vary in opposite directions when temperature and amount are constant.

Question 2

What kelvin temperature corresponds to

27.0\ ^{\circ}\mathrm{C}

?

$246.2\ \mathrm{K}$
$300.2\ \mathrm{K}$
$27.0\ \mathrm{K}$
correctIndex: 1

Show answer and explanation

300.2\ \mathrm{K}

Add

273.15

to the Celsius temperature:

27.0+273.15=300.15\ \mathrm{K}

, which rounds to

300.2\ \mathrm{K}

.

Question 3

Which law is the best choice when a fixed amount of gas changes pressure, volume, and temperature between two conditions?

Boyle’s law
Combined gas law
Avogadro’s law
correctIndex: 1

Show answer and explanation

Combined gas law

The combined gas law relates pressure, volume, and temperature for a fixed amount of gas.

Key terms

Pressure: The force of gas particles pushing on a unit of surface area.
Volume: The space occupied by a gas.
Kelvin: The temperature scale used in gas-law calculations.
Mole: The chemistry unit used to count particles.
Ideal gas law: The relationship among pressure, volume, amount, and kelvin temperature.
Significant digits: The digits in a measured value that show its precision.

Continue through SCH3U

View the complete SCH3U Ontario Grade 11 Chemistry curriculum and lessons

About this lesson and its review

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Chemistry (SCH3U), expectation F2.3. 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.

Official curriculum reference

Report a correction or ask a question

F2.3 · Solve problems with major gas laws and the ideal gas law

Ontario Grade 11 Chemistry

Ontario Grade 11 Chemistry — F2.3

What you will learn

1. What gas particles help explain

2. The major relationships

3. Choosing an equation and using units

4. A reliable problem-solving routine

Finding the final pressure

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