F2.2 Investigate pressure, volume, and temperature relationships

Ontario Grade 11 Chemistry

Gases and Atmospheric Chemistry

Investigating gas behaviour when the amount of gas stays constant

A sealed syringe is harder to push when its opening is blocked. A balloon can expand when warmed, and gas pressure in a sealed container can rise as the container gets hotter. These observations point to relationships among a gas’s pressure, volume, and temperature. In this lesson, you will connect those observations to particle motion and use equations to describe them. The amount of gas must stay the same when applying the relationships.

What you will learn

Describe how pressure, volume, and temperature are related for a fixed amount of gas.
Use a particle model to explain the observed relationships.
Plan a fair investigation by changing one variable and controlling the others.
Use gas-law equations with consistent units and temperature in kelvins.

1. Begin with the variables and the particle model

A gas has no fixed shape or volume. It spreads through the space available to it. Before studying how gas variables change, recall that matter is made of particles. Gas particles move freely and collide with the walls of their container.

Volume is the space occupied by the gas. Common units are litres (L) and millilitres (mL). Pressure describes how strongly the gas pushes on each area of the container wall. It can be measured in kilopascals (kPa) or atmospheres (atm). Use the same pressure unit throughout a calculation.

Temperature tells us how hot or cold something is. For gas relationships, use the kelvin scale, which starts at absolute zero. Convert a Celsius temperature by adding 273.15. For example,

20\ ^\circ\mathrm{C}=293.15\ \mathrm{K}

. Do not put a Celsius temperature directly into a gas-law equation.

The particle model helps explain the observations. If gas particles collide with the container walls more often or with greater impact, pressure can increase. Changing the space available to the particles can also change how often they reach the walls. Temperature is linked to the particles’ average kinetic energy, meaning their average energy of motion.

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

Pressure, volume, and temperature describe different properties of a gas.
For the relationships in this lesson, keep the amount of gas constant.
Use kelvins for temperature in gas-law calculations.

2. Observe and investigate one relationship at a time

A fair investigation changes one variable while keeping the other relevant conditions constant. A controlled variable is a condition deliberately kept the same. For gas-law investigations, keep the amount of gas constant and record the units of each measurement.

To investigate pressure and volume, a learner could use a sealed syringe containing gas. At a steady temperature, reducing the gas volume should increase its pressure. The particles have less space, so they hit the walls more frequently. This is an inverse relationship: as one variable rises, the other falls. The product of pressure and volume stays constant for a fixed amount of gas at constant temperature.

To investigate volume and temperature, consider a flexible container such as a balloon. If the pressure stays approximately constant and the gas is warmed, its volume increases. Faster-moving particles would otherwise hit the walls harder, so the flexible container expands. This is a direct relationship: both variables rise together. Compare volume with temperature in kelvins, not degrees Celsius.

To investigate pressure and temperature, consider gas in a rigid, sealed container. Its volume cannot change. As the gas is warmed, particle motion becomes faster, and collisions with the walls become more forceful. Pressure rises. Pressure and kelvin temperature are directly related when volume and amount of gas stay constant.

These are predictions from the gas model, not measurements from a completed experiment. In an investigation, collect readings only after choosing suitable equipment and a safe procedure. Do not heat a sealed container unless the equipment and procedure are designed and approved for that purpose.

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

Pressure and volume have an inverse relationship at constant temperature.
Volume and kelvin temperature have a direct relationship at constant pressure.
Pressure and kelvin temperature have a direct relationship at constant volume.

3. Represent changes with equations and units

The subscripts 1 and 2 mean the initial and final conditions. Initial means before a change; final means after it. Choose the equation that matches the variable being changed and the conditions being held constant. For example, use the pressure–volume equation only when temperature and the amount of gas stay constant.

For a change involving all three variables, a combined relationship can be used if the amount of gas stays constant. It links an initial state to a final state. A state is the set of pressure, volume, and temperature values at one point. The combined equation requires kelvins and consistent units for pressure and volume.

Keep units visible as you substitute values. If a problem gives millilitres and asks for a volume in litres, convert before or after the calculation with the conversion shown. Use appropriate significant digits: the final answer should reflect the precision of the measured values. A calculated value should not appear more precise than the measurements support.

Before calculating, check the direction of change. If a gas is compressed at constant temperature, the final volume is smaller and the final pressure should be larger. This prediction can reveal an equation setup or arithmetic error.

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

Match the equation to the conditions held constant.
Use kelvins and consistent pressure and volume units.
Check whether the calculated direction of change makes physical sense.

Conditions and predicted changes

Variables compared	Conditions held constant	Relationship	Prediction
Pressure and volume	Temperature and amount of gas	Inverse	Volume decreases, pressure increases
Volume and temperature	Pressure and amount of gas	Direct	Temperature rises, volume increases
Pressure and temperature	Volume and amount of gas	Direct	Temperature rises, pressure increases

Worked example

Finding the pressure after compression

A gas has a volume of

2.40\ \mathrm{L}

at

98.0\ \mathrm{kPa}

. It is compressed to

1.60\ \mathrm{L}

while its temperature and amount stay constant. Find its final pressure.

Choose the relationship
Temperature and amount are constant, so use the pressure–volume relationship. The pressure should rise because the volume gets smaller.
$P_1V_1=P_2V_2$
Rearrange and substitute
Solve for the final pressure by dividing both sides by the final volume. The pressure units are the same, and the volumes are both in litres.
$P_2=\frac{P_1V_1}{V_2}=\frac{(98.0\ \mathrm{kPa})(2.40\ \mathrm{L})}{1.60\ \mathrm{L}}$
Calculate and report
The litres cancel, leaving kilopascals. The supplied measurements have three significant figures, so report the result to three significant figures.
$P_2=147\ \mathrm{kPa}$

Answer: The final pressure is

147\ \mathrm{kPa}

.

Check: The volume decreases from

2.40\ \mathrm{L}

to

1.60\ \mathrm{L}

, so pressure should increase above

98.0\ \mathrm{kPa}

. The calculated result has the expected direction.

Common mistakes and how to avoid them

Using Celsius in a gas-law equation.

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

Treating pressure and volume as a direct relationship.

Correction: At constant temperature, pressure and volume are inversely related. Compression raises pressure.

Changing more than one condition in an investigation and attributing the result to only one variable.

Correction: Change one variable at a time and control the others, including the amount of gas.

Mixing units without converting them.

Correction: Use matching units for the same quantity on both sides of an equation, or convert before substituting.

Lesson summary

Gas particles collide with container walls; these collisions are connected to pressure.
At constant temperature, decreasing volume increases pressure.
At constant pressure, increasing kelvin temperature increases volume.
At constant volume, increasing kelvin temperature increases pressure.
Use only equations whose conditions match the situation, and check units and significant digits.

Check your understanding

Question 1

A gas is warmed in a flexible container while pressure and amount stay constant. What happens to its volume?

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

Show answer and explanation

It increases.

Volume and kelvin temperature are directly related at constant pressure. Warming the gas increases its volume.

Question 2

A gas is compressed at constant temperature. Which change is expected?

Pressure decreases.
Pressure increases.
Pressure stays the same.
correctIndex

Show answer and explanation

Pressure increases.

Pressure and volume are inversely related when temperature and amount are constant. A smaller volume corresponds to a greater pressure.

Key terms

Pressure: A measure of how strongly a gas pushes on the walls of its container.
Volume: The space occupied by a gas.
Kelvin: The temperature scale used in gas-law relationships.
Direct relationship: A relationship in which two variables rise or fall together when other conditions stay constant.
Inverse relationship: A relationship in which one variable rises as the other falls when other conditions stay constant.
Controlled variable: A condition kept the same during an investigation.

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F2.2 · Investigate pressure, volume, and temperature relationships