Characteristics of Gases Explained by the Particle Model
- According to the particle model of matter, gases are made up of tiny particles (atoms or molecules) that are in constant, random motion.
- The distance between gas particles is much greater than in solids or liquids.
- Intermolecular forces between gas particles are very weak (often treated as negligible in simple models).
- Gas particles move in straight lines until they collide with one another or with the walls of the container.
In the ideal gas model, we assume gas particles:
- have negligible volume compared to the space they occupy
- experience no intermolecular forces except during collisions.
Why Gases Can Be Compressed and Expand
Compression
Because gas particles are far apart, there is a lot of empty space between them.
- When pressure is applied, the particles can be pushed closer together, reducing the volume of the gas.
- The particles themselves do not get smaller; instead, the spaces between them decrease.
- Gas particles only interact significantly when they collide.
- Between collisions they move independently, so compressing them mostly reduces empty space, not particle size.
Expansion
- Gases naturally spread out to fill any container.
- When a gas is allowed to expand, its particles move apart and spread out to occupy the entire volume available.
- If gas is transferred from one container to a larger one (at the same temperature and pressure), the particles simply distribute themselves throughout the new volume.
- Unlike solids, gases have no fixed volume and no fixed shape – they always take the shape and volume of their container.
For a fixed mass of gas at constant temperature, the relationship between pressure and volume is inversely proportional:
$$P \propto \frac{1}{V}$$
This is Boyle’s Law, which you will study in more detail later.
The large empty spaces between oxygen particles in a balloon:
- allow the gas to be compressed when you squeeze the balloon,
- give the gas a low density compared with solids and liquids,
- help the balloon float if the gas inside is less dense than the surrounding air.
Low Density
- Gases generally have a much lower density than liquids and solids.
- Because gas particles are so far apart, there are fewer particles per unit volume, so the mass per unit volume (density) is low.
- When a gas is cooled, its particles move more slowly and can come closer together.
- As the particles lose enough energy, intermolecular forces become more significant and the gas can condense into a liquid.
- If the liquid is cooled further, the particles lose more energy, move even less, and may form a solid as the forces of attraction fully organise them into a more fixed structure.
Fluidity
- Gases, like liquids, are fluids.
- Gas particles are not fixed in place.
- They move freely and can flow around obstacles.
- Gas particles can flow and spread out, so gases have no fixed shape.
- They will “pool” in a container, filling all available space, much like liquids flow to fill the bottom of a container (but gases fill the entire volume, not just the bottom).
- This property of fluidity is why we can pump air through pipes, use gases in spray cans, and breathe air as it flows in and out of our lungs.
Understanding Gas Pressure
Pressure
Pressure is force exerted per unit area on a surface.
Each collision exerts a tiny force; together, these collisions create a measurable pressure on the container’s surface.
How Pressure Relates to Temperature
Temperature is directly linked to the average kinetic energy of gas particles. When the temperature of a gas increases:
- The average kinetic energy of the particles increases.
- The particles move faster.
- Collisions with the container walls become more frequent and more forceful → the pressure increases (if volume is constant).
- When gas particles in a container are heated and the volume is kept constant, their average kinetic energy increases, they hit the walls harder and more often, and the pressure rises.
- Conversely, when the temperature decreases, particles move more slowly and the pressure drops (at constant volume).
Boyle's Law
Boyle’s Law describes how the pressure and volume of a fixed mass of gas are related at constant temperature.
Boyle’s Law
For a fixed amount of gas at constant temperature, pressure is inversely proportional to volume.
$$P \propto \frac{1}{V}$$
$$P V=\text { constant }$$
In practical form:
$$P_1 V_1=P_2 V_2$$
- If volume decreases, pressure increases.
- If volume increases, pressure decreases.
Think of a syringe or a balloon:
- When you push the plunger in (decreasing volume), the gas is compressed and pressure rises.
- When you pull it out (increasing volume), the gas expands and pressure falls.
When applying Boyle's Law, always check that the temperature remains constant.
Charles's Law
Charles’s Law describes how the volume of a gas changes with temperature when pressure is constant.
Charle's Law
Charles’s Law describes how the volume of a gas changes with temperature when pressure is constant.
$$V \propto T$$
$$\frac{V}{T}=\text { constant }$$
In practical form:
$$\frac{V_1}{T_1}=\frac{V_2}{T_2}$$
- If temperature increases (in K), volume increases.
- If temperature decreases, volume decreases.
- A balloon taken from a warm room into a freezer will shrink.
- The gas inside cools, the particles move more slowly, and the volume decreases while the pressure remains (approximately) constant.
Always convert temperatures to Kelvin (K) when using gas laws:
$$
T(\mathrm{~K})=T\left({ }^{\circ} \mathrm{C}\right)+273
$$
Gay-Lussac’s Law
Gay-Lussac’s Law describes the relationship between pressure and temperature of a gas when the volume is kept constant.
Gay-Lussac’s Law
For a fixed amount of gas at constant volume, pressure is directly proportional to temperature (in Kelvin).
$$P \propto T$$
$$\frac{P}{T}=\text { constant }$$
In practical form:
$$\frac{P_1}{T_1}=\frac{P_2}{T_2}$$
- If temperature increases, pressure increases (at constant volume).
- If temperature decreases, pressure decreases.
- A sealed aerosol can becomes dangerous if heated.
- The gas inside gets hotter, the particles move faster, and pressure rises.
- If the pressure becomes too high (and the can cannot expand), it may burst.
- This is why aerosol cans often carry a warning: Do not expose to high temperatures.
Boyle's Law (P-V, constant T):
$$
P_1 V_1=P_2 V_2
$$
Charles's Law (V-T, constant P):
$$
\frac{V_1}{T_1}=\frac{V_2}{T_2}
$$
Gay-Lussac's Law (P-T, constant V):
$$
\frac{P_1}{T_1}=\frac{P_2}{T_2}
$$
The Combined Gas Law
- So far, you’ve seen three separate gas laws:
- Boyle’s Law – relates pressure and volume (constant temperature)
- Charles’s Law – relates volume and temperature (constant pressure)
- Gay-Lussac’s Law – relates pressure and temperature (constant volume)
- The combined gas law brings all three together into one equation.
- It describes how pressure (P), volume (V) and temperature (T) of a fixed amount of gas change when more than one of these variables is altered.
For a fixed mass of gas, the ratio $\frac{PV}{T}$ remains constant, as long as the amount of gas does not change.
This can be written as:
$$\frac{P_1 V_1}{T_1}=\frac{P_2 V_2}{T_2}$$
where:
- $P_1, V_1, T_1$ are the initial pressure, volume and temperature
- $P_2, V_2, T_2$ are the final pressure, volume and temperature
- Temperature must always be in Kelvin (K)
The combined gas law assumes the mass (number of moles) of gas is constant and the gas behaves ideally.
The combined gas law is essentially Boyle's, Charles's and Gay-Lussac's laws merged.
If temperature is constant, $T_1=T_2$, so the equation simplifies to:
$$P_1 V_1=P_2 V_2$$
→ Boyle's Law
If pressure is constant, $P_1=P_2$, so:
$$\frac{V_1}{T_1}=\frac{V_2}{T_2}$$
→ Charles's Law
If volume is constant, $V_1=V_2$, so:
$$\frac{P_1}{T_1}=\frac{P_2}{T_2}$$
→ Gay-Lussac's Law
This makes the combined gas law a useful all-in-one tool for many gas problems.
A sample of gas has a volume of 2.0 dm³ at a pressure of 100 kPa and a temperature of 27 °C. What will its volume be if the pressure is increased to 150 kPa and the temperature is raised to 127 °C? (Assume the amount of gas remains constant.)
Solution
Step 1 - List known values
- $V_1=2.0 \ \mathrm{dm}^3$
- $P_1=100 \ \mathrm{kPa}$
- $T_1=27^{\circ} \mathrm{C}=27+273=300 \mathrm{~K}$
- $P_2=150 \ \mathrm{kPa}$
- $T_2=127^{\circ} \mathrm{C}=127+273=400 \mathrm{~K}$
- $V_2=$ ?
Step 2 - Use the combined gas law
$$\frac{P_1 V_1}{T_1}=\frac{P_2 V_2}{T_2}$$
Rearrange to solve for ${V}_{2}$ :
$$V_2=\frac{P_1 V_1 T_2}{T_1 P_2}$$
Step 3 - Substitute values
$$
\begin{gathered}
V_2=\frac{(100 \mathrm{~kPa}) \times\left(2.0 \mathrm{~dm}^3\right) \times(400 \mathrm{~K})}{(300 \mathrm{~K}) \times(150 \mathrm{~kPa})} \\
V_2=\frac{100 \times 2.0 \times 400}{300 \times 150} \mathrm{~dm}^3=\frac{80000}{45000} \mathrm{~dm}^3 \approx 1.78 \mathrm{~dm}^3
\end{gathered}
$$
Answer: The new volume of the gas will be approximately $1.8 \mathrm{~dm}^3$.
Experimental Evidence Supporting Gas Models
Experiments with everyday equipment such as syringes, balloons and sealed containers provide strong evidence for the particle model of gases and the gas laws (Boyle’s, Charles’s and Gay-Lussac’s laws).
Syringe Experiments
Materials
A sealed syringe filled with air (tip blocked or capped)
Procedure
Step 1: Initial setup
- Ensure the syringe contains a fixed amount of air.
- Seal the opening so that no gas can escape.
Step 2: Applying pressure
- Slowly push the plunger in to reduce the volume of the gas.
- Observe the increasing resistance as the air is compressed.
Step 3: Releasing pressure
- Let go of the plunger and allow it to return to (about) its original position.
- Observe that the gas expands back towards its original volume once the extra pressure is removed.
Observations
- When the plunger is pushed in:
- The volume decreases.
- The pressure increases (you feel more resistance).
- This supports Boyle’s Law (inverse relationship between pressure and volume at constant temperature).
- When the plunger is released:
- The gas expands and the volume increases again.
- The gas continues to fill the entire space available in the syringe (no “empty corner” with no gas).
In conclusion, the syringe experiment:
- Shows that pressure and volume are inversely related for a fixed amount of gas at constant temperature (Boyle’s Law).
- Demonstrates the compressibility of gases (volume can be reduced) and their expansive nature (they expand to fill available space), as predicted by the particle model.
Balloon Experiments
Materials
- A balloon
- A warm water bath
- A cold water bath (e.g. ice water)
Procedure
Step 1: Initial measurement
- Inflate the balloon to a moderate size and tie it off.
- Measure and record its circumference or estimate its volume.
Step 2: Heating the balloon
- Place the balloon in warm water.
- Observe any change in size (the balloon usually expands).
Step 3: Cooling the balloon
- Then place the balloon in ice water.
- Observe any change in size (the balloon usually shrinks).
Observations
- In warm water:
- The balloon expands, showing that the volume increases when temperature increases (at roughly constant external pressure).
- This supports Charles’s Law (V ∝ T at constant pressure).
- In ice water:
- The balloon contracts, showing that the volume decreases when temperature decreases.
- In all cases, the gas inside the balloon fills the balloon completely, showing that gases expand to fill their container.
In conclusion, the balloon experiment:
- Provides evidence that gas volume is directly proportional to temperature when pressure is constant (Charles’s Law).
- Highlights the fluid and expansive nature of gases, consistent with the particle model (faster-moving particles at higher temperature spread further apart).
Pressure-Temperature Relationship Demonstration
Materials
- A rigid, sealed container with a pressure gauge
- A heat source (e.g. hot plate, warm water bath)
- A cold source (e.g. ice bath)
Procedure
Step 1: Initial pressure measurement
- Fill the container with a fixed amount of gas.
- Measure and record the initial pressure at room temperature.
Step 2: Heating the gas
- Gently heat the container.
- Measure and record the pressure at several higher temperatures.
Step 3: Cooling the gas
- Place the container in an ice bath.
- Measure and record the pressure at lower temperatures.
Observations
- As the temperature increases, the pressure rises (at constant volume).
- As the temperature decreases, the pressure falls.
- The container is always filled with gas, showing again that gases have no fixed volume or shape and always occupy the space available.
In conclusion, this experiment shows that:
- Gas pressure is directly proportional to temperature (in Kelvin) when volume is constant: this is Gay-Lussac’s Law.
- The results agree with the kinetic theory: higher temperature → higher average kinetic energy → more forceful collisions with the container walls → higher pressure.
- How does the particle model explain the compressibility and expansive behaviour of gases?
- What is the relationship between pressure and volume in gases, and which experiment above supports this?
- How do temperature changes affect the pressure and volume of a gas (name the relevant gas laws)?
- How do the syringe and balloon experiments demonstrate Boyle’s Law and Charles’s Law in action?
- In the sealed-container experiment, why does the pressure increase when the temperature rises, even though the volume does not change?
