Difficulty: Introductory | Prerequisites: Basic understanding of states of matter.
Gases behave differently from solids and liquids because their particles move freely and fill whatever container they occupy. Four measurable variables describe any gas sample: pressure (P), volume (V), temperature (T), and amount in moles (n). This topic explores how those variables relate to each other, starting with what happens inside a rigid container where the volume cannot change. Understanding these relationships is the foundation for every gas-law calculation you will meet later in the course. If you have not yet covered the kinetic molecular theory or the concept of moles, review those first.
Pressure, volume, temperature and moles are the four variables that describe a gas. In a nonflexible (rigid) container the volume stays fixed, so adding more gas or raising the temperature increases the internal pressure. Both relationships are direct proportions.
Pressure (P)
The force exerted per unit area by gas molecules colliding with the walls of their container. Measured in atmospheres (atm), kilopascals (kPa), or millimetres of mercury (mmHg).
Think of it as how hard and how often the molecules are hitting the container walls.
Volume (V)
The amount of three-dimensional space occupied by the gas. Measured in litres (L) or millilitres (mL).
In simple terms, this is the size of the container the gas fills.
Temperature (T)
A measure of the average kinetic energy of the gas molecules. Must be expressed in kelvins (K) for gas-law calculations.
Think of it as how fast the molecules are moving on average. Hotter gas means faster molecules.
Moles (n)
The amount of gas present, counted in units of 6.022 x 10^23 particles (Avogadro's number). More moles means more molecules in the container.
In simple terms, this is how much gas you have.
Internal pressure
The pressure exerted by the gas molecules inside the container, pushing outward against the walls.
External pressure
The pressure exerted on the outside of the container by the surrounding atmosphere or another force, pushing inward.
Nonflexible (rigid) container
A container whose walls do not stretch or compress, so the volume remains constant regardless of pressure changes inside. Examples: a glass flask, a steel cylinder.
Think of it as a container that keeps its shape no matter what the gas inside is doing.
Kinetic energy
The energy an object possesses due to its motion. For gas molecules, average kinetic energy is directly proportional to temperature in kelvins.
Atmosphere (atm)
A unit of pressure. 1 atm is the average pressure of the Earth's atmosphere at sea level. Equal to 101.325 kPa or 760 mmHg.
Each dot in the diagrams represents one gas molecule (or particle).
The arrows on the molecules represent their motion and speed. Longer arrows mean higher average kinetic energy, which means higher temperature.
Setup: a rigid flask held at 200 K. Gas molecules are added in each step while temperature and volume stay constant.
A1: 4 molecules, internal pressure = 1 atm
A2: 8 molecules, internal pressure = 2 atm
A3: 12 molecules, internal pressure = 3 atm
Independent variable: number of moles of gas (n)
Dependent variable: internal pressure (P)
Controlled variables: volume (V) and temperature (T)
Molecular-level explanation: more molecules in the same space means more collisions with the container walls per unit time. The molecules are hitting the walls just as hard (same temperature, same kinetic energy), but they are hitting more often because there are more of them. More frequent collisions produce higher pressure.
Relationship: direct proportion. When you double the moles, you double the pressure. When you triple the moles, you triple the pressure.
Setup: the same rigid flask with a fixed number of molecules. Temperature is increased in each step.
B1: T = 200 K, internal pressure = 1 atm
B2: T = 400 K, internal pressure = 2 atm
B3: T = 600 K, internal pressure = 3 atm
Independent variable: temperature (T)
Dependent variable: internal pressure (P)
Controlled variables: volume (V) and number of moles (n)
Molecular-level explanation: raising the temperature increases the average kinetic energy of the molecules. They move faster and hit the container walls harder and more often. Both factors increase the pressure.
Relationship: direct proportion. When you double the temperature (in kelvins), you double the pressure.
Volume is a controlled variable in both experiments. The internal pressure is allowed to differ from the external pressure (1 atm) because the rigid walls cannot expand. If the container were flexible (like a balloon), the walls would stretch until internal and external pressures equalised, and you could not observe a pressure increase, only a volume increase.
Pressure depends on how molecular movement interacts with the container:
How often molecules hit the walls (collision frequency). More molecules or faster molecules both increase this.
How hard molecules hit the walls (force per collision). Faster molecules at higher temperatures hit harder.
Experiment A (constant V and T, varying n):
P = kn
Pressure is directly proportional to the number of moles. The constant k absorbs the fixed values of volume and temperature.
Experiment B (constant V and n, varying T):
P = kT
Pressure is directly proportional to temperature (in kelvins). The constant k absorbs the fixed values of volume and moles.
In both cases, k is a proportionality constant whose value depends on whichever variables are being held constant. These are not the full gas law yet, just the individual relationships isolated by controlling the other variables.
These pressure relationships explain everyday phenomena. A sealed aerosol can warns against heating because the rigid metal walls cannot expand; as temperature rises, internal pressure climbs (P = kT) and the can may burst. Car tyres gain pressure on a long motorway drive for the same reason: friction heats the air inside, and the tyre's shape is essentially fixed. Scuba divers carry air in rigid steel tanks at very high pressure, packing many moles of gas into a small volume so they have enough to breathe at depth.
Students often think that pressure and temperature can never differ between the inside and outside of a container. They can, but only in a rigid container. A flexible container always equalises.
Students sometimes assume that increasing temperature "creates" more gas. It does not. The number of moles stays the same; the molecules simply move faster.
A common mistake is using Celsius in gas-law calculations. Temperature must be in kelvins. Zero degrees Celsius is 273.15 K, not zero energy.
Students sometimes confuse "directly proportional" with "equal." P = kn does not mean P equals n. It means if n doubles, P doubles, provided k stays constant.
You will almost certainly be asked to identify independent, dependent and controlled variables for a gas experiment. Practise filling in those tables from memory.
Expect a question that asks you to explain, at the molecular level, why pressure increases when gas is added or heated. "More collisions" is not enough on its own; specify whether molecules are hitting more often, harder, or both.
The distinction between flexible and nonflexible containers is a favourite conceptual question. Know that a rigid container allows internal pressure to differ from external pressure, and that a flexible container forces them to match.
Proportionality expressions (P = kn, P = kT) may appear as matching or multiple-choice items. Be ready to write them from the experimental data.
True or False: In a rigid container, adding more gas at constant temperature will increase the internal pressure. ___
True or False: The length of the arrows in the particle diagrams represents the number of moles. ___
Fill in the blank: Pressure is caused by molecules _______ the sides of a container.
True or False: If a flexible container is used, internal pressure can be greater than external pressure at equilibrium. ___
Fill in the blank: In Experiment B, doubling the temperature from 200 K to 400 K caused the pressure to _______.
Q: In Model 1, what does each dot represent?
A: Each dot represents one gas molecule (particle).
Q: Name two materials a nonflexible container could be made from.
A: Glass and steel (or metal, ceramic, thick rigid plastic).
Q: Which gas variable is most closely related to the length of the arrows in the particle diagrams?
A: Temperature (T). Longer arrows indicate higher average kinetic energy, which corresponds to higher temperature.
Q: In Experiment A, what is the independent variable and what is the dependent variable?
A: Independent variable: number of moles (n). Dependent variable: internal pressure (P).
Q: Provide a molecular-level explanation for why pressure increases when gas is added to a rigid container at constant temperature.
A: More molecules are present in the same volume, so there are more collisions with the container walls per unit time. Each collision has the same average force (temperature is unchanged), but the total number of collisions increases, raising the pressure.
Q: Why does a nonflexible container allow internal pressure to differ from external pressure?
A: The rigid walls do not expand or contract. In a flexible container, the walls would adjust until internal and external pressures equalise. Rigid walls hold their shape, so the gas inside can exert a different pressure from the atmosphere outside.
Q: Write the algebraic expression for the relationship in Experiment A.
A: P = kn (pressure is directly proportional to the number of moles, at constant volume and temperature).
Q: If a flexible container were used instead in Experiment A, predict what would happen to the volume and internal pressure as gas is added.
A: The volume would increase (the container stretches) and the internal pressure would remain equal to the external pressure (1 atm), because the flexible walls adjust until the pressures match.
This material connects directly to the gas laws covered in Part 2 of these notes (flexible containers, Boyle's Law, Charles's Law, and the Ideal Gas Law). The P = kn relationship here is the basis of Avogadro's Law, and P = kT is the basis of Amontons's (Gay-Lussac's) Law. Understanding pressure at the molecular level also ties into kinetic molecular theory, which you will study in more depth later in the course.
Related Terms / Search Tags
gas variables, gas laws, pressure volume temperature moles, P V T n, nonflexible container, rigid container, kinetic energy of gas molecules, collision frequency, collision force, direct proportion, P = kn, P = kT, Amontons Law, Gay-Lussac Law, Avogadro Law, internal pressure vs external pressure, POGIL gas variables, CHEM 25, introductory chemistry gas behaviour
Self-test answers: 1. True. 2. False (arrows represent kinetic energy/temperature). 3. hitting / colliding with. 4. False (internal always equals external in a flexible container at equilibrium). 5. double (from 1 atm to 2 atm).