Difficulty: Introductory | Prerequisites: Part 1 of these notes (Pressure and Nonflexible Containers).
Part 1 showed what happens to pressure when you change the amount of gas or the temperature inside a rigid container. This second set of notes asks the same questions but in a flexible container, such as a balloon, where the walls can stretch. Because the walls adjust, the dependent variable flips: instead of pressure changing, volume changes. This part also introduces the four named gas laws and ties them together into the Ideal Gas Law (PV = nRT), the single equation that governs ideal gas behaviour.
In a flexible container, adding gas, heating it, or reducing external pressure all cause the volume to expand while internal and external pressures stay equal. These relationships are formalised as Avogadro's, Charles's, and Boyle's Laws. Combined with Amontons's Law from Part 1, they merge into PV = nRT.
Flexible container
A container whose walls can stretch or compress so that its volume adjusts. In a flexible container, internal pressure always equals external pressure at equilibrium. Examples: a latex balloon, a plastic bag.
Boyle's Law
At constant temperature and moles, pressure and volume are inversely proportional: PV = k, or equivalently P = k/V. Named after Robert Boyle.
In simple terms, if you squeeze a gas into a smaller space (less volume), the pressure goes up, and vice versa.
Charles's Law
At constant pressure and moles, volume is directly proportional to temperature: V = kT. Named after Jacques Charles.
Think of it as: heat a balloon and it expands; cool it and it shrinks.
Amontons's Law (Gay-Lussac's Law)
At constant volume and moles, pressure is directly proportional to temperature: P = kT. Named after Guillaume Amontons.
This is the rigid-container relationship from Part 1.
Avogadro's Law
At constant temperature and pressure, volume is directly proportional to the number of moles: V = kn. Named after Amedeo Avogadro.
In simple terms, more gas means a bigger balloon, as long as temperature and pressure stay the same.
Ideal Gas Law
The single equation that combines all four relationships: PV = nRT. It describes the behaviour of an ideal gas under any conditions.
R (universal gas constant)
The proportionality constant in the Ideal Gas Law. Its value depends on the units used. The most common value is 0.0821 L atm / (mol K).
Inverse proportion
A relationship where one variable increases as the other decreases, such that their product remains constant. If P goes up, V goes down, and P x V stays the same.
Direct proportion
A relationship where both variables increase or decrease together, such that their ratio remains constant. If T doubles, V doubles.
In a flexible container (balloon, latex bag), internal and external pressure are always equal at equilibrium. If internal pressure momentarily exceeds external pressure, the walls expand until the pressures match again. This means the dependent variable in a flexible container is volume, not pressure.
Setup: a balloon at 200 K with external pressure held at 1 atm.
C1: 4 molecules, V = 1 unit
C2: 8 molecules, V = 2 units
C3: 12 molecules, V = 3 units
Independent variable: number of moles (n)
Dependent variable: volume (V)
Controlled variables: temperature (T) and pressure (P, both internal and external = 1 atm)
Molecular-level explanation: adding more molecules means more collisions with the walls. In a flexible container this would momentarily increase internal pressure, but the walls stretch outward until the collision rate per unit area drops back to match the external pressure. The result is a larger volume.
Relationship: direct proportion. V = kn (Avogadro's Law).
Setup: the same balloon with a fixed number of molecules. Temperature is increased.
D1: T = 200 K, V = 1 unit
D2: T = 400 K, V = 2 units
D3: T = 600 K, V = 3 units
Independent variable: temperature (T)
Dependent variable: volume (V)
Controlled variables: moles (n) and pressure (P = 1 atm)
Molecular-level explanation: higher temperature means molecules move faster and hit the walls harder and more often. The flexible walls expand until the increased kinetic energy is spread over a larger surface area, bringing the collision rate per unit area back down to match external pressure.
Relationship: direct proportion. V = kT (Charles's Law).
Setup: a balloon with fixed gas amount at 200 K. External pressure is decreased.
E1: P_ext = 1 atm, V = 1 unit
E2: P_ext = 0.50 atm, V = 2 units
E3: P_ext = 0.33 atm, V = 3 units
Independent variable: external pressure (P)
Dependent variable: volume (V)
Controlled variables: temperature (T) and moles (n)
Molecular-level explanation: when external pressure drops, it no longer pushes as hard on the container walls. The internal molecules are still hitting with the same force and frequency, so the balloon expands. It keeps expanding until the molecules are spread across enough wall area that the internal collision rate per unit area matches the new, lower external pressure.
Relationship: inverse proportion. PV = k, or V = k/P (Boyle's Law). When pressure is halved, volume doubles.
Experiment A vs C (adding gas): both increase n as the independent variable. In a rigid container (A), pressure rises. In a flexible container (C), volume rises. The underlying cause is the same: more molecules, more collisions.
Experiment B vs D (heating): both increase T as the independent variable. In a rigid container (B), pressure rises. In a flexible container (D), volume rises. The underlying cause is the same: faster molecules, harder collisions.
Experiment E in a rigid container: if external pressure were reduced around a rigid flask, nothing would change inside. The rigid walls do not move, so the internal pressure, volume, temperature and moles all remain the same.
Scientist | Law | What is held constant | Relationship | Expression |
|---|---|---|---|---|
Robert Boyle | Boyle's Law | T, n | P and V inversely proportional | PV = k |
Jacques Charles | Charles's Law | P, n | V and T directly proportional | V = kT |
Guillaume Amontons | Amontons's Law | V, n | P and T directly proportional | P = kT |
Amedeo Avogadro | Avogadro's Law | T, P | V and n directly proportional | V = kn |
Experiment C (constant T and P, varying n) -- Avogadro's Law:
V = kn
Experiment D (constant P and n, varying T) -- Charles's Law:
V = kT
Experiment E (constant T and n, varying P) -- Boyle's Law:
PV = k (or equivalently, V = k/P)
From Part 1, Experiment B (constant V and n, varying T) -- Amontons's Law:
P = kT
The Ideal Gas Law (all four combined):
PV = nRT
This is the equation that describes gas behaviour when all four variables can change. R is the universal gas constant. The most commonly used value is R = 0.0821 L atm / (mol K).
To see why PV = nRT works: P is directly proportional to n (from Experiment A), P is directly proportional to T (from Experiment B), and P is inversely proportional to V (from Experiment E). Putting those together gives P proportional to nT/V, so PV = (constant) x nT. That constant is R.
Charles's Law is why a hot-air balloon rises: heating the air inside the envelope increases its volume, making the air less dense than the cooler air outside, producing lift. Boyle's Law is at work every time you use a bicycle pump: pushing the piston reduces the volume, which increases the pressure, forcing air into the tyre. Avogadro's Law explains why blowing more air into a balloon makes it bigger. Divers experience Boyle's Law directly: as they descend and water pressure increases, the volume of air in their lungs and equipment decreases, which is why they must equalise regularly.
Students often think Boyle's Law is a direct proportion. It is not. Pressure and volume are inversely proportional: when one goes up, the other goes down. The product PV stays constant.
A frequent error is confusing which law applies to which pair of variables. A reliable method: identify what is held constant first, then the law follows.
Students sometimes assume that reducing external pressure on a rigid container changes the gas inside. It does not. The rigid walls isolate the gas from changes in external pressure.
When ranking temperature across samples of the same gas at the same pressure, students forget that a larger volume with fewer molecules (more spread out) can be colder than a smaller volume with more molecules packed in. Temperature depends on kinetic energy per molecule, not on density alone.
Students sometimes write gas-law expressions with Celsius temperatures. All gas-law calculations require kelvins. Always convert before substituting.
Matching each scientist to the correct law and algebraic expression is a common exam item. Memorise the table in the Core Content section.
Be prepared to explain, at the molecular level, why volume increases in each flexible-container experiment. Your explanation should reference collision frequency, collision force, or both.
Expect a question asking you to compare a rigid-container experiment with its flexible-container counterpart (e.g. Experiment A vs C). The key: same cause (more molecules or higher temperature), different outcome (pressure change vs volume change), determined by the container type.
The Ideal Gas Law (PV = nRT) will appear in calculations throughout the rest of the course. Know how to rearrange it to solve for any single variable.
Questions about ranking gas samples by temperature when given different volumes and numbers of molecules test whether you understand that temperature relates to average kinetic energy per molecule, not total energy or density.
True or False: In a flexible container, internal pressure can be different from external pressure at equilibrium. ___
Fill in the blank: Boyle's Law describes an _______ proportion between pressure and volume.
True or False: Doubling the temperature (in kelvins) of a gas in a balloon at constant pressure will double the volume. ___
Fill in the blank: The Ideal Gas Law equation is PV = _______.
True or False: Reducing external pressure on a rigid container changes the internal pressure of the gas. ___
Q: Name two materials a flexible container could be made from.
A: Latex (rubber) and thin plastic (e.g. a plastic bag or cling film).
Q: What is always true about internal and external pressure in a flexible container?
A: They are always equal at equilibrium. If one changes, the container expands or contracts until they match again.
Q: In Experiment C, what is the independent variable, the dependent variable, and the controlled variables?
A: Independent: moles (n). Dependent: volume (V). Controlled: temperature (T) and pressure (P).
Q: Provide a molecular-level explanation for why volume increases in Experiment D.
A: Heating increases the average kinetic energy of the molecules, so they hit the flexible walls harder and more often. The walls stretch outward, increasing the volume, until the collision rate per unit area matches the unchanged external pressure.
Q: How are Experiment A (rigid) and Experiment C (flexible) similar and different?
A: Both add gas (increasing n) as the independent variable. In Experiment A the rigid container keeps volume constant, so pressure increases. In Experiment C the flexible container keeps pressure constant (internal = external), so volume increases.
Q: If Experiment E were done in a nonflexible container, what would happen when external pressure is reduced?
A: Nothing would change inside the flask. The rigid walls prevent expansion, so internal pressure, volume, temperature and moles all remain the same.
Q: Match each scientist to the correct gas law expression: Boyle, Charles, Amontons, Avogadro.
A: Boyle: PV = k. Charles: V = kT. Amontons: P = kT. Avogadro: V = kn.
Q: Which algebraic equation best combines all four gas variable relationships?
A: PV = nRT (the Ideal Gas Law).
The Ideal Gas Law (PV = nRT) is the starting point for stoichiometry problems involving gases, which you will encounter in the next unit. It also connects to Dalton's Law of Partial Pressures and to real-gas corrections (van der Waals equation) later in the course. The molecular-level reasoning here ties into kinetic molecular theory, where these proportionality relationships are derived from first principles. Understanding flexible vs rigid containers also prepares you for discussions of atmospheric pressure and weather systems in Earth science courses.
Related Terms / Search Tags
gas laws, Boyle's Law, Charles's Law, Amontons's Law, Gay-Lussac's Law, Avogadro's Law, Ideal Gas Law, PV = nRT, flexible container, balloon, pressure volume relationship, inverse proportion, direct proportion, gas constant R, POGIL gas variables, CHEM 25, introductory chemistry, kinetic molecular theory, gas behaviour, temperature in kelvins
Self-test answers: 1. False (they are always equal in a flexible container). 2. inverse. 3. True (Charles's Law). 4. nRT. 5. False (rigid walls isolate the gas; nothing changes inside).