← Unit 2: Molecular interactions and reactions
Topic 1: Intermolecular forces and gases
Explain the behaviour of gases using the kinetic theory of matter, and apply Boyle's law, Charles's law and the combined gas law to predict the effect of changing pressure, volume and temperature
A focused answer to the QCE Chemistry Unit 2 dot point on gas behaviour. States the assumptions of the kinetic theory of gases, derives Boyle's, Charles's and Gay-Lussac's laws qualitatively from particle behaviour, and works through combined gas law problems of the kind QCAA poses in EA Paper 1.
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What this dot point is asking
QCAA wants you to describe gases using the kinetic theory of matter and predict the effect on a gas of changing pressure, volume or temperature using the named gas laws. The dot point sets up the ideal gas equation and gas stoichiometry that follow.
The answer
The kinetic theory of gases models gas particles as small, hard, freely moving objects whose macroscopic properties (pressure, volume, temperature) follow from the average behaviour of huge numbers of collisions. The gas laws (Boyle, Charles, Gay-Lussac, combined) are quantitative summaries of how these macroscopic properties trade off when one is held constant.
Kinetic theory of an ideal gas
Five assumptions:
- Gas particles are in continuous, random, straight-line motion.
- The particles have negligible volume compared with the volume of the container.
- The particles exert no intermolecular forces on each other except during instantaneous elastic collisions.
- Collisions between particles and with the walls are perfectly elastic (no kinetic energy lost).
- The average kinetic energy of the particles is directly proportional to the absolute (Kelvin) temperature.
Real gases approximate ideal behaviour best at low pressure and high temperature, where the particles are far apart and moving fast enough that intermolecular forces are negligible. They deviate from ideal behaviour at high pressure and low temperature, where particle volume and intermolecular attractions matter.
Pressure from the particle picture
Pressure is the total force exerted by particle-wall collisions divided by the wall area. Three things can change pressure:
- More particles in the same volume: more collisions per second, higher pressure.
- Smaller volume at the same particle count: collisions concentrated on a smaller area, higher pressure.
- Higher temperature: particles move faster, collide harder and more often.
This intuition underwrites every gas law.
Boyle's law: P and V at constant T and n
At constant temperature, pressure is inversely proportional to volume for a fixed amount of gas.
Compressing a gas to half its volume doubles the pressure (twice as many wall collisions per second). A P-V graph is a hyperbola; P against 1/V is a straight line through the origin.
Charles's law: V and T at constant P and n
At constant pressure, volume is directly proportional to absolute temperature.
T must be in Kelvin (K = degrees C + 273.15). A V-T graph extrapolates to zero volume at 0 K (absolute zero), which is the experimental basis for the Kelvin scale.
Gay-Lussac's law: P and T at constant V and n
At constant volume, pressure is directly proportional to absolute temperature.
A sealed container heated from 300 K to 600 K doubles its internal pressure. This is why aerosol cans warn "do not heat".
Combined gas law
When more than one variable changes simultaneously (and n is fixed):
Use this when a gas sample moves between two different sets of conditions. T must always be in Kelvin; P and V can use any units provided they are consistent on both sides.
Worked example: combined gas law
A 2.50 L sample of air at 20 degrees C and 100 kPa is heated to 80 degrees C and compressed to 1.00 L. Find the new pressure.
Convert: T_1 = 293 K, T_2 = 353 K.
Sanity check: compression should increase pressure (it did, factor of 2.5), heating should also increase pressure (it did, factor of 1.20). Final factor is about 3.0.
Units and conventions used in QCE
- Pressure: kPa preferred (or Pa, atm, mmHg). 1 atm = 101.325 kPa = 760 mmHg.
- Volume: L or mL. Convert mL to L by dividing by 1000.
- Temperature: must be in Kelvin for gas-law calculations. K = degrees C + 273 (273.15 for exact).
- Amount: mol.
QCAA's data sheet lists R = 8.314 J/(mol K) for use with P in kPa and V in L (yielding J units). Get used to the unit set early.
Common traps
Using degrees C in a gas law. Always convert to Kelvin first. Using degrees C in Charles's law gives nonsense (a sample at 0 degrees C does not have zero volume).
Confusing direct and inverse proportions. Boyle is inverse (P up, V down); Charles and Gay-Lussac are direct (T up, V or P up).
Forgetting "fixed amount of gas". All four laws assume n is constant. If gas is added or escapes during the change, you cannot use these laws directly.
Reading P-V or V-T graphs without checking axes. A P-V graph is a hyperbola; P-(1/V) is linear. A V-T graph is linear in Kelvin but does not pass through the origin if T is in degrees C.
Assuming real gases obey the laws exactly. They only approximately do, especially at high pressure or low temperature. QCAA usually qualifies questions with "assuming ideal behaviour".
In one sentence
The kinetic theory pictures gases as freely moving particles whose pressure comes from wall collisions; Boyle's law (P inversely proportional to V at fixed T), Charles's law (V directly proportional to T in K at fixed P) and Gay-Lussac's law (P directly proportional to T in K at fixed V) combine into the combined gas law P_1 V_1 / T_1 = P_2 V_2 / T_2 for a fixed amount of gas moving between two sets of conditions.
Past exam questions, worked
Real questions from past QCAA papers on this dot point, with our answer explainer.
2024 QCAA-style4 marksA sample of helium gas occupies 250 mL at 27 degrees C and 101.3 kPa. (a) Calculate the new volume if the pressure is increased to 152.0 kPa at the same temperature. (b) Calculate the new volume if, instead, the temperature is raised to 127 degrees C at constant pressure.Show worked answer →
A 4-mark answer needs both calculations with correct laws stated and Kelvin conversions.
(a) Boyle's law (constant T and n). P_1 V_1 = P_2 V_2.
V_2 = (P_1 V_1) / P_2 = (101.3 x 250) / 152.0 = 166.6 mL.
Pressure rose by a factor of 1.5, so volume falls to about two-thirds of the original.
(b) Charles's law (constant P and n). V_1 / T_1 = V_2 / T_2.
Convert: T_1 = 300 K, T_2 = 400 K. V_2 = V_1 x (T_2 / T_1) = 250 x (400 / 300) = 333 mL.
Temperature ratio is 4/3, so volume increases by the same ratio.
Markers reward the correct law named, Kelvin conversions, and units. Forgetting to convert degrees C to K is the most common single-mark loss.
2023 QCAA-style3 marksExplain, in terms of the kinetic theory of gases, why the pressure of a fixed mass of gas in a rigid container increases when its temperature is raised.Show worked answer →
A 3-mark answer needs three linked claims.
Particle speed. Temperature is a measure of the average kinetic energy of the particles. Heating the gas increases the average kinetic energy, so particles move faster.
Collision frequency and force. Faster particles strike the container walls more often per second and with greater momentum per collision.
Pressure. Pressure is force per unit area delivered by these collisions. More frequent and harder collisions deliver more force per unit area, so pressure rises.
In a rigid container the volume is fixed, so the increase in particle activity has nowhere to go except into pressure. This is Gay-Lussac's law: P / T = constant at fixed V and n.
Markers reward the kinetic-energy link, the collision-rate-and-force link, and the pressure conclusion.
Related dot points
- Apply the ideal gas equation (PV = nRT) and the concept of molar volume at standard conditions to calculate amounts of gases under varying conditions of temperature and pressure
A focused answer to the QCE Chemistry Unit 2 dot point on PV = nRT. Sets out the ideal gas equation with QCAA's preferred units, derives molar volume at standard laboratory conditions (24.79 L/mol at SLC), and works through calculations linking pressure, volume, temperature and amount of gas.
- Apply stoichiometric relationships to reactions involving gases, calculating volumes, masses or amounts of reactants and products using the mole ratio and molar volume or ideal gas equation
A focused answer to the QCE Chemistry Unit 2 dot point on gas stoichiometry. Sets out the four-step mole map for reactions with gas reactants or products, applies the molar volume at SLC and the ideal gas equation, and works through limiting-reactant and percent-yield calculations of the type QCAA poses in EA short response.