DSE Physics | Gas laws tutoring guide | Boyle, Charles and the ideal gas equation

2026-11-01

Tutor lesson-prep guides · Secondary Physics

Students hunt for a formula the moment they see a gas, yet the three laws differ only in which quantity is fixed. Without naming the fixed quantity, Boyle becomes Charles. This lesson opens with a two-column fixed/changing table and fills it before any calculation.

Objectives — Students can: (1) state the fixed condition of each gas law; (2) convert Celsius to kelvin before substituting; (3) use PV = nRT for an unknown with correct units; (4) choose the law from the fixed/changing table.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Pressure	P = F/A and common units	1 atm is about 101 kPa
Unit conversion	litres to m3, kPa to Pa	1 L = 0.001 m3
Absolute temperature	K = C + 273	27 C = 300 K

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-10 min	Fixed/changing table	decide the law first	fixed T means Boyle
10-22 min	Boyle	P and V inverse	2.0 atm x 3.0 L = 1.5 atm x 4.0 L
22-34 min	Charles	V and T proportional	2.0 L at 300 K gives 3.0 L at 450 K
34-48 min	Ideal gas	PV = nRT once	n = 2.0, T = 300 K
48-56 min	Units and figures	answers carry units	4.99 L, not 4.99
56-60 min	Exit check	three questions, marked at once	independent work

03 Teaching script (read it out)

Scene 1: Opening move: fill the fixed/changing table

Every question starts with two columns: which quantity is fixed, which changes. Fixed T means Boyle, fixed P means Charles, fixed V means the pressure law. If all three change, only PV = nRT applies.
The step takes ten seconds and blocks most wrong-formula errors. Ask the student: 2.0 atm in 3.0 L expands to 4.0 L at constant temperature; the new pressure? (1.5 atm, because P1V1 = P2V2.) Student task: fill the table for three textbook questions without calculating, then check each other.

Scene 2: The three laws are one equation in disguise

Boyle: fixed T, P1V1 = P2V2. Charles: fixed P, V1/T1 = V2/T2. Ideal gas: PV = nRT with R = 8.314 J mol-1 K-1. Example: 2.0 mol at 300 K in 24.6 L gives P = nRT/V = 202.8 kPa.
Start from PV = nRT and show that fixing two quantities collapses it into each law, so nobody needs to memorise three unrelated formulas. Reminder: temperature must be in kelvin; substituting Celsius is the classic disaster because negative Celsius produces a negative volume. Student task: heat the same gas from 300 K to 450 K; the volume against 2 L? (3 L.)

Scene 3: Units and significant figures: marks come at the end

Use Pa with R = 8.314, volume in m3, n in mol, T in K. With n = 0.5 mol, P = 250 kPa, T = 300 K, V = nRT/P = 4.99 L.
Answers need units and the figures the question gave, usually three. With 250 kPa (three figures), 4.99 L is right and 4.9880 is false precision. Ask the student: why write 250 kPa as 250000 Pa? (Because R carries pascal-metre cubed.) Student task: circle the unit on each of three answers and repair the missing ones.

04 Question types and worked steps

Type	Example	Steps	Answer
Boyle	fixed T, new pressure	P1V1 = P2V2	2.0×3.0=1.5×4.0
Charles	fixed P, new volume	V1/T1 = V2/T2	2.0/300=3.0/450
Ideal gas	find n, P or V	PV = nRT	P = 202.8 kPa
Mixtures	add partial pressures	P total = P1 + P2	same T and V

Sanity check (teach this): A negative pressure or volume means Celsius was substituted. Boyle is inverse: bigger volume must mean smaller pressure (3.0 L to 4.0 L, 2.0 to 1.5 atm). Charles is direct: heat raises volume and the ratio V/T is constant. Unit check: Pa times m3 gives joules, matching nRT. Order of magnitude also matters: 2.0 mol near room conditions fills about 24 L, so 0.02 L signals a conversion slip.

05 Independent practice (3 questions)

Question	Answer	What to watch
2 atm, 3 L, then 4 L	1.5 atm	P1V1 = P2V2
2 L at 300 K, then 450 K	3.0 L	V/T constant
0.5 mol, 250 kPa, 300 K	4.99 L	V = nRT/P

06 Common mistakes and what to say

Mistake	Student writes	Say this
Substituting Celsius	negative volume	“The formula wants kelvin, add 273 before anything.”
Picking the law at random	using V/T with fixed T	“Fill the fixed/changing table before touching numbers.”
Skipping unit conversion	treating L as m3	“1 L is 0.001 m3, skip it and you are out by a thousand.”
Unitless answers	writing 4.99	“A physics answer without units is not an answer.”

07 Homework (paper, section and question numbers)

Secondary physics chapter index — questions 2 and 4 are the same type
Prep guide home — other chapters in this subject
DSE physics papers — gas question warm-up

08 Exit check (last 5 minutes)

Question	Answer	Decision
25 C in kelvin	298 K	all three correct means move to heat
Fixed quantity in Boyle	temperature	one wrong means reteach
R and its unit	8.314 J mol-1 K-1	two wrong means back to act one

09 Tutor FAQ

When do I use PV = nRT instead of P1V1 = P2V2?

Use a law when one quantity is fixed between two states; use PV = nRT when all three change or you need moles.

Why must temperature be in kelvin?

Because the laws come from ratios of absolute temperature; Celsius has an arbitrary zero and breaks the ratio.

How many significant figures?

Match the data, usually three; keep one extra through the working and round at the end.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.