Senior 2 practice book · Unit 7 of 10

Ideal Gas Laws

50 questions that complete the Senior 2 quiz for this unit: 27 core and 23 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

A temperature of 0 °C means the gas has no heat energy, so its volume or pressure should be zero.0 °C is only the melting point of ice (273 K). Gas laws use kelvin; the volume or pressure would become zero only at 0 K (−273 °C).
A temperature RISE of 20 °C must be converted to 293 K.A change of 1 °C is the same size as a change of 1 K, so a rise of 20 °C is a rise of 20 K. Only actual temperatures need + 273.
The pressure shown on a tyre gauge is the pressure to use in the gas laws.A tyre gauge shows the pressure ABOVE atmospheric (gauge pressure). The gas laws need the absolute pressure = gauge reading + atmospheric pressure.
When a gas is compressed at constant temperature, its particles move faster.The average speed depends only on temperature. In a slow compression the particles keep the same speed but hit the walls more often because they have less space.
Gas particles slow down and settle to the bottom of a container after a while.Gas particles collide elastically and keep moving randomly for as long as the temperature stays the same; the gas always fills its container.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

Quantities of state of a gas and their units: pressure (Pa, kPa, atm, absolute and gauge) and volume (cm³, L, m³)
The kelvin (absolute) temperature scale and absolute zero
Boyle's law: statement and calculations
Charles's law: statement and calculations
Pressure (Gay-Lussac's) law: statement and calculations
General gas equation P₁V₁/T₁ = P₂V₂/T₂
Gas-law graphs and extrapolation to absolute zero
Ideal gas equation PV = nRT and the amount of gas (moles)
Dalton's law of partial pressures
Kinetic theory explanation of gas pressure and the gas laws
Experiments to verify the gas laws: apparatus, readings and precautions
Real gases and the ideal-gas model
Everyday applications: tyres, syringes, breathing, balloons, sealed packets

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 23 harder ones are marked ★ Challenge.

1True or false
All real gases turn into liquids before absolute zero is reached.
Show answer
Answer: True
Every real gas condenses when cooled enough; even helium liquefies at about 4 K.
Common mistakeSome think gases stay gases at any temperature, but cooling slows the particles until attractions hold them together.
2True or false · ★ Challenge
Gas particles in a closed container at constant temperature gradually slow down and finally settle on the floor.
Show answer
Answer: False
Collisions between gas particles and with the walls are elastic, so they keep their kinetic energy and keep moving as long as the temperature is constant.
Common mistakeThinking of gas particles like balls that lose energy at every bounce is the error; their collisions do not lose energy.
3True or false
At constant pressure, the volume of a gas is directly proportional to its Celsius temperature.
Show answer
Answer: False
V is proportional to the KELVIN temperature; in °C the V–θ line does not pass through the origin.
Common mistakeThe word 'temperature' in Charles's law always means absolute temperature, not °C.
4Multiple choice · ★ Challenge
When a real gas is squeezed to a very high pressure, PV is found to differ from its value at low pressure. What is the main reason?
1. AThe gas loses mass as it is squeezed
2. BParticle volume and attractions now matter
3. CDalton's law no longer applies
4. DThe temperature is not in kelvin
Show answer
Answer: B. Particle volume and attractions now matter
Packed close together, the particles' own volume and the attractions between them are no longer negligible, so the gas is not ideal.
Common mistakeChoosing 'the gas loses mass' assumes a leak; with a sealed gas the deviation comes from the particles themselves.
5True or false
The general gas equation P₁V₁/T₁ = P₂V₂/T₂ can be used only if the mass of gas stays the same.
Show answer
Answer: True
The equation is for a fixed mass of gas; if gas leaks out or is added, PV/T changes.
Common mistakeSome apply it to a tyre that is being pumped up, but adding air changes the amount of gas.
6True or false
In a mixture of gases that do not react, each gas exerts the same pressure it would exert if it alone filled the whole container.
Show answer
Answer: True
This is Dalton's law: each gas has its own partial pressure, and the total is their sum.
Common mistakeSome think the gases share one pressure equally; each gas's pressure depends on its own amount.
7Multiple choice · ★ Challenge
A fixed mass of gas is compressed at constant temperature until its pressure is 5 times as large. Its density becomes:
1. AOne fifth as large
2. BUnchanged, as the mass is fixed
3. C25 times as large
4. D5 times as large
Show answer
Answer: D. 5 times as large
Boyle: the volume becomes 1/5 as large; the mass is unchanged, so density = m ÷ V becomes 5 times as large.
Common mistake'Unchanged' looks only at the mass; density also depends on volume, which falls to one fifth.
8Fill in the blank · ★ Challenge
At the same temperature and pressure, 2 mol of a gas occupies ______ times the volume of 0.5 mol of the gas.
Show answer
Answer: 4
V = nRT/P, so V ∝ n at fixed T and P: 2 ÷ 0.5 = 4.
Common mistakeSome answer 2 by reading only the '2 mol'; compare the two amounts: 2 is four times 0.5.
9True or false
When PV = nRT is used, the pressure must be in pascals and the volume in cubic metres.
Show answer
Answer: True
R = 8.31 J/(mol K) is in SI units, so P must be in Pa, V in m³ and T in K.
Common mistakeUnlike Boyle's law, PV = nRT has a constant with units, so kPa or cm³ give wrong answers.
10Multiple choice · ★ Challenge
A gas is compressed SLOWLY so that its temperature stays constant. What happens to the average speed of its particles?
1. AIt stays the same
2. BIt doubles if the volume is halved
3. CIt increases
4. DIt decreases
Show answer
Answer: A. It stays the same
Average speed depends only on temperature; at constant temperature it is unchanged. The pressure rises because collisions with the walls are more frequent.
Common mistake'It increases' mixes up a slow compression with a fast one; only a fast compression warms the gas.
11Fill in the blank
For a fixed mass of gas at constant volume, P/T = constant. This is called the ______ law.
Show answer
Answer: pressure (Gay-Lussac's)
At constant volume the pressure is proportional to the kelvin temperature: the pressure law, also called Gay-Lussac's law.
Common mistakeNaming Charles's law mixes up which quantity is held constant: Charles's law has constant PRESSURE.
12Multiple choice
Under which conditions does a real gas behave most like an ideal gas?
1. AHigh pressure and low temperature
2. BLow pressure and high temperature
3. CLow pressure and low temperature
4. DHigh pressure and high temperature
Show answer
Answer: B. Low pressure and high temperature
At low pressure the particles are far apart (their own volume is negligible) and at high temperature they move fast, so attractions matter little.
Common mistake'High pressure' is tempting because gases are often studied in cylinders, but squeezed particles feel each other's forces.
13Multiple choice · ★ Challenge
A gas is at 7 °C. To what Celsius temperature must it be heated to DOUBLE its kelvin temperature?
1. A287 °C
2. B280 °C
3. C560 °C
4. D14 °C
Show answer
Answer: A. 287 °C
7 °C = 280 K; doubled = 560 K; 560 − 273 = 287 °C.
Common mistake14 °C doubles the Celsius number, which does not double the kelvin temperature; 560 °C forgets to convert back to °C.
14Multiple choice
In an experiment to verify Boyle's law, which two quantities must be kept constant?
1. AThe mass of gas and its temperature
2. BThe pressure and the volume
3. CThe volume and the mass of gas
4. DThe pressure and the temperature
Show answer
Answer: A. The mass of gas and its temperature
Boyle's law relates P and V for a FIXED MASS of gas at CONSTANT TEMPERATURE; P and V are the variables being measured.
Common mistakeRemembering only 'constant temperature' and forgetting that leaking gas (changing mass) also spoils the result is common.
15Multiple choice · ★ Challenge
In Kigali, where atmospheric pressure is about 85 kPa, a tyre gauge on a moto reads 200 kPa. What absolute pressure must be used in gas-law calculations?
1. A200 kPa
2. B170 kPa
3. C285 kPa
4. D115 kPa
Show answer
Answer: C. 285 kPa
A gauge reads pressure above atmospheric: absolute pressure = 200 + 85 = 285 kPa.
Common mistakeUsing 200 kPa directly ignores that the gauge reads zero, not 85 kPa, when the tyre is flat and open to the air.
16Fill in the blank
An empty plastic bottle is tightly closed at the top of Mount Bisoke and carried down to Musanze, where the air pressure is higher. The bottle is ______ (crushed / swollen).
Show answer
Answer: crushed
The higher outside pressure squeezes the bottle until the air inside is compressed to the same pressure (Boyle's law).
Common mistakeThinking it swells reverses the effect: going DOWN a mountain, the outside pressure increases.
17Short answer · ★ Challenge
Explain, using Charles's law, why a hot-air balloon rises when the air inside it is heated.
Show answer
Model answer: Heating the air at (about) atmospheric pressure makes it expand (V ∝ T). Some air leaves through the open bottom, so the balloon contains less mass of air in the same volume: the hot air is less dense than the cool air outside. The upthrust from the surrounding air becomes greater than the total weight, so the balloon rises.
Common mistakeSaying 'hot air rises' without explanation misses the key step: heating lowers the DENSITY of the air inside.
18Multiple choice
A blown-up balloon placed in a fridge shrinks. Which gas law does this show most directly?
1. ADalton's law
2. BThe pressure law
3. CCharles's law
4. DBoyle's law
Show answer
Answer: C. Charles's law
The pressure in the balloon stays about the same as the air outside while the temperature falls, so the volume decreases: V ∝ T (Charles's law).
Common mistakeBoyle's law is tempting because the volume changes, but Boyle's law needs constant TEMPERATURE, and here the temperature falls.
19Fill in the blank · ★ Challenge
The barrel of a bicycle pump holds 300 cm³ of air at 100 kPa. The plunger is pushed in slowly (constant temperature) until the valve to the tyre opens at 250 kPa. The volume of air in the barrel when the valve opens is ______ cm³.
Show answer
Answer: 120
P₁V₁ = P₂V₂: V₂ = 100 × 300 ÷ 250 = 120 cm³.
Common mistakeMultiplying instead of dividing (300 × 250 ÷ 100 = 750 cm³) gives a larger volume at a higher pressure, which is impossible.
20Fill in the blank
In a Charles's law experiment with a capillary tube of uniform bore, the volume of trapped air is represented by the ______ of the air column.
Show answer
Answer: length
V = cross-section area × length; with a uniform bore the area is constant, so V ∝ length.
Common mistakeSome try to measure the volume directly; with a uniform tube the length is enough.
21Multiple choice · ★ Challenge
A student plots volume against temperature (°C) for the same mass of gas at two different constant pressures. Line A is steeper than line B. What can be concluded?
1. AA is at the lower pressure; both meet −273 °C
2. BThe two lines cannot be for the same gas
3. CA is at the lower pressure; they meet the axis at different points
4. DA is at the higher pressure; both meet −273 °C
Show answer
Answer: A. A is at the lower pressure; both meet −273 °C
At lower pressure the gas has a larger volume at each temperature, so its line is steeper; for any pressure, V becomes zero at −273 °C.
Common mistakeThinking higher pressure gives a steeper line forgets Boyle's law: a higher pressure means a SMALLER volume at the same temperature.
22Multiple choice
The temperature of the water in a beaker rises by 15 °C. What is this rise in kelvin?
1. A288 K
2. B30 K
3. C15 K
4. D258 K
Show answer
Answer: C. 15 K
A kelvin and a Celsius degree are the same size, so a CHANGE of 15 °C is a change of 15 K.
Common mistake288 K adds 273 to a temperature difference; + 273 is only for converting an actual temperature.
23Multiple choice · ★ Challenge
A gas changes from 100 kPa, 3.0 L and 300 K to 150 kPa and 2.5 L. What is its new temperature?
1. A240 K
2. B375 K
3. C250 K
4. D450 K
Show answer
Answer: B. 375 K
T₂ = T₁ × P₂V₂/(P₁V₁) = 300 × (150 × 2.5) ÷ (100 × 3.0) = 300 × 375 ÷ 300 = 375 K.
Common mistake450 K ignores the change in volume (uses only 150/100); in the general gas equation both P and V change.
24True or false
A temperature of −20 °C is equal to 253 K.
Show answer
Answer: True
T = θ + 273 = −20 + 273 = 253 K.
Common mistakeLearners sometimes subtract 273 or ignore the minus sign, getting 293 K.
25Multiple choice
A chemistry book writes the ideal gas law as PV = nRT. What quantity does n measure, and in what unit?
1. AThe amount of gas, in moles
2. BThe number of molecules, with no unit
3. CThe collisions per second, in hertz
4. DThe density of the gas, in kg/m³
Show answer
Answer: A. The amount of gas, in moles
n is the amount of substance in moles; R = 8.31 J/(mol K) is the molar gas constant.
Common mistake'The number of molecules' is tempting, but that would need a different constant; in PV = nRT, n is in MOLES.
26Multiple choice · ★ Challenge
A sample of gas in a syringe occupies 250 cm³ when it is at 77 °C. The syringe is put in a freezer box at −23 °C with the pressure unchanged. What volume does the gas now occupy?
1. A350 cm³
2. B75 cm³
3. C250 cm³
4. D179 cm³
Show answer
Answer: D. 179 cm³
T₁ = 350 K, T₂ = 250 K. V₂ = V₁ × T₂/T₁ = 250 × 250 ÷ 350 ≈ 179 cm³.
Common mistake75 cm³ comes from using Celsius temperatures (250 × 23 ÷ 77, ignoring the sign); temperatures must be in kelvin.
27Fill in the blank
A 1.5 L bottle of water has a volume of ______ cm³.
Show answer
Answer: 1500
1 L = 1000 cm³, so 1.5 L = 1.5 × 1000 = 1500 cm³.
Common mistakeLearners often use 1 L = 100 cm³; a litre is a cube 10 cm on each side, so it holds 1000 cm³.
28Short answer · ★ Challenge
Explain why, in Boyle's law, pressures may be put in kPa and volumes in cm³, but in Charles's law the temperatures may NOT be put in °C.
Show answer
Model answer: In P₁V₁ = P₂V₂ the same unit appears on both sides, so any pressure unit and any volume unit cancel, as long as each is used consistently. In V₁/T₁ = V₂/T₂, V is proportional to T only when T is measured from absolute zero; the Celsius scale has a different zero (0 °C = 273 K), so °C values give wrong ratios. Temperatures must be in kelvin.
Common mistakeA typical error is to think kelvin is needed just because it is the SI unit; the real reason is that the gas laws need temperatures measured from absolute zero.
29Multiple choice
More air is pumped into a tyre whose volume and temperature stay the same. Why does the pressure rise?
1. AThe particles attract each other more strongly
2. BThe particles move faster
3. CMore particles hit each part of the walls per second
4. DThe particles become bigger
Show answer
Answer: C. More particles hit each part of the walls per second
At the same temperature the particles have the same average speed, but with more particles in the same space there are more collisions per second on each square centimetre.
Common mistake'The particles move faster' is wrong because the temperature, which sets their average speed, is constant.
30Multiple choice · ★ Challenge
How many moles of gas are there in 0.0249 m³ at 100 kPa and 27 °C? (R = 8.31 J/(mol K))
1. A11 mol
2. B1.0 × 10³ mol
3. C1.0 × 10⁻³ mol
4. D1.0 mol
Show answer
Answer: D. 1.0 mol
n = PV/(RT) = (100 000 × 0.0249) ÷ (8.31 × 300) = 2490 ÷ 2493 ≈ 1.0 mol.
Common mistake11 mol uses 27 instead of 300 K; 1.0 × 10⁻³ mol uses 100 (kPa) instead of 100 000 Pa.
31Multiple choice
A gas syringe holds 450 cm³ of air. What is this volume in cubic metres?
1. A0.45 m³
2. B4.5 × 10⁻⁶ m³
3. C4.5 × 10⁻⁴ m³
4. D4.5 × 10⁻² m³
Show answer
Answer: C. 4.5 × 10⁻⁴ m³
1 m³ = 1 000 000 cm³, so 450 cm³ = 450 ÷ 1 000 000 = 4.5 × 10⁻⁴ m³.
Common mistake0.45 m³ divides by 1000 (the factor for litres); a cubic metre is 100³ = 10⁶ cm³.
32Short answer · ★ Challenge
The V–θ graph for a gas at constant pressure extrapolates to zero volume at −273 °C. Explain why no real gas actually reaches zero volume at this temperature.
Show answer
Model answer: Real gases turn into liquids (and then solids) before −273 °C is reached, and their particles have their own volume, so the volume cannot fall to zero. The extrapolated line describes an ideal gas, whose particles are treated as points with no attractions.
Common mistakeThe error is to treat the extrapolated line as a measured result; it is only an idealised prediction.
33Multiple choice
When you breathe in, your diaphragm moves down and your chest volume increases. What happens to the air pressure in your lungs?
1. AIt rises above atmospheric, so air flows in
2. BIt falls below atmospheric, so air flows in
3. CIt stays equal to atmospheric all the time
4. DIt falls to zero until the lungs are full
Show answer
Answer: B. It falls below atmospheric, so air flows in
Larger volume means lower pressure (Boyle's law); air flows from the higher outside pressure into the lungs.
Common mistake'It rises' reverses Boyle's law; air always flows from higher to lower pressure.
34Multiple choice
A sealed packet of crisps bought in Rubavu, on the shore of Lake Kivu, is carried up to a high village in the Virunga mountains. The packet swells. Why?
1. AAir leaks into the packet
2. BThe air in the packet becomes hotter
3. CThe outside air pressure is higher there
4. DThe outside air pressure is lower there
Show answer
Answer: D. The outside air pressure is lower there
Higher up, atmospheric pressure is lower, so the air inside the sealed packet expands until its pressure matches the outside (Boyle's law).
Common mistake'The air is hotter' is unlikely: it is usually colder in the mountains, which would make the packet shrink, not swell.
35Short answer · ★ Challenge
A gas cylinder can safely hold a pressure of up to 1500 kPa. It is filled to 1000 kPa at 17 °C. Assuming its volume stays constant, at what temperature (in °C) would it reach its safe limit? Why are gas cylinders kept in the shade?
Show answer
Model answer: Pressure law: T₂ = T₁ × P₂/P₁ = 290 × 1500 ÷ 1000 = 435 K = 162 °C. In the sun or near a fire the gas heats up and its pressure rises; keeping cylinders in the shade keeps the pressure well below the safe limit.
Common mistakeUsing 17 °C directly gives 25.5 °C, which would make normal sunny days dangerous; always convert to kelvin first.
36Short answer · ★ Challenge
A fixed mass of gas at constant pressure has volume 54.6 cm³ at 0 °C, 64.6 cm³ at 50 °C and 74.6 cm³ at 100 °C. Show that the volume would become zero at about −273 °C.
Show answer
Model answer: The volume rises by 10 cm³ for every 50 °C, i.e. 0.2 cm³ per °C (a straight line). To fall from 54.6 cm³ to zero needs a drop of 54.6 ÷ 0.2 = 273 °C below 0 °C, i.e. −273 °C.
Common mistakeA common slip is to divide 54.6 by 10 instead of by the rate per degree (0.2 cm³/°C).
37Multiple choice
In a Charles's law experiment, a capillary tube of trapped air is placed in a water bath with a thermometer. Why is the water stirred before each reading?
1. ATo keep the pressure of the air constant
2. BTo stop the water from boiling
3. CTo push the trapped air down the tube
4. DSo the water and air are at the thermometer's temperature
Show answer
Answer: D. So the water and air are at the thermometer's temperature
Stirring makes the temperature of the water uniform, so the trapped air and the thermometer are at the same temperature.
Common mistakeChoosing 'to keep the pressure constant' confuses stirring with the open top of the tube, which is what keeps the pressure constant.
38Multiple choice
Air is about 21 % oxygen by number of molecules. In Kigali the atmospheric pressure is about 85 kPa. What is the partial pressure of oxygen there?
1. A66 kPa
2. B85 kPa
3. C18 kPa
4. D21 kPa
Show answer
Answer: C. 18 kPa
Partial pressure = fraction × total = 0.21 × 85 ≈ 18 kPa.
Common mistake21 kPa is the sea-level value (21 % of 100 kPa); at Kigali's height the total pressure is lower, so the oxygen partial pressure is too.
39Short answer · ★ Challenge
In a pressure-law experiment, a flask of air is heated in a water bath and connected to a pressure gauge by a long rubber tube that stays at room temperature. Explain how this affects the results and suggest an improvement.
Show answer
Model answer: The air inside the long tube is not heated, so the average temperature of the trapped air is lower than the bath temperature. The pressure rises less than expected, so P/T is not constant (the values come out too low at high temperatures). Improvement: use a short, narrow tube and keep the whole flask under the water, so almost all the air is at the bath temperature.
Common mistakeLearners often ignore the air in the connecting tube; all the trapped air must be at the measured temperature.
40Multiple choice
A sealed glass jar contains air at 27 °C and 100 kPa. It is placed in boiling water at 100 °C. Ignoring expansion of the jar, what is the new pressure of the air?
1. A124 kPa
2. B173 kPa
3. C80 kPa
4. D370 kPa
Show answer
Answer: A. 124 kPa
P₂ = P₁ × T₂/T₁ = 100 × 373 ÷ 300 ≈ 124 kPa.
Common mistake370 kPa comes from 100 × 100 ÷ 27, using °C; only kelvin temperatures give the correct ratio.
41Short answer · ★ Challenge
Hydrogen is collected over water in a gas jar at 25 °C. The total pressure inside is 98 kPa and the water vapour pressure at 25 °C is 3 kPa. Find the pressure of the dry hydrogen and state the law you used.
Show answer
Model answer: Dalton's law of partial pressures: total pressure = sum of partial pressures. p(hydrogen) = 98 − 3 = 95 kPa.
Common mistakeLearners often give 98 kPa, forgetting that the water vapour in the jar also contributes to the total pressure.
42Short answer
Use the particle (kinetic) model to explain why a gas pushes equally on all the walls of its container.
Show answer
Model answer: The gas particles move randomly in all directions at high speed. Because no direction is favoured, on average the same number of particles hit each square centimetre of every wall per second with the same speed, so the pressure is the same on every wall (gravity has only a tiny effect on a gas).
Common mistakeSome think gas pressure acts mostly downwards like the weight of a solid; random motion makes it act equally in all directions.
43Short answer · ★ Challenge
At a depth of 10 m in Lake Kivu the absolute pressure is about 185 kPa; at the surface (1460 m above sea level) it is about 85 kPa. A diver fills her lungs with 6.0 L of air from her tank at 10 m depth and then swims to the surface holding her breath. Calculate the volume the air would try to take and explain why divers are taught to breathe out while rising (temperature constant).
Show answer
Model answer: Boyle's law: P₁V₁ = P₂V₂, so V₂ = 185 × 6.0 ÷ 85 ≈ 13 L. The air would try to more than double in volume, which could over-stretch and damage the lungs, so the diver breathes out steadily to let the extra air escape as the pressure falls.
Common mistakeA common slip is to think the volume decreases as the diver rises; lower pressure means a LARGER volume.
44True or false
For a fixed mass of gas at constant volume, a graph of pressure against temperature in °C passes through the origin.
Show answer
Answer: False
P ∝ T in kelvin. Against °C the line is straight but cuts the temperature axis at −273 °C, not at 0 °C.
Common mistakeLearners forget that 0 °C is not the zero of gas pressure; at 0 °C the gas still has a large pressure.
45Multiple choice
A syringe containing 20 cm³ of air at 100 kPa is sealed and its plunger is pulled out slowly until the volume is 50 cm³. What is the pressure of the trapped air now?
1. A70 kPa
2. B40 kPa
3. C100 kPa
4. D250 kPa
Show answer
Answer: B. 40 kPa
P₂ = P₁V₁ ÷ V₂ = 100 × 20 ÷ 50 = 40 kPa (lower than atmospheric, so the plunger is pushed back in when released).
Common mistake250 kPa uses V₂/V₁ instead of V₁/V₂; a bigger volume must give a SMALLER pressure.
46Short answer · ★ Challenge
An oxygen tank for a hospital in Huye has a volume of 0.050 m³; the oxygen inside is at an absolute pressure of 400 kPa and 27 °C. How many grams of oxygen does it hold? (molar mass 32 g/mol, R = 8.31 J/(mol K))
Show answer
Model answer: n = PV/(RT) = (400 000 × 0.050) ÷ (8.31 × 300) = 20 000 ÷ 2493 ≈ 8.02 mol. Mass = 8.02 × 32 ≈ 257 g (about 0.26 kg).
Common mistakeForgetting to change kPa to Pa makes the answer 1000 times too small.
47Short answer · ★ Challenge
A student's Boyle's law results are: P (kPa) 100, 125, 160, 200, 250; V (cm³) 40, 32, 25, 20, 16. Show that the results obey Boyle's law, and predict the volume at 80 kPa.
Show answer
Model answer: PV = 100 × 40 = 4000; 125 × 32 = 4000; 160 × 25 = 4000; 200 × 20 = 4000; 250 × 16 = 4000. PV is constant, so Boyle's law is obeyed. At 80 kPa: V = 4000 ÷ 80 = 50 cm³.
Common mistakeChecking only that V falls as P rises is not enough; you must show that P × V is CONSTANT.
48Short answer
The nozzle of a gas syringe is sealed with a finger and the plunger is pushed in slowly. Explain why it gets harder and harder to push the plunger.
Show answer
Model answer: As the plunger moves in, the volume of the trapped air decreases. By Boyle's law (PV constant) its pressure rises. The trapped air therefore pushes back on the plunger with a larger force (F = PA), so a bigger push is needed.
Common mistakeSome say the air 'runs out of space'; the key idea is that the PRESSURE rises as the volume falls.
49Multiple choice
For a fixed mass of gas at constant temperature, what does a graph of PV (y-axis) against P (x-axis) look like?
1. AA straight line through the origin
2. BA horizontal straight line
3. CA straight line sloping down
4. DA curve that falls steeply
Show answer
Answer: B. A horizontal straight line
By Boyle's law PV is constant, so it does not change as P changes: a horizontal line.
Common mistake'Straight line through the origin' describes P against 1/V, not PV against P.
50Short answer · ★ Challenge
In a diesel engine, air at 100 kPa and 27 °C is squeezed from 500 cm³ to 50 cm³, and its pressure rises to 2000 kPa. Find the temperature of the air in °C, and explain why diesel engines need no spark plug.
Show answer
Model answer: P₁V₁/T₁ = P₂V₂/T₂: T₂ = 300 × (2000 × 50) ÷ (100 × 500) = 300 × 2 = 600 K = 327 °C. The compressed air becomes hot enough to ignite the diesel fuel sprayed into it, so no spark is needed.
Common mistakeLearners often use Boyle's law here, but the temperature changes, so the general gas equation is needed.