Question bank › GCSE Physics › Particle model of matter
Density and changes of state (RP5)
Answer on paper first, then reveal the mark scheme one mark at a time.
1Grade 1–3Foundation3 marks
The diagram shows the arrangement of particles in three states of matter, X, Y and Z.
(a) Which box, X, Y or Z, shows a gas? [1]
(b) Describe the motion of the particles in a solid. [1]
(c) Name the change of state when a gas turns into a liquid. [1]
(a) Y(1)
(b) they vibrate (about fixed positions) allow 'vibrate' / 'vibrate in place'; reject 'do not move' / 'move freely' / 'move around each other'(1)
(c) condensation / condensing(1)
Answer: (a) Y (b) vibrate about fixed positions (c) condensation
Examiner tip: Particles in a solid do move — they vibrate. 'They don't move' scores zero.
2Grade 4–53 marks
A metal block has a mass of 0.60 kg and a volume of $2.4 \times 10^{-4}$ m³.
(a) Write down the equation that links density ($\rho$), mass ($m$) and volume ($V$). [1]
(b) Calculate the density of the block. [2]
(a) $\rho = \dfrac{m}{V}$ allow density = mass ÷ volume in words(1)
(b) $\rho = \dfrac{0.60}{2.4 \times 10^{-4}}$(1)
(b) 2500 kg/m³ allow 2.5 × 10³ kg/m³(1)
Answer: (a) $\rho = m/V$ (b) 2500 kg/m³
Examiner tip: Type the standard form into the calculator with the ×10ˣ key, not as separate multiplications.
3Grade 4–55 marks
A student wants to find the density of a small, irregularly shaped stone.
(a) Describe how she could measure the volume of the stone using a measuring cylinder and water. [2]
(b) The mass of the stone is 54.0 g. The water level rises from 30.0 cm³ to 50.0 cm³ when the stone is added.
Calculate the density of the stone in g/cm³. [2]
(c) Give the density of the stone in kg/m³. [1]
(a) part-fill the measuring cylinder with water and read the volume; (carefully) lower the stone in so it is fully submerged and read the new volume alternative method for both marks: fill a displacement (eureka) can to the spout, lower the stone in and collect the displaced water in the measuring cylinder (1)(1)
(a) volume of stone = new volume − starting volume eureka-can method: volume of water collected = volume of stone (1)(1)
(b) $\rho = \dfrac{54.0}{20.0}$(1)
(b) 2.7 g/cm³ allow 2.70(1)
(c) 2700 kg/m³ allow ecf: their (b) × 1000(1)
Answer: (a) record water level, fully submerge stone, record new level; volume = difference (b) 2.7 g/cm³ (c) 2700 kg/m³
Examiner tip: Use the change in water level (20.0 cm³) as the volume, not the final reading.
4Grade 1–3Foundation4 marks
When iodine crystals are heated gently, they change directly from a solid into a purple gas.
(b) A teacher seals some iodine crystals inside a glass flask. The total mass of the flask and the iodine is 154.6 g.
The teacher heats the flask until all of the iodine has turned into a gas.
What is the total mass of the flask and the iodine now? Give a reason for your answer. [2]
(c) When the flask cools down, iodine crystals form on the inside of the glass again.
Give one reason why a change of state is a physical change and not a chemical change. [1]
(a) sublimation (only this box ticked; more than one box ticked = 0)(1)
(b) 154.6 g (allow 'the same' / 'it does not change')(1)
(b) (because) mass is conserved / no particles (of iodine) can escape from the sealed flask / the number of particles stays the same (ignore 'it is sealed' alone; reason only scores if the mass is stated as unchanged)(1)
(c) the change is reversible (allow the material recovers its original properties (when the change is reversed) / no new substance is formed; ignore 'it can change back' without reference to the original substance unless clearly meaning reversible)(1)
Answer: (a) sublimation; (b) 154.6 g — mass is conserved in a sealed flask; (c) it is reversible / no new substance is made
Examiner tip: In (b) many students think a gas is 'lighter' and give a smaller mass — in a sealed container the mass of a changing state never changes.
5Grade 4–5Foundation4 marks
A student wants to find the density of a rectangular block of wood. The diagram shows the dimensions of the block.
(a) Name a measuring instrument the student could use to measure the dimensions of the block. [1]
(b) Calculate the volume of the block. Give the unit. [1]
(c) 0.75 (g/cm³) (correct answer with no working scores 2 marks)(1)
Answer: (a) ruler; (b) 60 cm³; (c) 0.75 g/cm³
Examiner tip: Volume of a cuboid is length × width × height — adding the three lengths together is a common slip that loses all the follow-on marks.
6Grade 4–55 marks
A student determined the density of a liquid.
She measured the mass of an empty measuring cylinder. She poured some of the liquid into the cylinder and measured the mass again.
The diagram shows part of the measuring cylinder containing the liquid.
(a) Give the volume of liquid in the measuring cylinder. [1]
(b) Describe how the student should position her eye when reading the volume. [1]
(c) The table shows her mass readings.
Mass in g
empty measuring cylinder
85.2
measuring cylinder and liquid
122.0
Calculate the density of the liquid in g/cm³. [3]
(a) 46 cm³ (allow 46.0 cm³)(1)
(b) (eye) level with the bottom of the meniscus (allow at eye level with the liquid surface / looking horizontally at the scale; 'at eye level' alone is not enough unless linked to the meniscus or liquid level)(1)
(c) mass of liquid = 122.0 − 85.2 = 36.8 (g)(1)
(c) density = 36.8 / 46 (allow ecf from (a) and from their mass)(1)
(c) 0.80 (g/cm³) (allow 0.8; correct answer with no working scores 3 marks; 122.0/46 = 2.65 scores 1 mark for the method, max 1)(1)
Answer: (a) 46 cm³; (b) level with the bottom of the meniscus; (c) 0.80 g/cm³
Examiner tip: Subtract the mass of the empty cylinder first — dividing 122.0 g by the volume gives the density of 'cylinder plus liquid', which is meaningless.
7Grade 6–75 marks
A kettle contains 0.50 kg of water. The water is boiled until all of it has turned into steam.
(a) Give the mass of the steam produced. [1]
(b) The density of the steam is 0.60 kg/m³.
Calculate the volume of the steam. [2]
(c) The density of liquid water is 1000 kg/m³.
Explain, in terms of particles, why the density of steam is much lower than the density of liquid water. [2]
(a) 0.50 kg (allow 500 g)(1)
(b) V = 0.50 / 0.60 (allow ecf from (a); allow 0.60 = 0.50 / V)(1)
(b) 0.83 m³ (allow 0.833 m³ or 0.8 m³; correct answer with no working scores 2 marks)(1)
(c) the mass / number of particles stays the same (when water turns into steam) (allow the particles are the same / particles do not change)(1)
(c) the particles in steam are much further apart, so the same mass takes up a much larger volume (allow particles in water are close together / touching but in steam they are far apart; do not accept particles get bigger / expand)(1)
Answer: (a) 0.50 kg; (b) 0.83 m³; (c) same particles/mass, but much further apart in a gas so much larger volume
Examiner tip: Particles do not grow when a liquid boils — say the particles move much further apart, so the same mass occupies a bigger volume.
8Grade 8–9Higher7 marks
A student used a displacement (eureka) can to find the density of a small metal statue.
She filled the can with water until water flowed out of the spout and then stopped. She placed an empty beaker under the spout and lowered the statue into the can until it was completely under water.
Measurement
Value
mass of statue
84.2 g
mass of empty beaker
48.3 g
mass of beaker and water collected
79.5 g
density of water = 1.00 g/cm³
(a) Calculate the volume of the statue. [2]
(b) Calculate the density of the statue. Give your answer to 3 significant figures. [2]
(c) The table gives the densities of some metals.
Metal
Density in g/cm³
aluminium
2.70
titanium
4.51
zinc
7.13
brass
8.50
Which metal is the statue most likely to be made of? [1]
(d) Another student did the same experiment but did not fill the can up to the spout before lowering the statue in.
Explain the effect this would have on the value of density he calculated. [2]
(a) mass of water collected = 79.5 − 48.3 = 31.2 g(1)
(a) volume = 31.2 cm³ (allow ecf: their mass of water ÷ 1.00 with unit cm³)(1)
(b) density = 84.2 / 31.2 (allow ecf from (a))(1)
(b) 2.70 g/cm³ (must be 3 s.f.; 2.6987… or 2.7 scores 1 mark; allow 2700 kg/m³)(1)
(c) aluminium (allow ecf: the metal whose density is closest to their (b))(1)
(d) less water would be collected / some of the displaced water stays in the can, so the measured volume is too small (allow volume would be underestimated)(1)
(d) so the calculated density would be too high / larger than the true value (only scores if linked to a smaller volume; 'the result would be inaccurate' alone scores 0)(1)
Answer: (a) 31.2 cm³; (b) 2.70 g/cm³; (c) aluminium; (d) less water collected, volume too small, density too high
Examiner tip: In (d) you must give the direction of the error — 'the result would be inaccurate' scores nothing; say the volume is too small so the density is too big.
9Grade 6–76 marks
A student has a bag of 30 identical glass marbles. Each marble is a small sphere.
She has a balance, a 100 cm³ measuring cylinder and some water.
Describe a method the student could use to determine the density of the glass as accurately as possible.
In your answer you should explain how she should use her measurements to calculate the density. [6]
measure the mass of all the marbles (or a large number, e.g. 20) together on a balance(1)
check / zero (tare) the balance before use(1)
part-fill the measuring cylinder with water (enough to cover the marbles) and record the volume(1)
read the volume at eye level with the bottom of the meniscus(1)
tilt the cylinder / lower the marbles in gently so that no water splashes out(1)
make sure all the marbles are completely under water and there are no trapped air bubbles(1)
record the new volume reading(1)
volume of marbles = final reading − initial reading(1)
density = mass ÷ volume (using the same number of marbles for both)(1)
using many marbles gives a larger mass and a larger volume change, so the reading errors are a smaller fraction of the measurements (more accurate than one marble)(1)
repeat (with different groups of marbles / dry the marbles) and calculate a mean density(1)
Level
Marks
What it looks like
Level 3
5–6
A clear, logically ordered method that would give a valid result: mass of the marbles and volume by displacement (final minus initial reading) are both described, with density = mass ÷ volume, and at least one step that improves accuracy is explained (e.g. using many marbles, reading the meniscus at eye level, avoiding splashing or air bubbles, repeating).
Level 2
3–4
A method for finding both the mass and the volume of the marbles is given, with density calculated from them, but some steps are missing, out of order or unclear, and accuracy is mentioned only briefly or not explained.
Level 1
1–2
Simple, disjointed statements, e.g. weigh the marbles or put them in water, with no clear method for finding the volume or density.
No relevant content
0
Nothing worthy of credit.
Answer: Mass of many marbles on a balance; volume by displacement in a measuring cylinder (final − initial reading, eye level with meniscus, no splashing); density = mass ÷ volume; many marbles and repeats improve accuracy.
Examiner tip: Using lots of marbles is the key accuracy point — one small marble only raises the water level by about 2 cm³, so the reading error is a large fraction of the change.
10Grade 8–9Higher6 marks
A student investigated the density of cooking oil.
She placed an empty measuring cylinder on a balance. She added oil 20 cm³ at a time and recorded the total mass of the cylinder and oil after each addition.
The graph shows her results.
(a) What does the value where the line of best fit meets the vertical axis represent? [1]
(b) Use the graph to determine the density of the cooking oil.
Give your answer in kg/m³. [3]
(c) The student repeated the investigation using the same measuring cylinder and water instead of oil.
Water is more dense than cooking oil.
Describe how the line of best fit for water would compare with the line for oil. [2]
(a) the mass of the (empty) measuring cylinder (allow 60 g is the mass of the cylinder)(1)
(b) a gradient calculation using a large part of the line, e.g. (150 − 60) / (100 − 0) (allow any correct pair of points read from the line)(1)
(b) density = 0.90 g/cm³ (allow 0.88–0.92 g/cm³)(1)
(b) 900 kg/m³ (allow 880–920 kg/m³; allow ecf: correct ×1000 conversion of their g/cm³ value; an answer of 1.5 g/cm³ or 1500 kg/m³ from 150/100 scores 0 for the first two marks but can score the conversion mark)(1)
(c) the line would be steeper / have a greater gradient(1)
(c) (but) it would start at the same point on the vertical axis / have the same intercept (of 60 g) (allow it would pass through (0, 60) / (100, 160))(1)
Answer: (a) mass of the empty cylinder (60 g); (b) gradient 0.90 g/cm³ = 900 kg/m³; (c) steeper, same intercept
Examiner tip: The density is the gradient, not total mass ÷ volume read from one point — that includes the cylinder's mass and gives 1.5 g/cm³.
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