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14.1.3 Density and changes of state

Why density differs between states

Definition

Density

Density is the mass per unit volume of a substance.

  1. Density measures how much mass is packed into a volume, so it depends on how closely the atoms or molecules of a substance are spaced.
  2. In a solid the particles touch one another in a regular arrangement, so a given mass takes up the smallest volume and the density is the highest of the three states.
  3. In a liquid the particles are still close together but irregularly arranged, so the same mass usually occupies a slightly larger volume and the density is a little lower.
  4. In a gas the particles are widely separated with large gaps between them, so the same mass occupies a volume hundreds of times larger and the density is far lower.
  5. Water shows the pattern clearly: liquid water has a density of about 1000 kg/m31000\ \text{kg/m}^31000 kg/m3, while steam at atmospheric pressure has a density of well under 1 kg/m31\ \text{kg/m}^31 kg/m3.
  6. Water is unusual in one respect, because its molecules form an open structure when it freezes, so ice has a density of about 920 kg/m3920\ \text{kg/m}^3920 kg/m3 and floats on liquid water.
  7. The mass of each individual particle is the same in every state, so any change in density comes from a change in volume.

Naming the changes of state

Definition

Change of state

A change of state is a physical change in which a substance changes between the solid, liquid and gas states without becoming a different substance.

Definition

Sublimation

Sublimation is the change of state in which a solid turns directly into a gas without first becoming a liquid.

  1. Melting turns a solid into a liquid, and it happens at the melting point of the substance.
  2. Freezing turns a liquid into a solid, and for a given substance it occurs at the same temperature as melting.
  3. Evaporation turns a liquid into a gas at the surface only, and it can happen at any temperature below the boiling point.
  4. Boiling turns a liquid into a gas throughout the whole liquid, and it happens at one fixed temperature called the boiling point.
  5. Condensation turns a gas into a liquid, which is why droplets form on a cold window.
  6. Sublimation turns a solid straight into a gas, as solid carbon dioxide does at room temperature.
  7. Heating drives melting, evaporation, boiling and sublimation, while cooling drives freezing and condensation.
  8. Every one of these changes alters the spacing, arrangement and movement of the particles without altering the particles themselves.

Mass is conserved

Definition

Conservation of mass

Conservation of mass is the principle that the total mass of a system stays the same because particles are neither created nor destroyed.

  1. The number and the type of particles are unchanged by a change of state, so the total mass afterwards equals the total mass beforehand.
  2. A sealed container placed on a balance shows no change in reading while the substance inside melts, boils or freezes.
  3. An open container shows a falling reading while a liquid evaporates or boils, because vapour leaves the container and is no longer being weighed.
  4. That vapour still exists in the surrounding air, so the mass has been transferred out of the container rather than destroyed.
  5. The reading of an open container can also rise, because water vapour already in the air condenses onto a cold outer surface.
  6. Density can change while mass stays the same, because ρ=mV\rho=\dfrac{m}{V}ρ=Vm​ and only the volume has altered.
  7. For a fixed mass this means density is inversely proportional to volume, so doubling the volume halves the density.

Physical and chemical changes

Definition

Physical change

A physical change is a change in which no new substance is formed, so the material recovers its original properties when the change is reversed.

  1. A change of state is a physical change, because no new substance is produced.
  2. Reversing the conditions recovers the original properties, so ice that has melted and then been refrozen has the same melting point and the same density as before.
  3. The chemical formula is unchanged by a change of state, so ice, liquid water and steam are all H2O\text{H}_{2}\text{O}H2​O.
  4. Some chemical changes behave differently, because new substances with different properties are formed and cooling the products does not bring the original substances back.
  5. Magnesium burning in air is one such change, since the white magnesium oxide powder left behind cannot be turned back into shiny magnesium simply by letting it cool.
  6. Mass is conserved in both kinds of change, so conservation of mass on its own does not tell you whether a change is physical or chemical.
Example

Density change when water boils

  • A sealed container holds 0.018 kg0.018\ \text{kg}0.018 kg of liquid water occupying 1.8×10−5 m31.8\times10^{-5}\ \text{m}^31.8×10−5 m3.
  • Its density is ρ=0.0181.8×10−5=1000 kg/m3\rho=\dfrac{0.018}{1.8\times10^{-5}}=1000\ \text{kg/m}^3ρ=1.8×10−50.018​=1000 kg/m3.
  • All of the water is then boiled, and the steam produced occupies 0.030 m30.030\ \text{m}^30.030 m3.
  • The new density is ρ=0.0180.030=0.60 kg/m3\rho=\dfrac{0.018}{0.030}=0.60\ \text{kg/m}^3ρ=0.0300.018​=0.60 kg/m3.
  • The mass in the calculation is the same both times, because the same water molecules are still present in the sealed container.
  • The density has fallen by a factor of about 170017001700 purely because the molecules have moved much further apart and the volume has increased.
Exam technique

Explaining a density change

  • Start with the separation of the particles, because that is the first marking point in this kind of answer.
  • Move on to the volume of the fixed mass, saying whether it increases or decreases.
  • Finish with the density, using wording such as the same mass now occupies a larger volume, so the density is lower.
  • Write that particles are not created or destroyed whenever a question asks about conservation of mass.
  • Say where the escaped vapour has gone when the container is open, since the mark is for identifying that the system has changed rather than the mass.
  • Give the reason when you classify a change as physical, naming both the absence of a new substance and the recovery of the original properties.
Common Mistake
  • Do not write that particles become bigger, smaller, heavier or lighter during a change of state, because only their spacing, arrangement and movement change.
  • Do not write that mass is lost when a pan of water boils dry, because the mass is now in the water vapour spread through the room.
  • Do not use evaporation and boiling as though they mean the same thing, because evaporation happens only at the surface and at any temperature.
  • Do not assume water follows the usual pattern, because solid ice is less dense than liquid water and so floats on it.
  • Do not call melting or boiling a chemical change, because the substance keeps its identity throughout.
Self review
  • Explain in terms of particle arrangement why a gas has a much lower density than a liquid.
  • Name the change of state that turns a solid directly into a gas.
  • State the difference between evaporation and boiling.
  • Explain why the balance reading falls when an open beaker of water is left in a warm room.
  • Explain how a change of state can alter density while conserving mass.
  • Give one reason why melting ice is a physical change rather than a chemical change.
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14.1.3 Density and changes of state Revision Guide

  1. GCSE
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Revision notes for Edexcel GCSE Physics 14.1.3 Density and changes of state: explanations and worked examples.

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