Density across states

Take the same lump of iron and imagine it as a solid bar, a puddle of molten metal, and a wisp of vapour. Same iron, same mass of particles — yet three very different densities. Density across states asks why, and the answer turns out to hinge on nothing more exotic than how tightly a substance's particles are packed together. For almost every substance the order is simple: solid is densest, liquid next, gas least dense. But water refuses to play along — ice, a solid, floats on its own liquid, and that single stubborn exception is one of the most-tested facts in this chapter. This article builds the general trend from particle spacing, works through the water exception with real numbers, and gives you the calculation skills to handle any solid-liquid-gas density question ICSE Class 8 can throw at you.

The core insight

For a given substance, density falls as solid to liquid to gas because the same mass of particles spreads into ever-larger volumes, except for water, where ice occupies more volume — hence less density — than the liquid it froze from.

The core idea

Density is defined for any sample as mass packed into volume:

ρ=mV\rho = \frac{m}{V}

where: ρ\rho is density, mm is the mass of the sample, and VV is the volume it occupies. For a fixed mass of a substance, density is entirely a story about volume — squeeze the same particles into less space and density rises; let them spread into more space and density falls.

Why the states differ. The three states differ in how closely their particles are packed and how strongly they attract one another.

  • In a solid, particles sit in fixed positions, held close by strong inter-particle attraction, so a given mass occupies the smallest possible volume.
  • In a liquid, particles are still close but free to slide past one another, leaving slightly more empty space than in the solid.
  • In a gas, particles fly about independently with negligible attraction between them, so the same mass spreads across a hugely larger volume.

Because volume grows sharply from solid to liquid to gas while mass stays fixed, density falls in the same order for a given substance:

ρsolid>ρliquid>ρgas\rho_{\text{solid}} > \rho_{\text{liquid}} > \rho_{\text{gas}}

Solid iron is denser than molten iron, which is far denser than iron vapour — the general rule most substances obey.

The water exception. Water breaks this pattern at the solid-liquid step. When water freezes, its molecules lock into an open hexagonal crystal that takes up more room than the same mass of liquid water — so, unusually,

ρice<ρliquid water\rho_{\text{ice}} < \rho_{\text{liquid water}}

This is why ice cubes float rather than sink, and why icebergs ride mostly submerged but never disappear beneath the surface. It is the one case examiners expect you to name by heart.

Temperature link. Heating a substance (without a change of state) usually expands it — volume rises, mass is unchanged, so density falls; cooling contracts it and density rises. This general heating-cooling rule is separate from water's freezing-point quirk described above.

Figure
Three boxes showing particles packed tightly in a solid loosely in a liquid and widely spaced in a gas with density falling from solid to liquid to gas
Same mass, different packing — density falls solid to liquid to gas Solid highest density Liquid medium density Gas lowest density
Derivation ADensity falls when the same mass spreads into a larger volume

The goal is to show, starting only from the definition ρ=m/V\rho = m/V, exactly why a fixed mass of particles must become less dense whenever the particles rearrange into a larger volume — the reasoning that underlies both the general solid-to-gas trend and the water exception, and that examiners expect you to reproduce with actual numbers rather than just quote as a rule.

Step 1. Fix the mass. Take a sample of a pure substance and let it change state — melt, vaporise, or freeze. No matter is added or removed in any of these changes, so the mass mm of the sample stays exactly the same throughout.

Step 2. Track the volume. A change of state rearranges how closely the particles are packed. Melting a solid loosens the fixed arrangement into a looser one, so VV increases a little. Vaporising a liquid scatters the particles far apart, so VV increases enormously. In water's special case, freezing into ice locks particles into an open hexagonal structure that is roomier than liquid water, so VV also increases on freezing, even though freezing is normally a "gain order, lose volume" change for most substances.

Step 3. Apply ρ=m/V\rho = m/V with mm held fixed. Since density is mass divided by volume, and the numerator mm does not change while the denominator VV grows, the fraction m/Vm/V must shrink. Algebraically, if V2>V1V_2 > V_1 and mm is unchanged, then m/V2<m/V1m/V_2 < m/V_1, so ρ2<ρ1\rho_2 < \rho_1.

Step 4. Read off both results at once. Applied to solid to liquid to gas, growing volume at each step gives ρsolid>ρliquid>ρgas\rho_{\text{solid}} > \rho_{\text{liquid}} > \rho_{\text{gas}}. Applied to water freezing, the unusually large volume increase gives ρice<ρliquid water\rho_{\text{ice}} < \rho_{\text{liquid water}} — the same single argument, mass fixed and volume compared, explains the general rule and its one famous exception.

Worked example

100 g100\ \text{g} of liquid water occupies 100 cm3100\ \text{cm}^3 at 00 degrees Celsius. When this water freezes completely into ice at 00 degrees Celsius, its volume increases to 109 cm3109\ \text{cm}^3, while its mass stays the same. Find the density of the ice and compare it with the density of the liquid water.

Step 1. Find the density of the liquid water using ρ=m/V\rho = m/V.

ρwater=100 g100 cm3=1 g/cm3\rho_{\text{water}} = \frac{100\ \text{g}}{100\ \text{cm}^3} = 1\ \text{g/cm}^3

Step 2. Find the density of the ice, using the same mass but the new, larger volume.

ρice=100 g109 cm3≈0.917 g/cm3\rho_{\text{ice}} = \frac{100\ \text{g}}{109\ \text{cm}^3} \approx 0.917\ \text{g/cm}^3

Step 3. Compare the two results directly.

ρice≈0.917 g/cm3<ρwater=1 g/cm3\rho_{\text{ice}} \approx 0.917\ \text{g/cm}^3 < \rho_{\text{water}} = 1\ \text{g/cm}^3

Answer: the ice is less dense than the liquid water it formed from (0.917 g/cm30.917\ \text{g/cm}^3 versus 1 g/cm31\ \text{g/cm}^3), because freezing expands water rather than contracting it — exactly why ice floats.

Competitive stretch

A metal has a density of 8.9 g/cm38.9\ \text{g/cm}^3 solid and 8.0 g/cm38.0\ \text{g/cm}^3 liquid, for the same mass. Since ρ=m/V\rho = m/V and mm is unchanged, the drop in density on melting tells you the volume must have increased — the molten metal's particles have loosened from their fixed positions into a slightly more spread-out arrangement, exactly the ordinary solid-denser-than-liquid pattern that water alone reverses.

Common traps

  • Assuming every solid is denser than its own liquid. True for almost all substances, but water/ice is the standard exception you must name — do not apply the general rule to water without flagging it.
  • Thinking a gas is "weightless" because it is least dense. Gases have mass and density; they are less dense than solids or liquids purely because their particles are spread far apart, not because they lack mass.
  • Believing mass changes during melting, freezing, or heating. For a fixed sample of a pure substance, mass stays constant through any change of state or temperature — it is the volume that changes, and that change is what drives the density change.
  • Stating the trend without the particle-spacing reason. Writing "solid is denser than gas" with no mention of tighter versus looser particle packing misses the explanation examiners are actually looking for.

Ask the tutor: Want to work through more solid-liquid-gas density comparisons or see why the water exception matters for icebergs and lakes freezing from the top down?

Does every liquid expand when it freezes, like water does?

No, water is unusual. Most substances contract on freezing, because the solid's fixed, tightly packed particle arrangement takes up less room than the liquid's looser one, which is exactly why most solids are denser than their own liquid. Water's molecules happen to lock into an open hexagonal crystal on freezing that takes up more space than liquid water, so ice is the exception rather than the rule. Always name water specifically when asked for an exception; do not generalise it to other substances.

If gas particles are far apart why do gases still have a measurable density at all?

Because density only needs mass and volume, not closeness of packing. A sample of gas still has real mass, made up of the same particles as its solid or liquid form, and it occupies a definite volume in its container. Dividing that mass by that (large) volume gives a small but perfectly real number — gas density is simply much lower than solid or liquid density because the same mass is spread across a far bigger space, not because the gas has no mass.

How do I remember whether density increases or decreases when something is heated?

Think mass first, volume second. Heating a fixed sample (without changing its state) almost always makes it expand, so its volume increases while its mass stays exactly the same. Since density is mass divided by volume, a bigger volume with the same mass gives a smaller density — so heating generally lowers density, and cooling generally raises it. The one place this simple rule needs care is water very close to its freezing point, which is a special case beyond this topic.

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