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School-college Physics Notes: Thermal energy 5.6 Density

Density & particle theory: 5.6 Density and the kinetic particle model - theoretically explaining relative densities of gases, liquids & solids

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5.6 DENSITY

and the particle model - explaining the relative densities of gases, liquids and solids

The density of a material depends on the nature of the material eg air, water, wood or iron AND the physical state of the material, which is how the particles are arranged.

In a closed system, when a substance changes state, it is a physical change (NOT chemical), there is no change in mass (same number of particles), but there is a change in particle arrangement which leads to a change in density.

We can use the particle model of matter to partly explain the differences in density between different materials, and in particular the difference in density between gaseous, liquid and solid state of specific substance.

When explaining different density values, you must consider both the kinetic energy of the particles and the arrangement of the particles.

Applying the particle model to the different densities of the states of matter

GASES: The particles have kinetic energy and can move around at random quite freely.

This enables the particles to spread out and fill all the available space giving a material a very low density compared to liquids and solids.

With very weak intermolecular forces (NOT chemical bonds) of attraction between the particles there is no constraint on their movement - they can't club together to form a liquid or solid.

In a substance like air, the particles are very widely spread out in the atmosphere giving air a very low density.

Density of air in the atmosphere is 1.2 kg/m3.

Density of steam = 0.6 kg/m3.

Hydrogen and helium are the 'lightest', lowest density gases, ρ (H2) = 0.10 kg/m3, ρ (He) = 0.17 kg/m3

Carbon dioxide sinks in air because it is 'heavier', it has a higher density than air, density = 1.9 kg/m3 (air is 1.2).

If you compress a gas, you force the molecules closer together, same mass in smaller volume, so the density increases.

If you heat a gas and it can expand, the particles are further apart and the density will decrease.

LIQUIDS: In liquids, the particles are close together, usually giving high densities a bit less than the solid, but have a much greater than the density of gases, but the particles are NOT in a fixed close packed ordered state as in solids..

The inter-molecular forces between liquid particles are much greater than those between gaseous particles and are strong enough, so they are attracted close together, with enough kinetic energy to just leave a little free space.

The random movement creates a little free space and on average are spaced out just that little bit more than in solids, hence their slightly lower density than the solid - water is a very rare exception to this rule.

Water has a density of 1000 kg/m3, more than 1600 times more dense than steam!

Density of liquid air is 974 kg/m3, see this sharply contrasts with gaseous air, which is over 800 times less dense at 1.2 kg/m3!

Hydrocarbon petroleum oil, typically has a density of 820 kg/m3, less dense than water, so it floats on it!

Mercury atoms have a much greater atomic mass than hydrogen, oxygen or carbon so liquid mercury has a density of 13 584 kg/m3, that is more than 13 times more dense than water!

If you heat a liquid, increasing its temperature, the particles gain kinetic energy and the collisions become more frequent and energetic and this enables the particles on average to spread out a bit more, increasing the liquid volume and lowering the density.

This effect is used in liquid thermometers e.g. those containing a capillary tube of mercury or coloured alcohol.

The thermal expansion is proportional to temperature so you can fit a calibrated linear scale next to the capillary tube.

SOLIDS: The strongest interparticle forces of attraction occur in solids where particles are attracted and compacted as much as is possible.

The particles are packed tightly together in an ordered array - giving maximum density.

In small molecules - covalent compounds it is intermolecular bonding, strong covalent bonds in giant covalent structures. Metals have strong chemical bonds between the atoms and similar very strong bonds between ions in ionic compounds.

The particles can only vibrate around fixed positions in the structure and do not have sufficient kinetic energy to overcome the binding forces and break free and move around creating a little space as in liquids.

The result is the highest density for the state of a specific material.

Although liquid densities for a specific material are just a bit less than those of the solid, both the solid and liquid states have much greater densities than the gaseous or vapour state.

Generally speaking the solid state exhibits the highest density, particularly metals.

In a very dense material like iron, the particles (iron atoms) are not only heavy, but very close together giving the high density of 7870 kg/m3.

Because of the particular crystal structure of ice (ρ = 931 kg/m3), solid water is less dense than liquid water (ρ = 1000 kg/m3), so ice floats on water! Very unusual! In the solid the water molecules form a very open crystal structure in which the water molecules are actually slightly further apart on average compared to their compactness in liquid water.

When dealing with insulating materials, beware!, their densities are much lower than the 'bulk' solid because very low density gases like air or carbon dioxide are trapped in them, considerably lowering the overall density of the original solid material.

If you heat a solid, increasing its temperature, the particles gain kinetic energy and the vibrations become more energetic and this enables the particles on average to spread out a bit more ('pushing' each other apart), increasing the solid volume and lowering the density.

See chemistry notes on chemical bonding

Keywords, phrases and learning objectives for density

Using kinetic particle theory model to explain the relative densities of gases, liquids and solids

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