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# Factors Affecting Density of Matter

by Ron Kurtus (revised 5 April 2014)

The density of an object or quantity of matter is its mass divided by its volume. This is usually measured under standard conditions for temperature and pressure: 0°C and 1 atmosphere of pressure.

One factor affecting the density of a material is how concentrated the atoms are in a given volume. In some cases, materials made of atoms with a lower atomic weight have a greater density than those with a higher atomic weight, due to the atoms being more tightly packed. This is especially true for solids.

Non-standard conditions can result in a change of volume, affecting the density of the materials. Also, certain temperatures and pressures can result in a change the state of the matter, which also affects the density.

Questions you may have include:

• How does atomic mass affect density?
• How does density change with temperature and pressure?
• How does change of state affect density?

This lesson will answer those questions. Useful tool: Units Conversion

## Concentration of atoms

An important factor in determining the density of a material is its mass for a given volume. Although you would think the total mass would only be a function of the material's atomic weight (relative atomic mass), it is not always the case.

The atoms in some materials—especially solids—are closely packed compared to those of other materials. Thus, it is possible for a material made of atoms of a lower atomic number to be heavier than that of a high atomic number for a given volume.

### Tin and Manganese

A good example is the comparison of the elements Tin and Manganese. Tin has the atomic number of 50 and the atomic weight of 118.7 μ (atomic mass unit or Dalton), while Manganese is number 25 with an atomic weight of 54.9 μ. However, Tin has a lower density at 7.31 g/cm3, while the density of Manganese is 7.43 g/cm3. In other words, even though the mass of Manganese atoms are one-half that of Tin, its density is higher than Tin.

The explanation is that although the Tin atoms are larger, they are more spread apart than the smaller Manganese atoms. One result of the Tin atoms having more separation is that Tin is softer, while the closely packed Manganese is hard and brittle.

Note: The separation of atoms in a metal is often related to the hardness of the material, but it is not always the case, since molecular structure also comes into play.

Atoms of Tin are larger but more spread apart

Atoms of Manganese are closely packed

## Change in volume

The volume of a material can change with temperature and pressure. This, in turn, changes the density of the material.

### Density and temperature

As the temperature increases, most materials expand or increase their volume. This results in a decrease in density. Likewise, when the temperature goes down, the density usually becomes greater.

For example, at normal atmospheric pressure, air at 0 °C has a density of ρ =1.29 kg/m3. But at 10 °C, the density of air is ρ =1.25 kg/m3, which is slightly less.

It is important to state the temperature of a material, because it is a factor in density.

### Density and pressure

Air pressure or the pressure from a container can change the volume and thus the density of an object. Pressure affects the density of gazes the most.

For example, the density of air is 1.225 kg/m3 or 0.001225 g/cm3. However, when confined in a balloon, the density can be much greater.

At a given temperature and at atmospheric pressure, solids and liquids will have a specific volume. By increasing the pressure on the material, you can often slightly decrease its volume and thus increase its density.

Unfortunately, most solids and liquids do not readily compress, so that method is not effective in changing the density.

## Change of phase or state

When a material changes its phase or state of matter, its volume and thus its density usually changes. Although pressure can influence the change of state of a material, temperature is the main factor.

### Solid versus liquid densities

The atoms or molecules in a solid are usually packed in an order or sometimes crystalline structure, while in the liquid form, they move about under few constraints. This results in the solid having a greater density.

#### Water and ice

Water has a density at the freezing point of 0.999 g/cm3, while ice has a density of 0.92 g/cm3. This is due to the fact that the material expands when turning to ice.

#### Iron

The density of iron is 7.874 g/cm3, while at temperatures above 1538 °C it becomes molten or a liquid with the density of 6.98 g/cm3.

### Liquid versus gaseous state densities

Once a liquid changes into a gas, its volume increases dramatically, thus reducing the density of the material.

Near its boiling point of 100 °C, water has a density of 1.03 g/cm3, while the density of steam dramatically drops to 0.006 g/cm3, because the steam expands so much.

## Summary

Density of a quantity of matter is its mass divided by its volume. The mass of an object depends on the atomic mass of the individual atoms or molecules and the how close the they are compressed together.

External pressure pushes the atoms or molecules closer together and increased temperature usually expands the volume of the material, pushing the molecules apart.

A change in the phase or state of a material usually results in a change in density.

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## Resources and references

Ron Kurtus' Credentials

### Websites

Density - Wikipedia

Densities of Solid Materials - Engineering Technology

Relationship between atomic number and density is not linear - Physics Stack Exchange

Element Density and Hardness - Ask a Scientist - Dept. of Energy

Matter Resources

Physics Resources

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