Explanation of the Factors in Density of Matter - Succeed in Physical Science. Also refer to mass, volume, weight, atom, molecule, compressed, expansion, temperature, pressure, uranium, lead, aluminum, gas, liquid, solid, physics, Ron Kurtus, School for Champions. Copyright © Restrictions
Factors in Density of Matter
by Ron Kurtus (12 June 2008)
Density of a quantity of matter is its mass divided by its volume, according to the equation ρ = m/V. The mass of an object depends on the atomic mass of the individual atoms or molecules that make up the material and the how close the molecules 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.
(See Density of Matter for background on the subject.)
Questions you may have include:
- How does atomic mass affect density?
- How does density change with compression?
- How does density with temperature?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
Useful tools: Metric-English Conversion | Scientific Calculator.
Atomic mass affects density
Atoms that have higher atomic numbers have greater mass that those of lower atomic numbers.
For example, an Uranium atom (number 92) has about 238 times the mass of a Hydrogen atom (number 1). This means that a piece of Uranium would be denser than a quantity of Hydrogen or most other natural elements, unless the other element was greatly compressed.
Materials that consist of atoms with higher atomic mass can have fewer atoms for a given volume, but still have greater density than those consisting of atoms with lower atomic mass.
An exception could be the case of radon, which has a high atomic number, but it is a gas, so its atoms are relatively spread out. Radon could have a lower density under normal conditions than, say, aluminum.
Aluminum and lead
Aluminum atoms are lighter than lead atoms. That means that lead is denser than aluminum under normal conditions. That also means that 1 kg of aluminum would have a greater volume than 1 kg of lead.
Iron and feathers
Although 100 pounds of feathers may take up much more room than 100 pounds of steel, they both still weigh 100 pounds. The steel is heavier for its size, due to the fact that it is a denser material.
Thus, a material such as feathers takes up much more room (volume) than a denser material such as steel, for the same mass or weight.
Gold and Uranium
The atomic mass or weight of Gold is 197 and its density under normal conditions is 19.3 g/cm3. The atomic mass of Uranium is 238 and its density is 19 g/cm3, slightly lower than Gold, even though its atomic mass is larger. How is that possible?
The reason is that the Gold atoms are packed in closer under normal conditions than the Uranium atoms. Most of the time, the heavier atom will result having greater density.
Compression with pressure
The compression of a material is how close its atoms or molecules are with each other. The molecules of a gas are normally much further apart than those of the liquid state for that material. Usually, the molecules of a liquid are further apart than those of the solid state for that material, but that is not always the case.
Solids and liquids don't readily compress
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.
Gases compress and change density
On the other hand, a gas has no set volume, so it must be placed in a closed container. If the container is something like a cylinder with a piston, you can apply pressure on the piston and compress the gas. Its mass stays the same, but since its volume decreases, its density increases.
Example
Suppose you had a cylinder that was 10 cm high and had a piston that had an area of 100 cm2. The volume would be 10 times 100 or 1000 cm3. The density of the air inside the cylinder would be 1.25 kg/m3 or 0.00125 g/cm3.
Since ρ = m/V or m = ρV, the mass of the air is
m = 0.00125 g/cm3 × 1000 cm3 = 1.25 g.If you pushed the piston into the cylinder, compressing the air to 1/2 its original volume, the density would then be 2 times the previous density or 0.0025 g/cm3 = 2.5 kg/m3.
ρ = m/V = 1.25 g / 500 cm3 = 0.0025 g/cm3.
Expansion with 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.
An exception of materials contracting when cooled is when water turns to ice. Water contracts until it is cooled to 4°C. At that point it stays pretty much the same until it starts freezing at 0°C, when it expands. Thus the density of water at 0°C is 1, while the density of ice at 0°C is 0.92.
It is important to state the temperature of a material, because it is a factor in density.
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.
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Resources
The following resources provide information on this subject:
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Books
Top-rated books on Physical Science
College-level books on Density Science
Mini-quiz to check your understanding
1. If Uranium atoms have greater mass than Gold atoms, why does Gold have a greater density?
2. Why does the density of air in a balloon greater than the density of air outside the balloon?
3. What happens to the density of a piece of iron when it is heated?
If you got all three correct, you are on your way to becoming a Champion in Physical Science. If you had problems, you had better look over the material again.
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Factors in Density of Matter