Density

Density is an important property and is often used by chemists to help identify substances. Density (d) is defined as the amount of mass per unit volume. For example, water has a density of 1 gram per milliliter. This figure can be experessed as 1 g/mL or 1 g/cm³ since one cubic centimeter is the same volume as one milliliter.

Definition:
           Mass          m
Density = ——————— or d = —
           Volume        V

To find the density of a sample, two measurements are required. First, you must measure the mass. Second, you must measure the volume. People often say that lead is heavy. What they really mean is that lead is dense. For example, which is heavier: a pound of lead or a pound of aluminum? This is a trick question, if you are wondering. What if you have the same volume of each metal? If you have exactly one mL (one cm³) of lead it will have a mass of 11.3 g. If you have the same volume of aluminum it will have a mass of 2.7 g. So which one is more dense?

Density is what determines whether a substance or an object will float. If the density of the object is less than the density of the liquid it will float. If the density of the object is greater than the density of the liquid it will sink. Most types of wood have a density less than the density of water so it floats. Many metals have densities much greater than the density of water. For example, iron has a density of 7.9 g/mL. So how is it possible to make ships out of iron?

1. You have a chunk of aluminum (Al) with a mass of 17.6 g and a volume of 6.5 cm³. What is the density of Al?
2. A cube of Al has a volume of 45.0 cm³ but you have no lab balance. What is its mass?
3. Another piece of Al has a mass of 89.3 g but its volume is too hard to measure. Calculate the volume of this piece of Al.

4. Balsa wood is extremely ‘light’. A cubic meter of the wood has a mass of only 170 kg. What is the density of balsa wood in g/cm³? Does it float in water?
5. What is the mass of 4.56 × 10⁹ mL of iron?
6. What volume of Pb has a mass of 4.0 kg?

7. How is it possible to make a ship out of iron actually float in water?