It is sometimes the job of a chemist to identify an unknown substance. One tool used by chemists in this work is the measurement of density. The identity of many simple substances can be narrowed down by comparing the density of a sample with the density of the known substances.
Density (symbol, d; or the Greek letter rho, ρ) is defined as mass per unit volume. Density is calculated by dividing the mass of an object by its volume. This is shown in equation form, as follows:
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?
We can calculate the density of a solid, liquid, or gas. The density of a gas will be dealt with elsewhere, because its density is very sensitive to temperature and pressure. Although the density of liquids and solids do change with temperature and pressure changes, the amount is fairly small. We will assume that temperature and pressure make little difference in our calculations. The density of a solid is often reported in units of grams per cubic centimeter (g/cm3). The density of a liquid is usually reported in units of grams per milliliter (g/mL). These units are perfectly equivalent because 1 mL = 1 cm3 exactly.
Density is an intensive property, which means that the density of a substance is the same no matter how large or small a sample of it is. Water has a density of 1 g/mL whether you have 1 mL or 1,000,000 mL. Other intensive properties include melting point, boiling point, temperature, and concentration. By contrast with intensive properties, things like duration, volume, mass, and length are extensive properties. This means that they measure things that change when the size of a sample changes.
Density determines what will float and what will sink in a given liquid. If a substance is more dense than a given liquid, then it will sink. If it is less dense, then it will float. For instance, aluminum (Al) has a density of 2.70 g/cm3 and mercury (Hg, a liquid at room temperature) has a density of 13.6 g/mL. Aluminum floats in mercury but not in water. Water has a density of 1 g/mL.
Buoyancy (the tendency to float) really depends on the amount of water or other fluid displaced by an object placed in it. For this reason, objects made of substances which have a density higher than that of the liquid can be made to float. This is possible by shaping them to displace more water; that is, by increasing their volume.
The useful thing about density is that if you know the mass of a sample you can simply calculate the volume. Similarly, if you know the volume of a sample you can caculate its mass. Just a very little algebra (or the unit factor process) can make this possible.
The density of lead (Pb) is 11.3 g/cm3. The unit equality for this is 11.3 g Pb = 1 cm3 Pb
You have 47 g of Pb: what is the volume of the sample? 1 cm3 47 g x -------- = 4.2 cm3 11.3 g
You have 1.3×103 mL of Pb: what is the mass of the sample? 11.3 g 1.3×103 mL x -------- = 1.5×104 g (or 15 kg) 1 mL
Show your work for all calculations. As much as possible do your work by setting things up as dimensional analysis calculations.