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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 cm^{3}) 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/cm^{3}). 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 cm^{3} 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/cm^{3} 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/cm^{3}. The unit equality for this is 11.3 g
Pb = 1 cm^{3} Pb

You have 47 g of Pb: what is the volume of the sample? 1 cm^{3}47 g x -------- = 4.2 cm^{3}11.3 g

You have 1.3×10^{3}mL of Pb: what is the mass of the sample? 11.3 g 1.3×10^{3}mL x -------- = 1.5×10^{4}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.

- A block of aluminum occupies a volume of 15.56 mL and weighs 42.0 g. What is its density?

- Mercury metal (Hg) is poured into a graduated cylinder and you read the volume to be 22.5 mL. The Hg used to fill the cylinder has a mass of 306.0 g. From this information, calculate the density of Hg.

- A flask that weighs 345.8 g is filled with 225 mL
of carbon tetrachloride (CCl
_{4}). The weight of the flask and CCl_{4}is found to be 703.6 g. From this information, calculate the density of CCl_{4}. - A sample of zinc pellets is weighed on a balance and the mass is found to be 19.54 g. The pellets are placed into a graduated cylinder containing 32.1 mL of water. After the zinc is placed in the water the volume in the cylinder reads as 34.8 mL. What is the density of zinc?
- Find the mass of 2500 mL of benzene
(C
_{6}H_{6}). The density of C_{6}H_{6}is 0.90 g/mL. - A strong-smelling liquid is given to you to identify. You find the mass of a 100 mL graduated cylinder is 373.92 g. When you have added some of the substance to the cylinder you measure the volume to be 51.2 mL and the new mass to be 420.0 g. What is the density of the substance? Can you identify it?
- What is the volume of 64.0 g of benzene?
- What volume of silver metal (Ag) will weigh exactly 2500 g? The density of
Ag is 10.5 g/cm
^{3}. - What mass of silver has a volume of 21.0 mL? Use the density given in the previous problem.

- What volume of lead (the density is in the introduction text) has a mass of 150. g?
- What mass of lead has a volume of 1,000 cm
^{3}? - A rectangular block of copper metal weighs 1896 g. The dimensions of the block are 8.4 cm by 5.5 cm by 4.6 cm. From these data, what is the density of copper? Will it float in the liquid metal mercury?
- A student counts 15 pieces of copper shot, weighs them and measures their volume by displacement. She then calculates the density: 9.0 g/cm
^{3}. Would the calculation have resulted in a different value if she had only counted out 12 pieces? Explain your answer with 1 or 2 complete sentences. - A piece of balsa wood of mass 0.128 kg will float on water. Will a piece of balsa wood with a mass of 170 kg float? Justify your answer with one or two complete sentences.
- Define the following terms in your own words. Give two examples for each word:

**intensive property**:

**extensive property**: