Determining the Density of a Solid and Liquid

By definition, all matter has mass and occupies volume. The density of a substance is the ratio of its mass to its volume. At constant temperature and pressure, the density of a substance is constant.

Density is an intensive property of a substance that doesn’t depend on the amount of substance present. Thus, density can be used to identify an unknown pure substance if a list of reference densities is available, and the experimenter can choose a convenient amount of substance to work with when measuring density.

To measure the density of a sample of a substance, it is necessary to measure its mass and volume. Mass is typically measured using an analytical balance, a precise instrument that relies on the force exerted by the sample due to gravity. The container to hold the sample (also used to measure volume) is weighed and tared, so only the sample mass appears on the balance display when the sample is added to the container.

For liquids, this container is typically a volumetric flask, which has one marking that corresponds to a specific volume. The container is filled to the line with the liquid sample and weighed again after the empty flask has been tared. The measured density is the ratio of the measured mass to the volume indicated on the flask.

Most solid substances are irregularly shaped, which complicates volume determination. It is inaccurate, for example, to determine the volume of a powder by measuring its dimensions. Instead of directly measuring dimensions or using glassware like a volumetric flask, it is necessary to make use of a liquid displacement method to measure the volume of an irregularly shaped solid. A graduated cylinder containing a known volume of liquid (in which the solid is insoluble) is tared. The solid is added to the cylinder, and the total mass is weighed again to determine the mass of the solid. Addition of the solid causes an upward displacement of the liquid, resulting in a new volume reading. The volume of the solid is equal to the change in volume due to liquid displacement (i.e., the difference in liquid volume before and after adding solid).

As for liquids, the measured density of a solid sample is the ratio of the measured mass to the measured volume.

Table 1 lists results for the determination of the density of ethanol using a 50-mL volumetric flask. Densities were calculated by dividing the measured mass by 50.0 mL. The mean measured density was 0.789 ± 0.001 g/mL. Table 2 lists results for the determination of the density of a sample of zinc metal using a 100-mL graduated cylinder and the liquid displacement method. Note that the measured densities are constant (within experimental error) for both substances. Table 2, in particular, demonstrates that density is independent of the amount of substance studied.

Table 1. Results for the determination of the density of ethanol using a 50-mL volumetric flask.

Table 2. Results for the determination of the density of a sample of zinc metal using a 100-mL graduated cylinder and the liquid displacement method.

Density is a characteristic intensive property of a substance. Thus, density measurements can be used to identify an unknown pure substance if a list of possible reference densities is available. For example, density can be used to distinguish between metals similar in outward appearance (Figure 2).

In contexts where very low or very high mass is desirable, density is a critical material property. Materials engineers carefully consider the density of materials for construction in these contexts. For example, the bodies of some lightweight laptop computers are made of aluminum, one of the least dense metals. Lightweight tennis rackets contain titanium, another low-density metal.

Figure 2: Equivalent masses of aluminum (Al) and zinc (Zn) metal. The zinc metal occupies a much smaller volume due to its higher density.