Introduction to the Density of Solids

For solids, mass is usually measured in grams (g), and volume in cubic centimeters (cm³), making the unit of density g/cm³. Because density is an intensive property—meaning it does not change with sample size—it serves as a reliable way to identify substances, especially metals.

To find the volume of a solid, you can use one of two main methods: geometric calculation (for regular shapes) or water displacement (for irregular shapes).

If the solid is a regular shape like a cube, rectangular prism, or cylinder, you can calculate volume using a standard formula:

• Rectangle or square prism:

$$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$

• Cube:

$$\text{Volume} = \text{side}^3$$

• Cylinder:

$$\text{Volume} = \pi r^2 h$$

For example, let’s say you have a rectangular metal block with a length of 5.00 cm, width of 3.00 cm, and height of 2.00 cm. Its volume would be:

$$\text{Volume} = 5.00 \times 3.00 \times 2.00 = 30.0\ \text{cm}^3$$

If the block’s mass is 240.0 g, the density would be:

$$\text{Density} = \frac{240.0\ \text{g}}{30.0\ \text{cm}^3} = 8.00\ \text{g/cm}^3$$

If the object has an irregular shape or a shape that’s hard to measure precisely, you can determine its volume by water displacement. In this method, you place the object into a graduated cylinder partly filled with water and observe how much the water level rises.

For example, if the initial water level is 45.0 mL and rises to 58.0 mL after adding the metal object, the volume of the object is:

$$\text{Volume} = 58.0\ \text{mL} – 45.0\ \text{mL} = 13.0\ \text{cm}^3$$

(Recall that 1 mL = 1 cm³.) If the object’s mass is 116.9 g, then its density would be:

$$\text{Density} = \frac{116.9\ \text{g}}{13.0\ \text{cm}^3} \approx 9.00\ \text{g/cm}^3$$

Once you calculate the density of your unknown metal, you’ll compare it to a list of known metals to propose its identity. To assess how accurate your value is, you’ll use the percent error formula:

$$\text{Percent Error} = \left( \frac{|\text{Measured Value} – \text{Accepted Value}|}{\text{Accepted Value}} \right) \times 100\%$$

For example, if your measured density is 9.00 g/cm³ and the accepted value for copper is 8.96 g/cm³:

$$\text{Percent Error} = \left( \frac{|9.00 – 8.96|}{8.96} \right) \times 100\% \approx 0.45\%$$

Understanding density and measurement techniques is not just a classroom exercise—it’s a vital skill used in science, engineering, and industry. From designing materials and identifying unknown samples to testing purity and controlling quality, precise density measurements are essential. This lab gives you hands-on practice applying careful measurements, calculations, and scientific reasoning to uncover the identity of a material—just like real scientists do.