Measuring the density of solids

Practical method

Aim

Determine the densities of a regular solid, an irregular solid and a liquid, with uncertainties.

Variables

Independent variable: the sample
Dependent variable: density from measured mass and volume
Control variables: the same zeroed balance; temperature of the liquid.

Apparatus

• Top-pan balance (0.01 g)
• Vernier calipers and micrometer
• Measuring cylinder or burette
• Displacement can
• Beaker
• Thermometer

Method

1. Regular solid: measure each dimension several times with calipers or a micrometer and calculate the mean volume; measure the mass.
2. Irregular solid: find the volume by displacement in a measuring cylinder or displacement can; measure the mass.
3. Liquid: measure the mass of an empty beaker, add a measured volume of liquid from a burette, and measure the mass again.
4. Calculate ρ = \(\dfrac{m}{V}\) for each and combine percentage uncertainties.
5. Record the liquid's temperature, as density changes with temperature.

Sample results

Brass cylinder and cooking oil.

Analysis

Brass: V = π × (0.635)² × 5.00 = 6.33 cm³, so ρ = \(\dfrac{53.7}{6.33}\) = 8.48 g cm⁻³ = 8480 kg m⁻³. Oil: ρ = \(\dfrac{46.0}{50.0}\) = 0.920 g cm⁻³ = 920 kg m⁻³.

Uncertainty

Brass: diameter ±0.01 cm (0.8%, doubled to 1.6% in V), height ±0.01 cm (0.2%), mass ±0.1 g (0.2%): total about 2%, so ρ = 8.5 ± 0.2 g cm⁻³. Oil: burette volume ±0.1 cm³ (0.2%) and mass difference ±0.02 g: about 0.3%.

Errors and improvements

Risk assessment

Common mistakes

• Using diameter instead of radius.
• Not subtracting the beaker's mass.
• Converting g cm⁻³ to kg m⁻³ incorrectly (multiply by 1000).

Worked analysis

Oil: beaker 52.30 g empty, 98.30 g with 50.0 cm³ of oil. Mass = 46.00 g; ρ = \(\dfrac{46.00}{50.0}\) = 0.920 g cm⁻³ = 920 kg m⁻³.

Common misconception

Density depends on temperature for liquids; a density without a temperature is incomplete for precise work.