Density
Measuring density experimentally
Overview — what you need to measure
To find density you need two measurements: mass and volume.
- Mass — always measured with a top-pan balance or beam balance.
- Volume — method depends on the shape of the object.
Regular solid (cuboid or cylinder)
Equipment: ruler (mm scale), vernier calipers for small objects, top-pan balance.
Method:
Method:
- Measure the three dimensions: length \( l \), width \( w \), height \( h \) (or diameter and height for a cylinder). Take each measurement at least twice and average.
- Calculate volume: cuboid \( V = l \times w \times h \); cylinder \( V = \pi r^2 h \).
- Measure the mass on a balance.
- Calculate: \( \rho = m / V \).
Worked example — density of a cuboid block
A wooden block measures 5.0 cm × 4.0 cm × 2.0 cm. Its mass is 28 g.
Volume: \( V = 5.0 \times 4.0 \times 2.0 = 40\,\text{cm}^3 \)
Density: \( \rho = \dfrac{28}{40} = 0.70\,\text{g/cm}^3 \)
Since \( 0.70 < 1.00 \) (water), the block will float.
Irregular solid (displacement method)
An irregular solid has a shape that cannot be calculated mathematically, so its volume is found using water displacement.
Method A — measuring cylinder:
Method B — eureka (displacement) can:
- Part-fill a measuring cylinder with water. Record the initial volume \( V_1 \).
- Carefully lower the solid into the cylinder on a thread (to avoid splashing).
- Record the new volume \( V_2 \).
- Volume of solid: \( V = V_2 - V_1 \).
- Measure mass on a balance. Calculate \( \rho = m / V \).
Method B — eureka (displacement) can:
- Fill the eureka can to the spout. Place an empty measuring cylinder under the spout.
- Lower the solid into the can; it displaces water which flows out of the spout.
- Collect the displaced water and read its volume — this equals the volume of the solid.
- Measure mass on a balance. Calculate \( \rho = m / V \).
Worked example — density of an irregular pebble
A pebble has mass 126 g. It is placed in a measuring cylinder: water level rises from 40 cm³ to 87 cm³.
Volume of pebble: \( V = 87 - 40 = 47\,\text{cm}^3 \)
Density: \( \rho = \dfrac{126}{47} = 2.68\,\text{g/cm}^3 \approx 2.7\,\text{g/cm}^3 \)
This is consistent with the density of granite or quartz.
Density of a liquid
Equipment: measuring cylinder, top-pan balance.
Method:
Method:
- Measure the mass of an empty measuring cylinder: \( m_1 \).
- Pour a known volume \( V \) of the liquid into the cylinder (read at the bottom of the meniscus, at eye level).
- Measure the mass of the cylinder + liquid: \( m_2 \).
- Mass of liquid: \( m = m_2 - m_1 \).
- Calculate: \( \rho = m / V \).
Always read the meniscus at eye level and from the bottom of the curve. A parallax error (reading from above or below) gives the wrong volume and therefore the wrong density.
Sources of error and how to reduce them
| Error | How to reduce it |
|---|---|
| Parallax when reading the ruler or measuring cylinder | Read at eye level; ensure eye is level with the scale marking |
| Air bubbles trapped on the irregular solid in the cylinder | Gently tap the cylinder; use a thread to fully submerge the solid |
| Water droplets remaining in the eureka can spout | Wait until dripping stops before reading the collected volume |
| Surface tension making the meniscus hard to read | Read the bottom of the meniscus for water; add one drop of detergent to reduce surface tension if needed |
| Balance not zeroed (tared) | Zero (tare) the balance before measuring; place the balance on a level surface |
For the displacement method, the solid must be fully submerged and must not dissolve in the liquid. If the solid dissolves in water, use a different liquid (e.g. oil) or coat the solid with a thin layer of wax.