CHEMISTRY · Stage 9 · Chapter 11: Patterns in the Periodic Table
Chemistry 11.3 Using density — Displacement Method for Irregular Solids
5 min read 6 parts Lesson 3 of 7
Lesson summary
11.3 Using density — Displacement Method for Irregular Solids — Alhussan International Academy — Chemistry (Stages 7–9) notes: Find the volume of an irregular solid by displacement, calculate its density, and describe how al-Biruni used density to identify gemstones.Irregular sol…
- Identifying the material
- Assumptions
- Floating objects
- Narrow cylinder
- Air bubbles
- Thin thread
Part 1 of 6The problem with irregular solids
- Irregular solid — a stone has no regular shape, so its volume cannot be found by multiplying length, width and height.
- Displacement — when an object is fully submerged it pushes aside a volume of water equal to its own volume.
- Measuring the water pushed aside gives the volume of the solid.
Part 2 of 6Method with a measuring cylinder
- Find the mass of the solid on a balance and record it in grams.
- Half-fill a measuring cylinder with water and record the volume V1, reading the bottom of the meniscus at eye level.
- Tie the solid to a thread and lower it gently into the water so it is fully covered and no water splashes out.
- Record the new volume V2.
- Volume of the solid = V2 - V1.
- Density = mass ÷ volume.
- Identifying the material — compare the result with a data table, for example 8.9 g/cm3 suggests copper.
Part 3 of 6Method with a eureka can
- Fill a displacement (eureka) can until water flows out of the spout and wait until dripping stops.
- Place a measuring cylinder under the spout.
- Lower the solid in and collect the water that overflows.
- The volume of the overflow is the volume of the solid.
- Assumptions — the solid does not dissolve or absorb water, and it sinks.
- Floating objects — tie a small weight to the object to push it under and allow for the volume of the weight.
Part 4 of 6Reducing errors
- Meniscusread it at eye level to avoid parallax error.
- Narrow cylinderuse one with small scale divisions for better precision.
- Air bubblesremove any stuck to the solid.
- Dry soliddry it before weighing.
- Thin threadthick string adds to the volume.
- Larger samplea larger volume change makes the percentage error smaller.
- Absorbent solidsa material such as brick absorbs water and gives a false result, so coat it in wax.
- Repeatsrepeat the measurement and calculate a mean density.
Part 5 of 6Al-Biruni and the density of gemstones
- Al-Biruni — more than 1000 years ago Abu Rayhan al-Biruni, born in what is now Uzbekistan, became a great scientist and mathematician.
- He wrote on astronomy, geology and medicines and built on earlier scientists to design new instruments for accurate measurements.
- Problem — quartz is common and cheap, and a cheating trader could pretend a lump of quartz is diamond, so al-Biruni asked how to identify gemstones reliably.
- Idea — use density, but gemstones have irregular shapes, so volume was difficult to measure.
- Apparatus — a flask with a side arm.
- He filled the flask until water overflowed through the side arm into a beaker, then emptied the beaker and put it under the side arm again.
- He lowered the gemstone into the flask and measured the volume of water that flowed into the beaker, which equals the volume of the gemstone.
- Calculation — density = mass ÷ volume.
| Material | Density calculated by al-Biruni (g/cm3) | Modern value (g/cm3) |
|---|---|---|
| Quartz | 2.58 | 2.58 |
| Ruby | 4.01 | 4.40 |
| Pearl | 2.70 | 2.70 |
- Precision — his measurements were very precise, and it was another 700 years before scientists in Europe could measure density as precisely.
- Other properties — he also classified gemstones by hardness, colour, crystal shape and whether the gemstone splits white light into a rainbow.
Part 6 of 6Science building on science
- Building on othersscientists build on others' work to develop scientific knowledge over time.
- Todaymost scientists specialise in one area, work in teams and publish papers in journals that scientists around the world read.
- Modern gemstone identificationscientists and jewellers still use a method like al-Biruni's, together with other techniques such as conductivity and how much a gemstone changes the direction of light.
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