Identifying Substances by Density

Introduction

According to a famous story, the Greek scientist Archimedes was asked to find out whether a king's crown was pure gold without damaging it. Whether or not the story is exactly true, the method attributed to him is sound: measure the crown's density and compare it with the density of gold. Density is a characteristic property — like a fingerprint for a pure substance — and it remains one of the simplest tools for identifying materials.

Core explanation

Characteristic properties. A characteristic property has a fixed value for a given pure substance under stated conditions, regardless of the size of the sample. Density, melting point and boiling point are the most commonly used examples. Colour or shape is not characteristic, because different substances can look alike and the same substance can come in many shapes.

The method. 1. Measure the mass of the sample. 2. Measure its volume (by dimensions or by displacement). 3. Calculate density = mass ÷ volume. 4. Compare with a data table and look for the closest match.

Reference densities (g/cm³, room temperature):

Substance Density Substance Density --- --- --- --- Magnesium 1.74 Nickel 8.91 Aluminium 2.70 Copper 8.96 Titanium 4.51 Silver 10.5 Zinc 7.13 Lead 11.3 Tin 7.29 Gold 19.3 Iron 7.87 Platinum 21.5

Allowing for error. Measured values are never exactly equal to reference values. A measured density of 8.8 g/cm³ could be copper (8.96) or nickel (8.91). When two candidates are close, a single density measurement cannot decide between them, and another property — colour, melting point, magnetism or a chemical test — is needed.

Detecting fakes and impurities. A mixture or alloy has a density between those of its components. Gold mixed with copper or silver has a density below 19.3 g/cm³. A "gold" bar with a tungsten core (tungsten, 19.25 g/cm³, is almost as dense as gold) is a well-known fraud that density alone cannot always detect, so assayers also use drilling, ultrasound or X-ray tests.

Step-by-step reasoning

A metal cylinder has a mass of 89.2 g and displaces 10.0 cm³ of water:

1. Density = 89.2 ÷ 10.0 = 8.92 g/cm³. 2. Closest reference values: nickel (8.91) and copper (8.96). 3. The two are too close to separate with this precision. 4. Check colour: copper is reddish-brown, nickel is silvery-grey; or test with a magnet — nickel is attracted, copper is not.

Visual explanation

A number line from 0 to 22 g/cm³ has each metal marked at its density. A red arrow at 8.92 falls between the marks for nickel and copper, with an error bar spanning both, showing why a second test is needed. A separate arrow at 2.69 falls clearly on aluminium, with no close neighbours.

Real-world analogy

Identifying a substance by density is like identifying a person by height. If the height is 2.10 m, there may be only one person in your school that tall — identification is easy. If the height is 1.60 m, many people match, and you need another clue, such as hair colour, to be sure.

Real-world example

Recycling plants sort shredded plastics using flotation tanks. Polypropylene and polyethylene (densities around 0.90–0.96 g/cm³) float in water, while PET and PVC (about 1.38 g/cm³ and above) sink. Density-based separation lets plants recover clean streams of each plastic for reuse.

Why?

Why is density characteristic while mass is not? Mass depends on how much of the substance you have, but density is a ratio of mass to volume; doubling the sample doubles both, leaving the ratio unchanged. That ratio is set by the kind of particles and how they pack, which is fixed for a given pure substance.

Common misconception

"If the density matches, the substance is definitely identified." A match only shows the sample is consistent with that substance. Several different materials can have very similar densities, and experimental error adds uncertainty, so good identification uses more than one property.

Worked example

Question: A ring has a mass of 12.4 g and a volume of 0.80 cm³. Is it pure gold (19.3 g/cm³)?

Reasoning: Density = 12.4 ÷ 0.80 = 15.5 g/cm³. This is well below 19.3 g/cm³, even allowing for measurement error.

Answer: No. Its density is consistent with a gold alloy (for example, 14-carat gold, which contains other metals) rather than pure gold.

Quick check

1. Why can a density of 8.9 g/cm³ not tell you for certain whether a metal is copper or nickel? Answer: Their densities (8.96 and 8.91 g/cm³) are too close to distinguish given normal measurement errors.

Exam focus

Show the density calculation with units, compare with the data given and justify your choice. If two values are close, say so and suggest another test. Questions about alloys expect you to state that the density lies between those of the component metals.

Advanced insight

In the laboratory, high-precision density measurement of liquids is done with oscillating-tube density meters, which can detect differences in the fourth decimal place. They are used to measure the alcohol content of drinks and the sugar content of fruit juices, which change density in a predictable way.

Summary

Density is a characteristic property, so a measured density can be compared with a data table to identify a pure substance. Measurement error and materials with similar densities mean that density is best combined with other properties. Alloys and mixtures have densities between those of their components, which helps detect impurities and fakes.

Practice questions

1. A block has a mass of 54.0 g and a volume of 20.0 cm³. Use the table to identify it. Answer: Density = 2.70 g/cm³: aluminium. 2. Suggest a second test to distinguish iron (7.87 g/cm³) from tin (7.29 g/cm³) if density measurements are imprecise. Answer: Use a magnet: iron is attracted, tin is not (or compare melting points). 3. A crown is supposed to be pure gold but has a density of 17.0 g/cm³. What can you conclude? Answer: It is not pure gold; it contains a less dense metal such as silver or copper. 4. Why are two plastics with densities of 0.92 and 1.38 g/cm³ easy to separate using water? Answer: The first is less dense than water and floats, the second is denser and sinks.