The Amazing World of Solutes, Solvents, and Solutions · Lesson 3 of 7
Density and Relative Density
“Understand density as mass packed into a given volume and learn to compare it using consistent units.”
• Explain density as mass per unit volume rather than total mass. • Calculate density from mass and volume. • Use g/cm³, g/mL, and kg/m³ consistently. • Explain and calculate relative density. • Predict what changes when a uniform material is divided or reshaped.
From Crowded Places to Matter
A crowded bus holds many people in a limited space. A dense forest has many trees in a given area, whereas a sparse forest has fewer. These comparisons help us imagine density, but scientists use a precise meaning for the density of a substance: how much mass occupies a given volume.
Mass is the quantity of matter in an object; volume is the space it occupies. An object may have a large mass simply because it is large. To compare the materials themselves, compare equal volumes. A small sample of a dense material can have less total mass than a large sample of a less dense material.
The mass per unit volume of a substance. It tells us the mass contained in one chosen unit of volume.
Calculating Density
Suppose you know both the mass of a sample and the space it occupies. Dividing its mass by its volume gives the mass for one unit of volume. The division is therefore not just a rule to memorise: it answers the question that defines density.
If mass is in grams and volume in cubic centimetres, the result is in grams per cubic centimetre, written g/cm³. A density of 2.7 g/cm³ means each 1 cm³ of a uniform sample has a mass of 2.7 g. It does not mean the entire sample must have a mass of 2.7 g.
Water near room temperature has a density close to 1 g/mL: about 10 mL has mass 10 g, and about 100 mL has mass 100 g. This convenient approximation belongs to water under these conditions, not to every liquid.
Problem
An aluminium block has mass 27 g and volume 10 cm³. Find its density.
- 1.Identify m = 27 g and V = 10 cm³.
- 2.Divide: density = 27 g ÷ 10 cm³ = 2.7 g/cm³.
- 3.Interpret the result: each cubic centimetre of this aluminium has a mass of 2.7 g under the stated conditions.
Problem
A packet contains 1 L of oil with mass 910 g. Calculate the oil’s density in g/mL.
- 1.Convert the volume: 1 L = 1000 mL.
- 2.Divide mass by volume: 910 g ÷ 1000 mL = 0.91 g/mL.
- 3.Water near room temperature has density about 1 g/mL. Equal volumes of this oil and water therefore have different masses; 1 L does not automatically mean 1 kg for every liquid.
Units and Conversion Reasoning
Density units contain both a mass unit and a volume unit. Changing just one of those units without adjusting the other produces an incorrect result. Start from the mass and volume conversions so that the density conversion has a reason behind it.
The standard international unit of density is kg/m³ because mass is measured in kilograms and volume in cubic metres. For small solids, g/cm³ is convenient; for liquids, g/mL is convenient. Since 1 mL occupies the same volume as 1 cm³, these last two density units have the same numerical size.
| Conversion | Meaning |
|---|---|
| 1 kg = 1000 g | Convert the mass unit. |
| 1 m³ = 1000 L = 1,000,000 cm³ | Convert the volume unit. |
| 1 L = 1000 mL | A litre contains a thousand millilitres. |
| 1 mL = 1 cm³ | The same volume in two unit systems. |
| 1 g/cm³ = 1000 kg/m³ | Equivalent density units. |
To convert 1 kg/m³, replace 1 kg by 1000 g and 1 m³ by 1000 L. The result is 1000 g ÷ 1000 L = 1 g/L. Since one litre contains 1000 mL, this is 0.001 g/mL, or 0.001 g/cm³. Working through both parts avoids accidentally multiplying when division is needed.
Problem
Convert 2.7 g/cm³ into kg/m³.
- 1.Use 1 g/cm³ = 1000 kg/m³.
- 2.Multiply the numerical value by 1000: 2.7 × 1000 = 2700.
- 3.The density is 2700 kg/m³. The material has not changed; only the units have changed.
Relative Density
Sometimes we want to compare a material with water rather than state its density in units. Relative density expresses that comparison as a ratio. The water and substance densities must use the same units and refer to the same temperature.
The density of a substance divided by the density of water at the same temperature. It is a ratio and has no unit.
Near room temperature, using about 1 g/cm³ for water is a useful approximation for these examples. This makes the relative density numerically close to a substance’s density in g/cm³, but the two quantities are still different: density has units; relative density does not.
Problem
Using aluminium density 2.7 g/cm³ and water density 1.0 g/cm³ at the same temperature, find aluminium’s relative density.
- 1.Write the ratio: 2.7 g/cm³ ÷ 1.0 g/cm³.
- 2.Divide the values and cancel the matching units: relative density = 2.7.
- 3.Aluminium has about 2.7 times the mass of an equal volume of water under these conditions. Do not attach g/cm³ to the relative-density answer.
Size, Shape, and Conditions
Density belongs to the material under specified conditions, rather than to one chosen sample size. Cutting a uniform block into two pieces changes each piece’s mass and volume together. Simply reshaping it also leaves density unchanged if no material is lost and its actual volume stays the same.
For example, halve a 20 g sample occupying 10 cm³. Each equal half has mass 10 g and volume 5 cm³. Both divisions give 2 g/cm³. Heating or compressing a material is different because its volume may change without the same proportional change in mass. Later we use this distinction to explain changes in density.
A 100 g object can be less dense than a 20 g object if it occupies sufficiently more space. Compare mass per equal volume. Also distinguish a material’s volume from the outside volume of a hollow object that encloses air.
Quiz
What does a density of 3 g/cm³ mean?
A solid has mass 40 g and volume 20 cm³. What is its density?
Which equals 1 g/cm³?
Which is the correct unit for relative density?
A uniform solid is divided into two equal pieces at unchanged temperature and pressure. What happens to each piece’s density?
Practice Problems
- Explain why a crowded-bus analogy is helpful but not the scientific definition of a substance’s density.
- A material has mass 84 g and volume 30 cm³. Calculate its density and explain the meaning of your answer.
- A liquid has mass 360 g and volume 400 mL. Find its density in g/mL and compare it with water using the room-temperature approximation.
- Convert 0.8 g/cm³ into kg/m³ and 2000 kg/m³ into g/cm³. Show the conversion used.
- A substance has density 2.5 g/cm³ and water has density 1.0 g/cm³ at the same temperature. Calculate its relative density and explain why no unit is attached.
- A 120 g piece of clay occupies 60 cm³. It is reshaped without losing material or changing its actual volume. Explain what happens to mass, volume, and density.
Key Takeaways
• Density is mass per unit volume, not total mass. • Calculate density by dividing mass by volume and include the resulting unit. • 1 mL = 1 cm³, so g/mL and g/cm³ have equal numerical size. • 1 g/cm³ = 1000 kg/m³; convert both mass and volume units. • Relative density compares a substance with water at the same temperature and has no unit. • Dividing or reshaping a uniform material alone does not change its density under unchanged conditions.