Density and How to Measure It
Density is mass per unit volume, found by weighing and by measuring volume, including displacement for an awkward shape. Particle spacing explains why the same substance has a much lower density as a gas.
What a learner can do afterwards
- Calculates density in kg per cubic metre or g per cubic centimetre and rearranges for mass or volume
- Measures the volume of an irregular solid by displacement and reports its density
- Uses particle spacing to explain why gases are usually much less dense than liquids and solids, while recognising exceptions to the solid-liquid density order
1 · Read
Density is mass per unit volume. Calculate it using density = mass / volume. Use g/cm3 for grams per cubic centimetre or kg/m3 for kilograms per cubic metre. Rearranging gives mass = density × volume and volume = mass / density. Keep mass and volume units consistent with the density units.
At equal mass, the object with the larger volume has the lower density. A sealed gas sample also becomes less dense if its volume increases: no gas leaves, so the same mass occupies more space. Heating does not always lower gas density. If a sealed rigid container keeps the volume fixed, its density stays the same.
For a sinking solid that does not dissolve, react with water or absorb it, measure mass on a balance. Record the cylinder's initial water volume, fully submerge the solid, remove trapped bubbles and record the final volume. Read the bottom of the water meniscus at eye level. Solid volume = final reading - initial reading. Then divide mass by this volume. One millilitre equals one cubic centimetre.
A suitable solid has mass 72 g. The cylinder reads 40 cm3 before immersion and 64 cm3 after it. Its volume is 64 - 40 = 24 cm3, so density is 72 / 24 = 3 g/cm3. To find mass instead, multiply density by volume: a 12 cm3 sample with density 6 g/cm3 has mass 72 g.
As in the particle model, particles in solids and liquids are close together. Gas particles are usually much farther apart, so the gas form of a substance usually has much less mass in the same volume. Solids are not always denser than liquids: ice is less dense than liquid water. Particle speed alone does not determine density; mass and occupied volume do.
A fluid exerts an upward force called upthrust equal to the weight of fluid displaced. For the same displaced volume, a denser fluid gives greater upthrust. Seawater is denser than fresh water, so it provides greater upthrust for the same submerged volume. Ignoring surface tension, an object with lower average density than the liquid floats; one with greater average density sinks.
Density = mass / volume. Displacement uses the change in water volume. Wider particle spacing usually lowers density; solids are not always denser than liquids.
Lesson, questions and flashcards written for this dataset.
Readings and flashcards written for this dataset. The linked video, Fluids and density, is by Khan Academy.
More to read
Using mass and volume
Two samples each have mass 60 g. One occupies 20 cm3 and the other occupies 30 cm3. Their densities are 60 / 20 = 3 g/cm3 and 60 / 30 = 2 g/cm3. Equal mass does not imply equal density: the volume matters too.
Use density = mass / volume. For an unknown mass, multiply density by volume. For an unknown volume, divide mass by density. A sample with mass 45 g and density 5 g/cm3 occupies 9 cm3.
Check units before calculating. Grams and cubic centimetres give g/cm3; kilograms and cubic metres give kg/m3. Comparing a measured density with reference values can suggest a material's identity, but does not prove it. Different materials can have similar densities, and measurements have uncertainty.
Measuring an uneven solid
Water displacement can measure the volume of an uneven solid. Choose a solid that sinks and does not dissolve, react with water or absorb it.
Measure its dry mass on a balance. Record the water volume in a measuring cylinder. Lower the solid gently until it is fully submerged, remove trapped air bubbles and record the new volume. Read the bottom of the water meniscus at eye level. Avoid splashing water out.
Readings of 35 mL and 47 mL give a displaced volume of 47 - 35 = 12 mL, equal to 12 cm3. The final reading alone includes water already in the cylinder. Divide the measured mass in grams by 12 cm3 to obtain density in g/cm3. Partial immersion, trapped bubbles or lost water would make the volume measurement unreliable.
Particle spacing and floating
Gas particles are usually separated by much larger gaps than particles in liquids and solids. This helps explain why the gas form of a substance usually has far less mass in a given volume. There is no universal solid-liquid density order. Ice is less dense than liquid water.
An immersed object receives an upward force equal to the weight of fluid displaced. If the displaced volume is held constant, a denser fluid gives greater upthrust. A freely floating object changes its submerged volume until upthrust balances its weight. Greater fluid density therefore does not mean a greater final supporting force on the same freely floating object.
Ignoring surface tension, an object with lower average density than the surrounding liquid floats partly above its surface. An object with greater average density sinks. Enclosed air spaces contribute to the object's volume, so a hollow object can behave differently from a solid lump of the same material.
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