The Amazing World of Solutes, Solvents, and Solutions · Lesson 6 of 7
Floating, Sinking, and Changes in Density
“Use density comparisons to explain floating and sinking, then investigate how temperature and pressure change density.”
• Use density comparisons to explain familiar floating and sinking observations. • Distinguish total mass, material density, and an object’s average density. • Explain how heating and compression can change density at constant mass. • Describe water’s unusual density behaviour near freezing. • Connect density with rafts, balloons, Earth’s layers, and aquatic life.
Why Total Mass Is Not Enough
When rice is washed, bits of husk may float while the rice grains sink. Oil stays above water, sawdust can remain at the surface, and sand collects at the bottom. These observations cannot be explained by saying that every object with a small mass floats and every object with a large mass sinks. Density compares mass with the space occupied.
A wood piece and an iron piece of the same size can have very different masses. The iron has more mass in the same volume and therefore greater density. Many everyday wood samples float in water while an ordinary solid iron piece sinks. Comparing equal volumes explains the material difference more clearly than the loose description that one is simply heavy.
For a fully immersed solid object in an ordinary freely moving situation, comparing its average density with the liquid gives a useful prediction: an object less dense than the liquid tends to rise and can float partly above the surface; an object denser than the liquid tends to sink. If the densities match, it can remain suspended. For simple non-mixing liquids, the less dense liquid tends to form the upper layer, as oil does on water.
The object’s total mass divided by the total volume considered for that whole object, including enclosed spaces when appropriate. It can differ from the density of its solid material.
The textbook warns that material density alone is not the only factor in every floating situation. Shape, enclosed air, wetting, and support at the liquid surface can matter. Use a whole object’s average density for hollow or air-containing objects; do not introduce a rule that all objects made of a dense material must sink in every form.
Problem
An oil has density 0.91 g/mL and water has density about 1.00 g/mL. They form separate layers. Which layer is on top?
- 1.Compare equal volumes: 1 mL oil has mass 0.91 g; 1 mL water has mass about 1.00 g.
- 2.The oil is less dense than the water.
- 3.The oil forms the upper layer. This does not mean every bottle of oil has less total mass than every glass of water.
Changing the Liquid Can Change the Result
Floating depends on the surrounding liquid as well as the object. If the liquid’s density changes while the object stays the same, the comparison can change. Adding dissolved salt to water provides a connection between the first part of the chapter and density.
In the egg investigation, a fresh raw whole egg may sink in plain tap water. Add salt gradually and stir gently to dissolve it without damaging the egg. Dissolved salt raises the solution’s mass per volume compared with the original water. With enough dissolved salt, the liquid may become dense enough for the same egg to rise and float. Avoid tasting the mixture and wash hands after handling the egg.
Problem
The same egg sinks in plain water but floats in a sufficiently concentrated salt solution. What changed?
- 1.The egg’s mass and structure have not been deliberately changed.
- 2.Dissolving salt has increased the liquid’s density enough to change the comparison.
- 3.The change in floating behaviour is evidence about the egg’s average density relative to each liquid, not evidence that the egg suddenly lost mass.
Bamboo and wooden rafts illustrate how materials and structure work together. Many wood materials are less dense than water, and hollow bamboo or logs can enclose air that lowers the whole object’s average density further. Traditional rafts have supported fishing, crossing waterways, trade, and travel. Their ability to float depends on their construction and the load they carry, not simply on being made from a familiar material.
Heating: Same Mass, More Volume
Think of a fixed amount of material that is warmed without losing any of it. Its particles generally move more vigorously and the material usually expands. The mass stays the same while the occupied volume increases, so dividing mass by volume gives a lower density.
This explains why hot air is less dense than comparable cooler air at similar pressure. In a hot-air balloon, warming the air lowers the density of the air inside relative to surrounding air. The balloon can rise when the resulting upward effect is sufficient to support the balloon and its load. The key density relationship is heating → expansion → lower mass per unit volume.
Problem
A fixed sample has mass 100 g. Its volume changes from 100 cm³ to 105 cm³ on heating. Compare its densities.
- 1.Initially, density = 100 ÷ 100 = 1.00 g/cm³.
- 2.After expansion, density = 100 ÷ 105 ≈ 0.952 g/cm³.
- 3.The density has decreased because the same mass occupies more space. These values illustrate the reasoning rather than describe a particular named substance.
The heated-water apparatus in the source uses a tube and a narrow glass tube to make a small expansion visible. Warming the contained water in a hot-water bath near 70°C makes the level rise. The narrow tube magnifies the visible height change, not the amount of material. With negligible loss of water, increased volume means decreased water density over this temperature range.
Pressure and Earth’s Layers
Pressure can also alter volume. Gases have enough space between their particles to be compressed substantially. If a fixed gas sample is squeezed into a smaller volume, its mass per unit volume increases, so its density rises.
In liquids, the particles are already much closer together, so ordinary pressure changes cause much smaller volume changes. Solids are generally less compressible still. The comparison is about the size of the effect; it does not mean liquids and solids can never change volume under pressure.
Problem
A gas sample has mass 2 g. At constant temperature it is compressed from 1000 cm³ to 500 cm³ without losing gas. What happens to its density?
- 1.Initially, density = 2 ÷ 1000 = 0.002 g/cm³.
- 2.After compression, density = 2 ÷ 500 = 0.004 g/cm³.
- 3.Its volume halves while mass stays fixed, so density doubles. Increased pressure is associated with the compression in this comparison.
Earth provides a much larger-scale application. Its layers include the crust, upper mantle, lower mantle, liquid outer core, and solid inner core. Density broadly increases toward the centre. Different materials and very high pressures both contribute. Do not explain this by claiming that higher temperature alone always increases density; that would contradict the expansion reasoning above.
Water’s Unusual Behaviour Near Freezing
The general statement that cooling increases density has an important exception in this chapter. Water is most dense at about 4°C under ordinary pressure. Cooling liquid water below that temperature toward freezing makes it expand rather than continue contracting.
When water freezes near 0°C, its particles form a more open arrangement than in liquid water. The same water mass then occupies a larger volume as ice. Ice is therefore less dense than liquid water and floats. It is better to say less dense than simply lighter, because an enormous iceberg can have far more total mass than a small bucket of water.
In cold conditions, surface water can freeze into a floating ice layer while water remains liquid below. The ice layer slows heat loss from the water beneath, helping aquatic organisms survive. Connect this with the earlier lesson: liquid water below supports life, and dissolved oxygen in that water is important for respiration.
Quiz
A large wooden raft floats while a small solid iron piece sinks. Which comparison is most useful?
Why can an egg rise after enough salt dissolves in its surrounding water?
A fixed sample expands on heating without losing material. What happens to its density?
A fixed gas sample is compressed at constant temperature. Which change is expected?
Why does ice float on liquid water?
Practice Problems
- Explain why rice husk can float while rice grains sink, and why small total mass alone is not a sufficient explanation.
- Describe how oil and water layers reveal a density comparison when the liquids do not mix.
- Explain how adding dissolved salt can change an egg’s floating behaviour. State what changes in the liquid and what stays approximately unchanged in the egg.
- A sample has mass 60 g and volume 50 cm³. On heating it expands to 55 cm³ without mass loss. Calculate both densities and describe the trend.
- A gas sample has mass 3 g. Its volume decreases from 1500 cm³ to 1000 cm³ at constant temperature. Calculate the initial and final densities.
- Explain how a hot-air balloon and a hollow bamboo raft both involve density while using different processes.
- Describe water’s density behaviour around 4°C and freezing. Explain why surface ice helps preserve liquid water underneath.
- Explain why Earth’s inner regions being denser does not prove that increasing temperature alone raises density.
- Predict what happens to the density of contained water when the level rises in a narrow tube during warming near 70°C, assuming no water is lost.
Key Takeaways
• Floating and sinking depend on density relative to the surrounding liquid, rather than total mass alone. • Enclosed air and structure can make whole-object average density differ from material density. • Dissolving salt can raise water’s density and change whether the same egg floats. • Expansion at constant mass lowers density; compression at constant mass raises it. • Pressure changes affect gases much more strongly than ordinary liquids and solids. • Water is most dense near 4°C; ice occupies more volume for the same mass and floats. • Density connects familiar observations with rafts, balloons, Earth’s layers, and aquatic survival.