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1.4 Density

Syllabus
0625–2026–2027
Topic
1.4
Level
—

Learning objectives

1.4.1Density as mass per unit volume• Define density as mass per unit volume; recall/use: ρ = m/V1.4.2To determine the density of a liquid• Describe how to determine the density of a liquid, of a regularly shaped solid and of an irregularly shaped solid which sinks in a liquid (volume by displacement), including appropriate calculations1.4.3Whether an object floats based on• Determine whether an object floats based on density data1.4.4Whether one liquid will float on• Determine whether one liquid will float on another liquid based on density data given that the liquids do not mix

Use density as mass per unit volume

Density is the mass per unit volume of a substance or object. It describes how much mass is packed into each unit of volume.

ρ=mV\rho = \frac{m}{V}

Symbol Meaning Common units
ρ\rho density kg/m3^3 or g/cm3^3
mm mass kg or g
VV volume m3^3 or cm3^3

Choose the form that makes the unknown the subject: m=ρVm=\rho V for mass and V=m/ρV=m/\rho for volume. Substitute only after the units are consistent.

Equivalent density
1.0 g/cm3^3 = 1000 kg/m3^3
To change g/cm3^3 to kg/m3^3, multiply by 1000.
To change kg/m3^3 to g/cm3^3, divide by 1000.

A block of mass 100 g and volume 40 cm3^3 has density 100/40=2.5100/40=2.5 g/cm3^3. The units come from the mass and volume used in the calculation.

Do not compare mass alone or volume alone when deciding which object is denser. Density is their ratio, and mixing kilograms with cubic centimetres gives an inconsistent result.

Determine density experimentally

For every sample, measure its mass and volume, then calculate ρ=m/V\rho=m/V. The method used to obtain volume depends on the sample.

Sample Measure mass Determine volume
liquid find mcontainer+liquid−mempty containerm_{container+liquid}-m_{empty\ container}, or tare the empty container read the liquid volume in a measuring cylinder
regular solid use a balance measure dimensions and use the correct shape formula, such as lwhlwh for a cuboid
irregular solid that sinks use a balance fully submerge it; Vobject=Vfinal−VinitialV_{object}=V_{final}-V_{initial}

For a liquid, keep the measuring cylinder upright and read the scale at eye level. Use the appropriate part of the meniscus, then divide the liquid mass—not the mass of liquid plus container—by its volume.

For a regular solid, measure every required dimension with a ruler or calipers. For a sinking irregular solid, lower it gently until it is fully submerged, remove trapped air and record the rise in liquid volume.

ρsample=msampleVsample\rho_{sample}=\frac{m_{sample}}{V_{sample}}

Zero or tare the balance, use suitable scale ranges, repeat measurements when practical and average consistent results. Record all readings with units before calculating.

The final cylinder reading is not the volume of an irregular object: subtract the initial reading. The displacement method specified here applies to an object that sinks and can be fully submerged without dissolving or reacting.

Predict whether an object floats from density data

Compare the object's average density with the density of the surrounding liquid. The comparison, not the object's mass by itself, predicts whether it floats or sinks.

Density comparison Prediction
ρobject<ρliquid\rho_{object}<\rho_{liquid} the object floats
ρobject>ρliquid\rho_{object}>\rho_{liquid} the object sinks
ρobject=ρliquid\rho_{object}=\rho_{liquid} the object can remain suspended without rising or sinking

If density is not given, calculate it using ρ=m/V\rho=m/V. Put both densities in the same units, compare their numerical values, then state the outcome and support it with the comparison.

A sealed object of mass 80 g and volume 100 cm3^3 has average density 0.80 g/cm3^3. In a liquid of density 0.88 g/cm3^3, it floats because 0.80 is less than 0.88.

Use the average density of the whole object, including enclosed air or combined parts. Joining a dense object to a low-density object can make their combined average density lower than the liquid's density.

A larger or heavier object is not automatically more likely to sink. Floating also does not require the object's density to equal the liquid's density; a floating object with lower average density is only partly submerged.

Order immiscible liquids by density

When liquids do not mix, the liquid with lower density floats on the liquid with higher density. Several immiscible liquids form layers from lowest density at the top to highest density at the bottom.

Step Action
1 confirm that the liquids are immiscible
2 calculate any missing density using ρ=m/V\rho=m/V
3 express all densities in the same units
4 arrange them in increasing density from top to bottom

Suppose three immiscible liquids have densities 0.60, 0.83 and 1.19 g/cm3^3. Their final order is 0.60 at the top, 0.83 in the middle and 1.19 at the bottom.

State both the position and the comparison: for example, liquid P is above liquid Q because ρP<ρQ\rho_P<\rho_Q. Equal volumes or total masses are not required for this comparison.

The layering rule assumes the liquids do not mix. Do not rank layers by the total mass or total volume poured; compare density, which is mass per unit volume.