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Density of Liquids and Gases

General Chemistry • Matter, Its Properties, and Measurement

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Matter, properties, and measurement

Density links what we measure to how particles are packed

Density describes how much mass is contained in a given volume. Liquids usually have closely packed particles and relatively stable density, while gases have widely spaced particles and density that changes strongly with temperature and pressure.

Learning target

  • Calculate density from measured mass and volume.
  • Compare density behavior of liquids and gases.
  • Connect particle spacing to macroscopic density.
  • Interpret how temperature and pressure affect gas density.
Density comparison of liquid and gas particles Two equal containers show many closely packed liquid particles and fewer widely spaced gas particles. Liquid sample Gas sample more mass in the same volume less mass in the same volume

Why it matters

Density is used to identify substances, check measurements, and predict behavior

Density connects laboratory data to real chemical reasoning. A density value can help identify an unknown liquid, compare gases, evaluate purity, or decide whether a material will float or sink.

Identification

Substances have characteristic densities

A measured density can be compared with reference values to help identify a liquid sample.

Gas behavior

Gas density changes with conditions

Increasing pressure compresses gas particles into a smaller volume, increasing density.

Quality control

Density reveals composition changes

Mixtures, solutions, and fuels can be checked by comparing measured density with expected density.

Particle spacing
Particles close together usually produce a high density.

explains

Macroscopic property
Mass per unit volume becomes a measurable substance property.

Core concept

Density compares mass to volume

Two samples can have the same mass but different volumes, or the same volume but different masses. Density helps compare them fairly by asking how much mass is packed into each unit of volume.

Same volume with different mass model Two identical boxes show different numbers of particles, representing different masses in the same volume. Lower density Higher density same volume, less mass same volume, more mass

Particle-level interpretation

Density increases when more particles or heavier particles occupy the same amount of space. Density decreases when the same mass spreads into a larger volume.

\[ \text{density} = \frac{\text{mass}}{\text{volume}} \]

Density is an intensive property for a pure liquid at fixed conditions: changing the sample size changes mass and volume together, so the ratio stays nearly constant.

Vocabulary and units

Density calculations depend on clear measurements and consistent units

Before calculating density, identify the measured mass, measured volume, and the correct unit pair.

Quantity or term Meaning Common units How it is used
Mass, \(m\) Amount of matter in the sample. g, kg Measured with a balance; placed in the numerator of density.
Volume, \(V\) Space occupied by the sample. mL, L, cm3, m3 Measured using glassware, displacement, or container dimensions.
Density, \(d\) or \(\rho\) Mass per unit volume. g/mL, g/cm3, g/L, kg/m3 Used to compare substances and calculate missing mass or volume.
Gas density Density of a gas at specific temperature and pressure. g/L is common Must state conditions because gas volume changes easily.

Unit habit

For liquids, density is often reported in g/mL or g/cm3. For gases, density is often reported in g/L because gases occupy much larger volumes for the same mass.

Main relationship

Density changes when mass or volume changes

The density equation is simple, but it explains many important trends. A larger mass in the same volume increases density; the same mass in a larger volume decreases density.

Density formula and rearrangements

\[ d = \frac{m}{V} \]
Find density

\(d = m/V\)

Use when mass and volume are measured.

Find mass

\(m = dV\)

Use when density and volume are known.

Find volume

\(V = m/d\)

Use when mass and density are known.

Liquids

Small temperature effect

Most liquids expand slightly when heated, so density usually decreases slightly as temperature increases.

Gases

Strong condition effect

Gas density increases with pressure and decreases with temperature because gas volume changes easily.

Interactive density model

Change mass and volume to see density update

Move the sliders. The model shows how the same formula applies to liquid and gas samples, while the particle spacing explains why their densities are usually very different.

Density 0.800 g/mL
Particle spacing close
Comparison moderate

A 20.0 g sample in 25.0 mL has a density of 0.800 g/mL.

Interactive density particle model A container changes its fill level and particle spacing based on mass, volume, and liquid or gas mode. sample container liquid: particles close together relative density high low 0.800 g/mL

Dynamic relationship

For a fixed mass, density decreases as volume increases

The graph shows an inverse relationship: if mass stays constant and volume becomes larger, the same matter is spread out more, so density becomes smaller.

Choose the fixed mass

For a 25 g sample, density is high at small volume and lower at larger volume. The curve follows density = mass ÷ volume.

Density versus volume graph Three inverse curves show density decreasing as volume increases for different fixed masses. volume density high low large small 50 g 25 g 10 g same volume comparison

Worked example

Calculate the density of an unknown liquid

A student measures \(18.64\ \text{g}\) of an unknown liquid. The liquid occupies \(23.5\ \text{mL}\). Calculate the density and report the answer with the correct significant figures.

  1. Identify the known values.

    Mass is \(m = 18.64\ \text{g}\). Volume is \(V = 23.5\ \text{mL}\).

  2. Choose the density equation.

    Use \(d = m/V\) because mass and volume are both measured.

  3. Substitute the values.

    \(d = 18.64\ \text{g} / 23.5\ \text{mL}\).

  4. Calculate.

    \(d = 0.793191...\ \text{g/mL}\).

  5. Round using significant figures.

    The volume has 3 significant figures, so the density should be reported as \(0.793\ \text{g/mL}\).

Final answer

The density of the unknown liquid is \(0.793\ \text{g/mL}\).

Common misconception

Mass alone does not determine density

A heavier sample is not automatically denser. Density depends on mass and volume together.

Mistake

“Sample A has more mass than Sample B, so Sample A must be denser.”

Correction

Compare mass per unit volume. A large sample can have more total mass but lower density if its volume is much larger.

Mass versus density misconception A large low-density sample has more mass but lower density than a smaller high-density sample. Large sample mass = 60 g volume = 100 mL density = 0.60 g/mL Smaller sample mass = 30 g volume = 20 mL density = 1.5 g/mL The smaller sample is denser because each mL contains more mass.

Practice check

Compare a liquid and a gas sample

A liquid sample has a mass of \(36.0\ \text{g}\) and a volume of \(40.0\ \text{mL}\). A gas sample has a mass of \(1.80\ \text{g}\) and a volume of \(1.20\ \text{L}\).

Question

Calculate each density. Which sample has the greater density? Be careful with units.

Show answer

Liquid density: \(d = 36.0\ \text{g} / 40.0\ \text{mL} = 0.900\ \text{g/mL}\).

Gas density: \(d = 1.80\ \text{g} / 1.20\ \text{L} = 1.50\ \text{g/L}\).

To compare directly, convert \(0.900\ \text{g/mL}\) to \(900\ \text{g/L}\). The liquid is much denser than the gas.

Reasoning check

Liquids usually have particles much closer together than gases, so the liquid density should be much larger when units are made comparable.

Apply the topic

Use density reasoning before and after calculations

Density problems are not only arithmetic. A strong solution explains the measured ratio and checks whether the value makes sense for a liquid or a gas.

Open calculator Density of Liquids and Gases Calculator

Calculate density, mass, or volume and compare how liquid and gas samples behave.

 Practice questions Density of Liquids and Gases Questions

Practice unit conversions, particle-level explanations, and density comparisons.

How to apply this topic

First identify mass and volume. Then calculate density with units. Finally, connect the result to particle spacing and ask whether the magnitude is reasonable for a liquid or a gas.

Final summary

The essential takeaways

Density is mass per unit volume.

Use \(d = m/V\) and always keep the units attached to the answer.

Particle spacing explains density.

Closer particles usually mean more mass in the same volume and therefore higher density.

Liquids are usually much denser than gases.

Liquid particles are close together; gas particles are far apart.

Gas density depends strongly on conditions.

Higher pressure increases gas density, while higher temperature usually decreases gas density.

Unit conversion matters.

Compare densities only after making units compatible, such as g/mL and g/L.

Significant figures come from measurements.

Round the final density based on the limiting measured value.