States of matter and density

In a gas, particles are far apart and move randomly in all directions. They spread throughout the available space, so a gas has neither a definite shape nor a fixed volume. Gases are easily compressed because the large gaps between particles can be reduced. Solids and liquids are much harder to compress because their particles are already close together.

The circles in a particle diagram represent atoms or molecules, not visible pieces of the substance. When a gas is compressed, the gaps between particles become smaller; the particles themselves do not shrink.

Density connects mass with volume

Density is mass per unit volume. It tells us how much mass is packed into a particular amount of space. Two objects can occupy the same volume but have different masses because their densities differ.

$$\rho = \frac{m}{V}$$

Here, $\rho$ is density in kilograms per cubic metre (kg/m³), $m$ is mass in kilograms (kg), and $V$ is volume in cubic metres (m³). Mass is measured using a balance; volume is the space occupied by the object or substance.

To calculate density, divide the measured mass by the measured volume. The equation can also be rearranged to find an unknown mass or volume:

$$m = \rho V \qquad V = \frac{m}{\rho}$$

Laboratory measurements often use grams and cubic centimetres. These give density in g/cm³ if used directly. To obtain kg/m³, convert the mass and volume first: $1000\text{ g} = 1\text{ kg}$ and $1\,000\,000\text{ cm}^3 = 1\text{ m}^3$. A measuring cylinder may be marked in millilitres; .

Why density differs between states

For the same substance, density depends on how closely its particles are packed. Solids and liquids usually have similar densities because their particles are close together in both states. A liquid is usually slightly less dense than the corresponding solid because its particles are generally a little further apart.

Water is an important exception: ice is less dense than liquid water. Its particles have a more open arrangement, so the same mass occupies a larger volume when frozen.

Gases have much lower densities because their particles are widely separated. A given mass occupies a much larger volume as a gas than as a solid or liquid. Since density is mass divided by volume, that larger volume gives a lower density.

Core practical: measuring the density of a regular solid

Every density investigation needs two measurements: mass and volume. For a regularly shaped solid, its dimensions can be used to calculate its volume.

1. Zero a balance, place the dry object on it and record its mass.
2. Measure the required dimensions using a ruler, or a suitable finer measuring instrument for a small object.
3. Repeat the dimension measurements and calculate mean values.
4. Calculate the volume using the formula for the object's shape. For a rectangular block, $V = \text{length} \times \text{width} \times \text{height}$.
5. Convert the measurements to suitable units and calculate $\rho = m/V$.

Measuring all three dimensions matters: a single length does not tell you the block's volume. Use a measuring instrument appropriate to the object's size and read its scale carefully.

Measuring an irregular solid by displacement

An irregular object does not have a simple shape whose volume can easily be calculated from dimensions. Instead, measure the volume of water it displaces. This method is suitable for an object that sinks and does not dissolve in or react with water.

Measure the dry object's mass using a balance. Fill a displacement can with water until water runs from the spout, then wait until the flow stops. Place an empty measuring cylinder beneath the spout. Carefully lower the object until it is completely submerged, and collect all the displaced water.

The volume collected is the volume of the object: the submerged object has taken up space previously occupied by that water. Read the measuring cylinder at eye level, using the bottom of the water's curved surface, or meniscus. Use this volume and the object's mass to calculate density.

Avoid splashing and trapped air bubbles, which would affect the volume measurement. Repeat the measurement after resetting the water level and calculate a mean volume.

Measuring the density of a liquid

For a liquid, a measuring cylinder provides its volume, but the balance reading includes the container's mass.

1. Zero the balance and measure the mass of an empty, dry measuring cylinder.
2. Remove the cylinder from the balance and add the liquid.
3. Read and record the liquid's volume at eye level.
4. Measure the mass of the cylinder containing the liquid.
5. Subtract the empty cylinder's mass to obtain the liquid's mass, then calculate its density.

$$m_{\text{liquid}} = m_{\text{cylinder + liquid}} - m_{\text{empty cylinder}}$$

Repeat the measurements and use mean values to reduce the effect of random variation. Handle glassware carefully and keep liquid away from the balance when filling containers.

Changes of state conserve mass

The names of the changes describe their starting and finishing states:

Evaporation occurs at a liquid's surface and can happen below its boiling point. Boiling occurs throughout the liquid at its boiling point, with bubbles of gas forming within it.

During each change of state, particles change their arrangement and movement, but no particles are created or destroyed. Mass is conserved, even though volume and density may change. For example, if 20 g of liquid completely evaporates, it produces 20 g of gas.

A container left open may appear to lose mass during evaporation because gas escapes into the surroundings. The total mass of the remaining liquid and the escaped gas is still the original mass.

Physical changes and chemical changes

Changes of state are physical changes: the substance remains the same, and reversing the change restores its original properties. Water that freezes into ice can be melted back into liquid water.

A chemical change produces different substances. Simply reversing a change of state does not undo that chemical reaction. Reversibility alone is not a rule for identifying every chemical change; the formation of different substances is the key distinction.

Gases compress easily because there are large gaps between particles.

Density

$$\rho = \frac{m}{V}, \qquad m = \rho V, \qquad V = \frac{m}{\rho}$$