Density and the Particle Model

What is Density?

A huge steel ship has a massive weight, yet it floats perfectly on the ocean while a tiny pebble sinks straight to the bottom. This happens because floating depends on density, not just mass.

Density is defined as the mass per unit volume of a substance.

The equation for calculating density is:

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

• $\rho$ = density in kilograms per cubic metre ($kg/m^3$)
• $m$ = mass in kilograms ($kg$)
• $V$ = volume in cubic metres ($m^3$)

Sometimes, secondary units are used in practicals, such as grams per cubic centimetre ($g/cm^3$) for density. To convert from $g/cm^3$ to $kg/m^3$, you multiply by $1000$ (for example, water has a density of $1\,g/cm^3$, which equals $1000\,kg/m^3$).

Calculating Density (Worked Example)

Let's look at how to apply the density equation to a solid block.

A metal block has a mass of $2.4\,kg$ and a volume of $0.0003\,m^3$. Calculate its density.

Step 1: Identify the known values.

• $m = 2.4\,kg$
• $V = 0.0003\,m^3$

Step 2: Substitute the values into the equation.

• $\rho = \frac{2.4}{0.0003}$

Step 3: Calculate the final answer with units.

• $\rho = 8000\,kg/m^3$

The Particle Model and States of Matter

The particle model is a theory describing all matter as being made of small, hard spheres whose movement and arrangement determine the properties of a substance. It helps explain why solids, liquids, and gases behave differently.

The total energy stored by particles in a system is called internal energy, which is the sum of kinetic energy (from motion) and potential energy (from bonds). According to kinetic theory, heating a substance increases the average kinetic energy of its particles, causing them to move faster.

When a substance changes state, this is a physical change where mass is conserved because the number of particles remains exactly the same.

Explaining Density Using Particle Arrangement

We can explain the differences in density and macro-properties between states by looking at how their atoms or molecules are packed together.

Solids: Particles are in a regular arrangement (a repeating lattice) and are closely packed and touching. They vibrate about fixed positions and do not move from place to place. Because they are held in a fixed lattice by strong forces, solids maintain a fixed shape. Furthermore, because particles are so tightly packed, solids usually have the highest mass per unit volume, making them the most dense state.

Liquids: Particles are in an irregular arrangement but are still mostly touching, with no gaps large enough for another particle to fit into. They can flow and move past each other. Because particles in solids and liquids are already touching, they are incompressible (they cannot be squashed into a smaller volume).

Gases: Particles are widely spaced (typically 10 times the diameter of a particle apart) and have no regular pattern. They exhibit random motion at high speeds in all directions. Gases can flow easily, and they have the lowest density (about 1/1000th of solids) due to the large empty spaces between particles, which also gives them high compressibility.

Drawing Particle Model Diagrams

In exams, you must follow strict rules when drawing simple diagrams to model states of matter. Ensure all circles representing particles of the same substance are drawn the exact same size.

• Solid: Draw circles in a neat, regular grid of rows and columns. Every circle must be touching its neighbours.
• Liquid: Draw circles in a random arrangement. At least 50% of the circles must still be touching, and you must not leave large gaps.
• Gas: Draw widely spaced circles with absolutely no contact between them. Add motion arrows or "whoosh" lines of different lengths to show fast, random movement.