Physical Properties, Density, Solubility, Conductivity

Drop a grape into a glass of water, it sinks. Drop a grape into a glass of fizzy lemonade, it bobs up and down. The grape hasn't changed; the liquid has. What changed is how much "stuff" is packed into each mL of liquid, which is exactly what density measures. The formula is:

density = mass ÷ volume (d = m / V)

Units are usually grams per cubic centimetre (g/cm³). Water has a density of 1.0 g/cm³, handy because it gives us a benchmark:

• If something is less dense than water (under 1.0 g/cm³), it floats.
• If something is more dense than water (over 1.0 g/cm³), it sinks.

That's how a battleship floats, even though steel is dense, the ship's huge hull is mostly air, so its average density (steel + air) is less than water. Pack the ship with too much cargo and it sinks.

Knowing that density is mass divided by volume is only half the job. To put a real number on a real object you have to measure both parts, and the measuring is where most of the thinking is.

Mass is the easy one. Put the object on an electronic balance and read the grams. Zero the balance first if the object is sitting in a container, so you weigh the object and not the container as well.

Volume depends on the shape, and this is the split that matters. A regular-shaped object, one with flat faces and square corners like a block or a cube, can be measured with a ruler: length times width times height gives the volume directly. An irregular-shaped object, like a stone or a screw or a lump of metal, has no length to measure. There is no formula for the shape of a rock.

So for irregular shapes we use displacement. Lower the object into a measuring cylinder that already has water in it, and read how far the water level rises. The rise is the volume of the object. Here is why that follows: the object and the water cannot be in the same place at once, so the object pushes aside exactly its own volume of water, and that pushed-aside water has nowhere to go but upwards. You are not measuring the stone directly at all, you are measuring the hole it makes in the water.

One number makes displacement easy to use: 1 mL of water takes up exactly 1 cm³ of space. So a water level that rises by 30 mL tells you the object's volume is 30 cm³, with no conversion needed.

For almost every substance, the solid form is more dense than its liquid form, particles in a solid are packed tighter, so they take less space. But water breaks the rule.

When water freezes, the particles arrange themselves into a six-sided crystal pattern with surprisingly large gaps. Ice particles take up more space than liquid water particles, so ice is less dense than water (0.92 g/cm³ vs 1.0 g/cm³), and floats.

Whether an object floats or sinks in water is called its buoyancy. Anything less dense than water (like ice, or a buoyant cork) floats; anything denser (like a steel nail) sinks. Buoyancy is really just density in action.

This is a huge deal for life on Earth:

• In winter, a lake freezes from the top down. Floating ice forms a lid that keeps the warmer liquid water underneath protected.
• Fish, frogs and aquatic plants survive winter under the ice, the ice insulates them.
• If ice were denser, lakes would freeze from the bottom up and most freshwater life would be wiped out every winter.

One quirky physical property of water keeps half the planet's freshwater ecosystems alive. Not bad.

If you stir sugar into your tea, it disappears, but the tea still tastes sweet. The sugar has dissolved. Stir sand into water and it sits at the bottom. The sand has not dissolved.

Solubility is how much of a substance will dissolve in a liquid (called the solvent, usually water in school chemistry).

Solubility usually increases with temperature for solids, that's why hot chocolate dissolves faster than cold. It's the opposite for gases, that's why a warm fizzy drink loses its bubbles quickly.

Some substances let heat or electricity flow through them; others block it. The flowing kind are called conductors; the blocking kind are insulators.

Pattern to remember: metals are almost always good conductors (both heat and electricity). Non-metals are almost always insulators. The big exception is graphite (a form of carbon in pencil leads), it's the rare non-metal that conducts electricity, which is why it's used in batteries.

That's why your saucepan is metal (to spread the heat from the stove) but the handle is plastic or wood (so you can hold it without burning your hand). And it's why power cables have a copper core wrapped in plastic, copper carries the electricity, plastic stops it touching you.

Fill a glass of water right to the brim, then keep adding drops. The water bulges above the rim in a dome without spilling, held in by an invisible "skin". Lay a dry paperclip flat on still water and it sits on the surface, even though steel is nearly eight times denser than water. That skin is called surface tension, and it is one of water's most important properties.

Water particles attract each other in every direction. Deep inside the liquid those pulls cancel out, but a particle at the surface has no water above it, so it gets pulled inward and sideways only. That uneven pull makes the surface behave like a stretched elastic film.

• Surface tension pulls water into round droplets (a falling raindrop is a tiny sphere).
• It lets insects such as water striders walk on ponds without sinking.
• It helps water climb up narrow tubes, which is part of how plants draw water up from their roots.

Adding soap or detergent breaks surface tension. That is why soapy water soaks into fabric and spreads out instead of beading up, the soap weakens the pull between the water particles.

Each substance has its own unique combination of physical properties. By measuring a few of them you can often work out what a mystery substance is.

Worked example. A silvery-grey lump has a density of 7.9 g/cm³, melts above 1500 °C and doesn't dissolve in water. Which substance is it most likely?

Iron. The density and high melting point match iron exactly. Aluminium is much less dense, gold is far denser, and the two soluble ones are ruled out.