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 calculations

1.4 Density 📏

What is Density?

Density (\$\rho\$) is the mass of a substance per unit volume. It tells us how tightly packed the particles are. Think of it as how heavy a sponge feels when you squeeze it – a denser sponge feels heavier for the same size.

Density of a Liquid 💧

To find the density of a liquid, simply divide its mass by the volume it occupies.

  1. Measure the mass of the liquid with a balance. (e.g., \$m = 200\,\text{g}\$)

  2. Measure the volume using a graduated cylinder. (e.g., \$V = 250\,\text{mL}\$)

  3. Calculate: \$\rho = \frac{m}{V} = \frac{200\,\text{g}}{250\,\text{mL}} = 0.80\,\text{g/mL}\$

Tip: Remember that 1 mL of water ≈ 1 g at 4 °C.

Density of a Regularly Shaped Solid 🧱

For solids with regular shapes (cube, sphere, cylinder), we can calculate volume using geometry.

ShapeVolume Formula
Cube\$V = a^3\$
Sphere\$V = \frac{4}{3}\pi r^3\$
Cylinder\$V = \pi r^2 h\$

Example: A cube of side \$a = 5\,\text{cm}\$ and mass \$m = 125\,\text{g}\$.

  1. Calculate volume: \$V = 5^3 = 125\,\text{cm}^3\$.

  2. Density: \$\rho = \frac{125\,\text{g}}{125\,\text{cm}^3} = 1.00\,\text{g/cm}^3\$.

Exam tip: Always convert units so that mass is in grams and volume in cubic centimetres (cm³) or cubic metres (m³) for SI.

Density of an Irregularly Shaped Solid that Sinks 🪨

When the solid is irregular, we can't use a simple formula. Instead, we use the displacement method.

  1. Fill a graduated cylinder with water and note the initial volume \$V_i\$.

  2. Carefully lower the solid into the water until it is fully submerged. Record the new volume \$V_f\$.

  3. Volume of solid: \$V = Vf - Vi\$.

  4. Measure the mass \$m\$ of the solid with a balance.

  5. Calculate density: \$\rho = \frac{m}{V}\$.

Analogy: Think of the solid as a tiny boat that pushes water out of the way when it sinks.

Exam tip: If the solid does not sink, remember that the method is for sinking solids only.

Quick Reference Cheat Sheet 📋

FormulaUnits
\$\rho = \frac{m}{V}\$g cm⁻³ or kg m⁻³
\$V_{\text{cube}} = a^3\$cm³ or m³
\$V_{\text{sphere}} = \frac{4}{3}\pi r^3\$cm³ or m³
\$V_{\text{cylinder}} = \pi r^2 h\$cm³ or m³

Exam Tips & Common Mistakes 🚨

  • Always check unit consistency before calculating.

  • For liquids, remember that 1 mL = 1 cm³.

  • When using displacement, ensure the solid is fully submerged and no air bubbles cling to it.

  • Remember that density is a scalar quantity – no direction.

  • Use the correct formula for the shape; mixing up cube and sphere formulas is a common slip.