Determining Density of Liquids and Solids

To calculate density:

Use the formula: \( \rho = \dfrac{m}{V} \)

You must measure:

• Mass — using a digital balance (in g or kg)
• Volume — using appropriate methods for different materials

A. Density of a Liquid

• Use a measuring cylinder to measure a known volume of the liquid (in cm³ or mL).
• Measure the mass of an empty beaker using a digital balance.
• Pour the liquid into the beaker and measure the total mass.
• Subtract to find the mass of the liquid:

\( m_{\text{liquid}} = m_{\text{beaker + liquid}} – m_{\text{beaker}} \)

Then use: \( \rho = \dfrac{m}{V} \)

B. Density of a Regularly Shaped Solid

• Measure the mass using a digital balance.
• Measure the dimensions using a ruler or caliper:
  
  • For a cuboid: \( V = \text{length} \times \text{width} \times \text{height} \)
  • For a cylinder: \( V = \pi r^2 h \)
• Use the volume in the density formula: \( \rho = \dfrac{m}{V} \)

C. Density of an Irregularly Shaped Solid (via Displacement Method)

• Measure the mass of the solid using a balance.
• Fill a measuring cylinder or overflow can with water to a known level.
• Gently lower the object into the water and note the volume of water displaced.
• This displaced volume = volume of the object (in cm³).
• Use: \( \rho = \dfrac{m}{V} \)