Overview
This lecture covers how to use the density equation to solve for density, mass, or volume, using practical examples with various materials.
The Density Equation
- The density equation is: density = mass ÷ volume.
- It is used to identify unknown substances or calculate missing values if two variables are known.
Example 1: Identifying an Unknown Metal
- To identify a metal, compare its density to known densities (e.g., gold: 19.3 g/mL; pyrite: 4.8 g/mL).
- Measure mass using a scale (example: mass = 1,119 g).
- Measure volume by water displacement (example: initial volume = 100 mL, final = 158 mL; object volume = 58 mL).
- Calculate density: 1,119 g ÷ 58 mL = 19 g/mL, close to gold.
- Conclusion: The object is gold.
Example 2: Solving for Mass
- Use density = 2.7 g/mL for aluminum.
- Find volume by water displacement (initial = 100 mL, final = 110 mL; volume = 10 mL).
- Rearrange equation: mass = volume × density.
- Calculate mass: 10 mL × 2.7 g/mL = 27 g.
Example 3: Solving for Volume
- Density of iron: 7.8 g/mL and mass = 92 g.
- Rearrange for volume: volume = mass ÷ density.
- Calculate volume: 92 g ÷ 7.8 g/mL = 12 mL.
Key Terms & Definitions
- Density — mass per unit volume of a substance, usually in grams per milliliter (g/mL).
- Mass — amount of matter in an object, measured in grams (g).
- Volume — amount of space an object occupies, measured in milliliters (mL).
- Water Displacement — method to measure volume by observing how much water an object displaces.
Action Items / Next Steps
- Practice using the density equation to solve for density, mass, and volume with different materials.
- Review definitions and rearrangements of the density equation.