Overview
This lecture covers the concepts of mass, volume, and density, including units, equations, and calculations, with example problems involving significant figures.
Mass, Volume, and Their Units
- Mass is the amount of matter in an object, measured in grams (g) or kilograms (kg).
- 1 kilogram (kg) equals 1,000 grams (g).
- Volume is the three-dimensional space occupied by an object, measured in liters (L), milliliters (mL), or cubic centimeters (cm³ or cc).
- 1 milliliter (mL) = 1 cm³ = 1 cc.
Density: Definition and Equation
- Density is the mass per unit volume of a substance.
- The formula for density: Density = Mass ÷ Volume.
- Typical units: grams per cubic centimeter (g/cm³) or grams per milliliter (g/mL).
- The “density triangle” helps rearrange the equation: Mass = Density × Volume; Volume = Mass ÷ Density.
Example Calculations
- Given mass (50 g) and volume (22.4 cm³), density = 50 g ÷ 22.4 cm³ = 2.23 g/cm³.
- When given density (0.785 g/mL) and volume (150 mL), mass = 0.785 g/mL × 150 mL = 117.75 g, rounded to two significant figures: 120 g.
- For a mass (3.90 g) and density (1.40 g/cm³), volume = 3.90 g ÷ 1.40 g/cm³ = 2.79 cm³ (rounded to three significant figures).
Significant Figures in Calculations
- Count significant figures carefully when multiplying or dividing values.
- Round the final answer to match the value with the fewest significant figures.
Key Terms & Definitions
- Mass — amount of matter in an object, measured in grams or kilograms.
- Volume — space occupied by an object, measured in liters, milliliters, or cubic centimeters.
- Density — mass per unit volume, measured in g/cm³ or g/mL.
- Significant Figures — digits in a number that reflect the precision of a measurement.
Action Items / Next Steps
- Practice identifying given information and selecting the correct formula for density problems.
- Complete assigned homework problems involving mass, volume, and density calculations with attention to significant figures.