Overview
This lecture explains the concept of density, how to calculate it, its role in floating and sinking, how to measure the volume of irregular objects, and the idea of specific gravity.
What Is Density?
- Density is defined as mass divided by volume:
d = m / v
- Common units: grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³).
- The density of liquid water at room temperature is 1.00 g/mL.
Floating and Sinking: Application of Density
- An object floats if its density is less than the liquid it is placed in.
- Example: Ice floats in water because its density is less than that of liquid water. When water freezes, it expands, so the same mass occupies more space, lowering its density.
- Ice sinks in isopropyl alcohol because the alcohol’s density (0.786 g/mL) is less than that of ice.
Calculating Density, Mass, and Volume
Example 1: Finding Density
Problem: Find the density of a 7.22 mL sample of metal with a mass of 23.88 g.
Step 1: Write the formula:
d = m / v
Step 2: Substitute the values:
d = 23.88 g / 7.22 mL
Step 3: Calculate:
d = 3.31 g/mL
Step 4: Significant figures:
- Mass (23.88 g): 4 sig figs
- Volume (7.22 mL): 3 sig figs
- Answer: 3 sig figs → 3.31 g/mL
Example 2: Finding Volume
Problem: What is the volume of a piece of wood with a mass of 18.3 g and a density of 0.24 g/mL?
Step 1: Write the formula and solve for volume:
d = m / v
v = m / d
Step 2: Substitute the values:
v = 18.3 g / 0.24 g/mL
Step 3: Calculate:
v = 76.25 mL
Step 4: Significant figures:
- Mass (18.3 g): 3 sig figs
- Density (0.24 g/mL): 2 sig figs
- Answer: 2 sig figs → 76 mL
- Always write units at every step and check that your final units match what you are solving for.
- Use the correct number of significant figures: the answer should have as many as the input with the fewest.
Measuring Volume: Regular and Irregular Objects
- For regular objects, use formulas (e.g., cube: volume = side³).
- For irregular objects, use water displacement:
- Measure initial volume in a graduated cylinder.
- Add the object and measure the new volume.
- Subtract: final volume – initial volume = object’s volume.
- When subtracting, keep the correct number of digits after the decimal based on significant figures rules.
Comparing Densities
- For equal volumes, the sample with higher density has more mass.
- Example: 20 mL of water (density 1.00 g/mL) vs. 20 mL of salt solution (density 1.2 g/mL):
20 mL × 1.00 g/mL = 20 g (water)
20 mL × 1.2 g/mL = 24 g (salt solution)
→ Salt solution is heavier.
Specific Gravity
- Specific gravity = (density of sample) / (density of water)
- This is a unitless number.
- Used clinically, for example, to check hydration with urine tests.
- To find density from specific gravity:
density = specific gravity × density of water (usually 1.00 g/mL)
Key Terms & Definitions
- Density: Mass per unit volume, usually in g/mL or g/cm³.
- Significant Figures: Digits in a measurement known with certainty plus one estimated digit.
- Method of Displacement: Technique to find the volume of irregular objects by measuring fluid volume increase.
- Specific Gravity: Ratio of the density of a substance to the density of water, with no units.
Action Items / Next Steps
- Memorize the density of water (1.00 g/mL) for quizzes and tests.
- Practice solving density, mass, and volume problems, showing all steps and using correct units and significant figures.
- Prepare for the next topic on energy.