Key Concept
Density (D) expresses how much mass is contained in a given volume of a substance. It connects three measurable quantities through the formula:
From this, we can rearrange:
Common Metric Units
| Quantity | Unit | Equivalent forms |
|---|---|---|
| Mass | grams (g) | kilograms (kg = 1000 g) |
| Volume | cubic centimeters (cm³) | milliliters (mL = cm³) |
| Density | grams per cubic centimeter (g/cm³) | grams per milliliter (g/mL) |
Worked Examples
Copper Bar
Given Data:
- • Mass = 216 g
- • Volume = 24 cm³
Find:
Density of the copper bar
Formula Used:
D = m ÷ V
Step-by-Step Solution:
Step 1: Identify the given values
Mass (m) = 216 g
Volume (V) = 24 cm³
Step 2: Apply the density formula
D = m ÷ V
D = 216 g ÷ 24 cm³
Step 3: Calculate
D = 9 g/cm³
Final Answer:
9 g/cm³
Candy Bar
Given Data:
- • Mass = 70 g
- • Volume = 55 cm³
Find:
Density of the candy bar
Formula Used:
D = m ÷ V
Step-by-Step Solution:
Step 1: Identify the given values
Mass (m) = 70 g
Volume (V) = 55 cm³
Step 2: Apply the density formula
D = m ÷ V
D = 70 g ÷ 55 cm³
Step 3: Calculate
D = 1.27 g/cm³
Final Answer:
1.27 g/cm³
Ice Cube
Given Data:
- • Mass = 33.2 g
- • Volume = 36 cm³
Find:
Density of the ice cube
Formula Used:
D = m ÷ V
Step-by-Step Solution:
Step 1: Identify the given values
Mass (m) = 33.2 g
Volume (V) = 36 cm³
Step 2: Apply the density formula
D = m ÷ V
D = 33.2 g ÷ 36 cm³
Step 3: Calculate
D = 0.92 g/cm³
Final Answer:
0.92 g/cm³
Pure Water
Given Data:
- • Density = 1 g/mL
- • Volume = 2 L = 2000 mL
Find:
Mass of the water
Formula Used:
m = D × V
Step-by-Step Solution:
Step 1: Identify the given values
Density (D) = 1 g/mL
Volume (V) = 2 L = 2000 mL
Step 2: Apply the mass formula
m = D × V
m = 1 g/mL × 2000 mL
Step 3: Calculate
m = 2000 g
Step 4: Convert to kilograms
2000 g = 2.0 kg
Final Answer:
2000 g (2.0 kg)
Ethyl Alcohol
Given Data:
- • Density = 0.789 g/mL
- • Volume = 200.0 mL
Find:
Mass of the ethyl alcohol
Formula Used:
m = D × V
Step-by-Step Solution:
Step 1: Identify the given values
Density (D) = 0.789 g/mL
Volume (V) = 200.0 mL
Step 2: Apply the mass formula
m = D × V
m = 0.789 g/mL × 200.0 mL
Step 3: Calculate
m = 157.8 g
Final Answer:
157.8 g
Silver Metal
Given Data:
- • Mass = 2500.0 g
- • Density = 10.5 g/cm³
Find:
Volume of the silver metal
Formula Used:
V = m ÷ D
Step-by-Step Solution:
Step 1: Identify the given values
Mass (m) = 2500.0 g
Density (D) = 10.5 g/cm³
Step 2: Apply the volume formula
V = m ÷ D
V = 2500.0 g ÷ 10.5 g/cm³
Step 3: Calculate
V = 238.1 cm³
Final Answer:
238.1 cm³
Summary
- • Density links mass and volume, helping identify or compare materials.
- • Denser substances have more mass per unit volume.
- • Unit consistency is crucial: convert liters to milliliters or cm³ before calculating.
- • Always label your final answer with correct units (e.g., g/cm³, g/mL, g, cm³).
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