Density and Its Applications

Definition and Formula

Density is a fundamental physical property of matter, defined as the mass of a substance per unit volume. It is commonly used to identify substances and predict their behavior in mixtures.

• Density (d): The ratio of mass (m) to volume (V).

• Formula:

• Units: Common units include grams per milliliter (g/mL), kilograms per cubic meter (kg/m3), and grams per cubic centimeter (g/cm3).

Calculating Mass from Density and Volume

Given the density and volume of a substance, its mass can be calculated by rearranging the density formula:

• Example: If the density of elemental bromine is 3.1 g/mL, the mass of 15.0 mL of bromine is:

Calculating Volume from Density and Mass

To find the volume when mass and density are known, use:

• Example: Methyl alcohol has a density of 792 kg/m3. The volume of 2.38 kg of methyl alcohol is:

Additional info: 1 m3 = 1000 L.

Calculating Density from Mass and Volume

To determine the density of a sample, divide its mass by its volume.

• Example: A 20.0 mL sample of olive oil has a mass of 18.4 g. The density is:

Density and Buoyancy: Floating and Sinking

Whether an object floats or sinks in water depends on its density relative to water (density of water ≈ 1.00 g/mL or 1000 kg/m3).

• If density of object < density of water: Object floats.

• If density of object > density of water: Object sinks.

Examples:

• A rectangular block (50 cm × 40 cm × 20 cm, mass 0.583 kg):

  • Volume = 50 × 40 × 20 = 40,000 cm3 = 40 L

  • Density = 0.583 kg / 0.04 m3 = 14.6 kg/m3

  • Since 14.6 kg/m3 < 1000 kg/m3, the block floats.

• A diving tank (80 cubic feet, weight 21 lbs):

  • Convert 80 ft3 to liters: 1 ft3 ≈ 28.32 L, so 80 ft3 ≈ 2266 L

  • 21 lbs ≈ 9.53 kg

  • Density = 9.53 kg / 2.266 m3 ≈ 4.2 kg/m3

  • Since 4.2 kg/m3 < 1000 kg/m3, the tank floats.

• Additional info: Real-world tanks may sink if filled with compressed air or metal; this example uses provided data.

Application: Value of Gold Statue

To find the value of gold in a statue, first calculate the mass using density and volume, then multiply by the price per unit mass.

• Given: Volume = 825 cm3, Density = 19.32 g/cm3, Price = $597.40/oz

• Mass = 825 cm3 × 19.32 g/cm3 = 15,939 g

• Convert grams to ounces: 1 oz = 28.35 g

• Mass in oz = 15,939 g / 28.35 g/oz ≈ 562.5 oz

• Value = 562.5 oz × $597.40/oz ≈ $336,712.50

Temperature: Units and Conversions

Temperature Scales

Temperature is a measure of the average kinetic energy of particles in a substance. The three most common temperature scales are Celsius (°C), Fahrenheit (°F), and Kelvin (K).

• Celsius (°C): Based on the freezing (0°C) and boiling (100°C) points of water.

• Fahrenheit (°F): Used primarily in the United States; water freezes at 32°F and boils at 212°F.

• Kelvin (K): The SI unit for temperature; absolute zero is 0 K.

Temperature Conversion Formulas

• Celsius to Fahrenheit:

• Celsius to Kelvin:

• Example: Convert 7.0°C to °F and K:

Summary Table: Density, Mass, and Volume Relationships