Density Formula

Density is mass per unit volume. It's a fundamental property that helps identify substances and explains why objects sink or float.

The Density Formula

d = m / V

Density equals mass divided by volume

Variable Definitions

d = Density

Common Units:

  • Solids: g/cm³ or kg/m³
  • Liquids: g/mL (= g/cm³) or kg/L
  • Gases: g/L or kg/m³

m = Mass

Units: g, kg, mg

Amount of matter in the object

V = Volume

Units: mL, cm³, L, m³

Space occupied by the object

💡 Note: 1 mL = 1 cm³

Rearranged Forms

Find Density:

d = m / V

Find Mass:

m = d × V

Find Volume:

V = m / d

Common Substance Densities

SubstanceDensity (g/cm³)State
Water (4°C)1.000Liquid
Ice (0°C)0.917Solid
Aluminum2.70Solid
Iron7.87Solid
Gold19.3Solid
Mercury13.6Liquid
Air (25°C, 1 atm)0.00118Gas

Step-by-Step Example

Problem: A metal cube has mass 85.0 g and volume 10.0 cm³. What is its density? Identify the metal.

Given:

  • Mass (m) = 85.0 g
  • Volume (V) = 10.0 cm³
  • Find: Density (d)

Step 1: Write the formula

d = m / V

Step 2: Substitute values

d = 85.0 g / 10.0 cm³

Step 3: Calculate

d = 8.50 g/cm³

Answer: d = 8.50 g/cm³

This is close to the density of brass (8.4-8.7 g/cm³) or possibly nickel (8.9 g/cm³).

Why Density Matters

⛵ Buoyancy

Objects float if their density is less than the liquid. Ice floats because d(ice) < d(water).

🔬 Identification

Density is unique to each substance - helps identify unknown materials.

🧪 Purity Testing

Impurities change density - compare measured vs expected values.

⚖️ Unit Conversions

Convert between mass and volume when density is known.

Common Mistakes

❌ Unit mismatches

If m is in grams, V must be in mL or cm³ to get g/mL or g/cm³. Don't mix kg with mL!

❌ Flipping the formula

It's d = m/V, NOT d = V/m. Density is mass PER volume, not volume per mass.

❌ Confusing mass and weight

Use mass (g, kg), not weight (N, lbs). Mass is constant; weight varies with gravity.

❌ Forgetting temperature dependence

Density changes with temperature! Hot substances expand (lower density), cold ones contract (higher density).

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