Density Formula

The Formula

d = \frac{m}{V} where m is mass and V is volume.

When to use: Density answers 'how heavy is this for its size?' A small lead ball is heavier than a large foam ball — lead is denser.

Quick Example

Water has a density of 1 g/cm³. Iron is 7.9 g/cm³ (sinks in water). Cork is 0.2 g/cm³ (floats on water).

What This Formula Means

The mass of a substance per unit volume. A measure of how tightly packed the particles are.

Density answers 'how heavy is this for its size?' A small lead ball is heavier than a large foam ball — lead is denser.

Worked Examples

Example 1

easy
A block of aluminum has a mass of 135 g and a volume of 50.0\,\text{cm}^3. Calculate its density.

Solution

  1. 1
    Use the density formula \rho = \frac{m}{V}.
  2. 2
    Substitute the given values: \rho = \frac{135\,\text{g}}{50.0\,\text{cm}^3}.
  3. 3
    Evaluate the quotient to get \rho = 2.70\,\text{g/cm}^3.

Answer

\rho = 2.70\,\text{g/cm}^3
Density is an intensive property — it does not depend on the amount of substance. Every sample of pure aluminum has the same density, making it useful for identification.

Example 2

medium
A piece of metal has a mass of 78.0 g. When placed in a graduated cylinder containing 25.0\,\text{mL} of water, the water level rises to 35.0\,\text{mL}. Calculate the density and identify the metal if possible. (Iron = 7.87\,\text{g/cm}^3, Copper = 8.96\,\text{g/cm}^3, Zinc = 7.13\,\text{g/cm}^3)

Why This Formula Matters

Density is used to identify substances, predict floating/sinking, and separate mixtures.

Frequently Asked Questions

What is the Density formula?

The mass of a substance per unit volume. A measure of how tightly packed the particles are.

How do you use the Density formula?

Density answers 'how heavy is this for its size?' A small lead ball is heavier than a large foam ball — lead is denser.

Why is the Density formula important in Chemistry?

Density is used to identify substances, predict floating/sinking, and separate mixtures.

What do students get wrong about Density?

Density is not the same as weight. A large block of wood can weigh more than a small piece of iron, but iron is still denser.

What should I learn before the Density formula?

Before studying the Density formula, you should understand: physical property.

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