Question

If a gas in a container expands to three times its initial volume, what happens to its density?

Answer and Detailed Explanation

Step 1: Understanding Density

The density of a gas is defined as its mass divided by its volume:
ρ = m / V

Step 2: Expansion of Volume

If the gas expands such that the new volume becomes three times the original volume, and the mass remains constant, the new volume is:
V′ = 3V

Step 3: New Density After Expansion

The new density becomes:
ρ′ = m / (3V)

This can be rewritten in terms of the original density ρ:
ρ′ = (1 / 3) × ρ

Therefore, the density of the gas becomes one-third of its original value.