The density of a gas is inversely proportional to its temperature, meaning that as temperature increases, density decreases, assuming pressure remains constant.
Explanation of the Relationship
The relationship between density, temperature, and pressure for a gas can be understood through the Ideal Gas Law:
PV = nRT
Where:
- P = Pressure
- V = Volume
- n = Number of moles
- R = Ideal gas constant
- T = Temperature (in Kelvin)
Density (ρ) is defined as mass (m) per unit volume (V):
ρ = m/V
We can rearrange the Ideal Gas Law to incorporate density. We know that the number of moles (n) is equal to mass (m) divided by molar mass (M):
n = m/M
Substituting this into the Ideal Gas Law:
PV = (m/M)RT
Rearranging to solve for density (ρ = m/V):
ρ = (PM)/(RT)
From this equation, it's clear that:
- Density (ρ) is directly proportional to pressure (P). Increasing pressure compresses the gas into a smaller volume, increasing density.
- Density (ρ) is inversely proportional to temperature (T). Increasing temperature causes the gas to expand, increasing its volume and decreasing density.
Factors Affecting the Relationship
While the inverse relationship generally holds, it's important to remember:
- Constant Pressure: This inverse relationship is most straightforward when pressure is held constant.
- Real Gases vs. Ideal Gases: The Ideal Gas Law is an approximation. Real gases may deviate from this behavior, especially at high pressures and low temperatures. Intermolecular forces, which are ignored in the Ideal Gas Law, become more significant under these conditions.
- Phase Changes: If the temperature changes enough to cause a phase change (e.g., gas to liquid), the relationship between density and temperature becomes much more complex and the Ideal Gas Law no longer applies.
Example
Imagine heating a balloon filled with air. As the air inside the balloon heats up (increasing temperature), the air expands (increasing volume). If the balloon's pressure remains relatively constant (atmospheric pressure), the density of the air inside the balloon decreases. The air becomes less dense than the surrounding air, which is why a hot air balloon rises.
