The density of an ideal gas is proportional to its pressure and inversely proportional to its temperature.
Explanation
The relationship between the density (ρ) of an ideal gas and its pressure (P), temperature (T), and molar mass (M) can be derived from the ideal gas law:
PV = nRT
where:
- P is the pressure
- V is the volume
- n is the number of moles
- R is the ideal gas constant
- T is the absolute temperature (in Kelvin)
Density is defined as mass (m) per unit volume (V):
ρ = m/V
We can express the number of moles (n) as mass (m) divided by molar mass (M):
n = m/M
Substituting this into the ideal gas law:
PV = (m/M)RT
Now, rearrange the equation to solve for density (ρ = m/V):
ρ = (PM)/(RT)
From this equation, we can see the following proportionalities:
- Density is directly proportional to pressure (P): At a constant temperature, if you increase the pressure on an ideal gas, its density will increase proportionally.
- Density is directly proportional to molar mass (M): At constant temperature and pressure, a gas with a higher molar mass will have a higher density.
- Density is inversely proportional to temperature (T): At constant pressure, if you increase the temperature of an ideal gas, its density will decrease proportionally.
In summary, for a given ideal gas with a fixed molar mass, density is proportional to pressure and inversely proportional to temperature.
