To calculate the density of a gas using the ideal gas law, you need to know four key parameters: the pressure, volume, temperature, and molar mass of the gas.

The ideal gas law is expressed mathematically as:

In this equation, $P$ represents the pressure, $V$ denotes the volume, $n$ signifies the number of moles of the gas, $R$ is the gas constant, and $T$ is the temperature measured in Kelvin. By rearranging this equation, we can derive the molar volume equation:

This equation represents the molar volume of the gas.

To find the density of the gas, you first need to determine its molar mass, which is the mass of one mole of the substance. This value can typically be found on the periodic table. Once you have the molar mass, you can calculate the number of moles of gas using the relationship:

where $m$ is the mass of the gas and $M$ is its molar mass.

After calculating the number of moles of the gas, you can use the molar volume equation to determine the volume occupied by one mole of gas under the specified temperature and pressure conditions. The density of the gas can then be calculated by dividing the mass of the gas by its volume:

It is crucial to remember that the ideal gas law assumes the gas is in a state of thermodynamic equilibrium. This means that the temperature, pressure, and volume are uniform throughout the gas. If the gas does not achieve thermodynamic equilibrium, the ideal gas law may not yield accurate results.