Which of the following expresses gas density ρ in terms of molar mass M, pressure P, the gas constant R, and temperature T?

• A. ρ = P/(R T)
• B. ρ = M/(R T P)
• C. ρ = M P /(R T)
• D. ρ = R T /(P M)

Answer: (C)

Gas density is how much mass sits in a given volume, ρ = m/V. The mass of a sample relates to moles by m = nM, so ρ = nM/V. From the ideal gas law, PV = nRT, which gives n/V = P/(RT). Substituting this in, ρ = M · (P/(RT)) = MP/(RT). This shows density increases with molar mass and pressure, and decreases with temperature, in line with how gases compress and respond to heat. The other forms miss the need for the molar mass factor or reverse the dependence on pressure and temperature, leading to incorrect units or relationships.