Which equation gives the density of a gas in terms of pressure, molar mass, and temperature?

• A. ρ = RT/(PM)
• B. ρ = PM/RT
• C. ρ = P/RT
• D. ρ = M/(RT)

Answer: (B)

The density of a gas is its mass per volume, which for a gas can be written as ρ = (nM)/V, where n is the number of moles and M is the molar mass. Start from the ideal gas law, PV = nRT. Solve for the number of moles per volume: n/V = P/(RT). Substituting into the density expression gives ρ = M·(n/V) = PM/(RT). This shows density depends on pressure, temperature, and molar mass in the exact way PM/RT, matching the correct choice. The other forms miss the molar mass factor or place the terms in the wrong order, so they don’t reflect how density scales with these variables.