Which expression correctly represents gas density ρ in terms of molar mass M, pressure P, and temperature T according to the ideal gas law?

Which expression correctly represents gas density ρ in terms of molar mass M, pressure P, and temperature T according to the ideal gas law?

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

Answer: (A)

Density comes from connecting the ideal gas law to how much mass is in a given volume. Start with PV = nRT and the definitions ρ = m/V and m = nM (M is molar mass). Put these together: ρ = (nM)/V. From PV = nRT, solve for n: n = PV/RT. Substitute: ρ = (PV/RT · M)/V = (P M)/(R T). So the density of an ideal gas is proportional to its pressure and molar mass, and inversely proportional to temperature, with the proportionality set by the gas constant. This form works with consistent units (P, T, R) and makes it clear why heavier gases at the same P and T are denser.

Density comes from connecting the ideal gas law to how much mass is in a given volume. Start with PV = nRT and the definitions ρ = m/V and m = nM (M is molar mass). Put these together:

ρ = (nM)/V.

From PV = nRT, solve for n: n = PV/RT. Substitute:

ρ = (PV/RT · M)/V = (P M)/(R T).

So the density of an ideal gas is proportional to its pressure and molar mass, and inversely proportional to temperature, with the proportionality set by the gas constant. This form works with consistent units (P, T, R) and makes it clear why heavier gases at the same P and T are denser.