If you know mass m, volume V, pressure P, and temperature T, which formula gives the molar mass M of the gas?

If you know mass m, volume V, pressure P, and temperature T, which formula gives the molar mass M of the gas?

• A. M = mRT/(PV)
• B. M = PV/(mRT)
• C. M = ρRT/P
• D. M = PV/(RT) × m

Answer: (A)

The main idea is using the ideal gas law to connect mass, molar mass, and the gas’s amount of substance. The ideal gas law says PV = nRT, where n is the number of moles. The number of moles relates to mass by n = m/M, with M being the molar mass. Substituting gives PV = (m/M)RT. Solve for M: M = mRT/(PV). This is the cleanest way to get M from the given quantities m, V, P, and T. If you use density ρ = m/V, you can also write M = ρRT/P, which is equivalent since ρ = m/V, but the direct form with mass, volume, pressure, and temperature is simplest.

The main idea is using the ideal gas law to connect mass, molar mass, and the gas’s amount of substance. The ideal gas law says PV = nRT, where n is the number of moles. The number of moles relates to mass by n = m/M, with M being the molar mass. Substituting gives PV = (m/M)RT. Solve for M: M = mRT/(PV).

This is the cleanest way to get M from the given quantities m, V, P, and T. If you use density ρ = m/V, you can also write M = ρRT/P, which is equivalent since ρ = m/V, but the direct form with mass, volume, pressure, and temperature is simplest.