Ideal Gas Law and Molar Mass

Steps:

• Start with the ideal gas law: PV = nRT, where n is the number of moles.
• Express n in terms of mass: n = m / M, with m as mass and M as molar mass.
• Substitute into the gas law: PV = (m / M) RT.
• Solve for M: Multiply both sides by M and divide by PV to get M = mRT / PV.

Why D is correct:

• It directly derives from rearranging PV = nRT with n = m/M, giving the standard formula for molar mass.

Why the others are wrong:

• A: Inverts the relationship, yielding PV/m (proportional to density, not molar mass).
• B: mV/RT rearranges incorrectly, ignoring P and producing units inconsistent with molar mass.
• C: mP/V simplifies to density (mass/volume) times P, unrelated to molar mass.

Final answer: D