Gas densities and molecular weights: If gas X has a density exactly twice that of gas Y at the same temperature and pressure, and the molecular weight of gas Y is M, what is the molecular weight of gas X?

Introduction / Context:
In ideal-gas behavior, density is directly linked to molecular weight at fixed temperature and pressure. This question tests the proportional relationship between density and molecular weight—useful in identifying gases and checking gas-mixture calculations.

Given Data / Assumptions:

• Both gases are compared at the same temperature and pressure.
• Ideal-gas approximation applies.
• Density of X is twice the density of Y.
• Molecular weight of Y is M.

Concept / Approach:
For an ideal gas, ρ = P * MW / (R * T). At the same P and T, density ρ is proportional to molecular weight MW. Hence, if ρX = 2 * ρY, then MWX = 2 * MWY.

Step-by-Step Solution:

Verification / Alternative check:
Compare molar volumes: At the same T and P, equal moles occupy the same volume; doubling density must arise from doubling mass per mole, that is, doubling molecular weight.

Why Other Options Are Wrong:

• M/2 or M/4: These would reduce density, contradicting the statement.
• M: Would keep densities equal, not doubled.

Common Pitfalls:
Confusing density proportionality when T or P change; here they are explicitly the same for both gases.

Final Answer:
2M