An unknown monatomic gas "X" is studied by effusion through a pinhole. Under identical laboratory conditions (298 K, constant pressure), 1.00L of krypton gas (molar mass = 83.80 g·mol⁻¹) effuses in 89.0 s, whereas the same volume of gas X effuses in 124 s.
Answer the following questions about the identity of gas X.
(a) Derive an expression that relates the effusion time required to collect a fixed volume of an ideal gas to its molar mass when temperature and pressure are held constant.
(b) Use the derived expression and the experimental data to calculate the molar mass of gas X.
(c) The following species are available for laboratory use: propane (C₃H₈, 44.1 g·mol⁻¹), chlorine (Cl₂, 70.9 g·mol⁻¹), xenon (Xe, 131 g·mol⁻¹), and n-butane (C₄H₁₀, 58.1 g·mol⁻¹). Identify which of these best matches the calculated molar mass of X and justify your choice.