A sample of an unknown gas has a density of 4.75 g/L at 3.00 atm and 45.0 °C. What is the molar mass of the gas?

• A. 62.0 g/mol
• B. 88.0 g/mol
• C. 39.0 g/mol
• D. 18.0 g/mol

Answer: (A)

Verified step by step guidance

1. Identify the known variables: density (d) = 4.75 g/L, pressure (P) = 3.00 atm, temperature (T) = 45.0 °C. Convert the temperature to Kelvin using the formula \(T(K) = T(^\circ C) + 273.15\).
2. Recall the ideal gas law in terms of molar mass and density: \(PV = nRT\) and \(n = \frac{m}{M}\), where \(m\) is mass and \(M\) is molar mass. Rearranging, the density \(d = \frac{m}{V} = \frac{PM}{RT}\).
3. Rearrange the density formula to solve for molar mass \(M\): \(M = \frac{dRT}{P}\).
4. Substitute the known values for density \(d\), gas constant \(R\) (use \$0.0821 \frac{L \cdot atm}{mol \cdot K}\(), temperature \)T\( in Kelvin, and pressure \)P\( into the equation for \)M$.
5. Calculate the molar mass \(M\) using the substituted values to find the molar mass of the unknown gas.