A gas has a density of 3.55 g/L at 2.00 atm and 55.0 °C. What is the molar mass of the gas?

• A. 71.2 g/mol
• B. 58.0 g/mol
• C. 28.0 g/mol
• D. 44.0 g/mol

Answer: (A)

Verified step by step guidance

1. Identify the known variables: density (d) = 3.55 g/L, pressure (P) = 2.00 atm, temperature (T) = 55.0 °C. Convert the temperature to Kelvin using the formula \(T(K) = T(°C) + 273.15\).
2. Recall the ideal gas law in terms of molar mass (M): \(PV = nRT\) and \(n = \frac{m}{M}\), where \(m\) is mass and \(n\) is moles. Rearranging, density \(d = \frac{m}{V} = \frac{PM}{RT}\).
3. Rearrange the density formula to solve for molar mass: \(M = \frac{dRT}{P}\).
4. Substitute the known values for density, gas constant \(R\) (use \$0.0821 \frac{L \cdot atm}{mol \cdot K}\(), temperature in Kelvin, and pressure into the equation for \)M$.
5. Calculate the molar mass \(M\) using the substituted values to find the molar mass of the gas.