An unknown gas has a density of 2.00 g/L at 1.00 atm and 25.0 °C. What is the molar mass of the gas?

• A. 2.00 g/mol
• B. 32.0 g/mol
• C. 22.4 g/mol
• D. 48.9 g/mol

Answer: (D)

Verified step by step guidance

1. Identify the known variables: density (d) = 2.00 g/L, pressure (P) = 1.00 atm, temperature (T) = 25.0 °C. Convert temperature to Kelvin using the formula \(T(K) = T(°C) + 273.15\).
2. Recall the ideal gas law equation: \(P V = n R T\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.
3. Express the number of moles \(n\) in terms of mass and molar mass: \(n = \frac{m}{M}\), where \(m\) is mass and \(M\) is molar mass.
4. Use the definition of density \(d = \frac{m}{V}\) to rewrite the ideal gas law in terms of density and molar mass: starting from \(P V = \frac{m}{M} R T\), rearrange to get \(M = \frac{d R T}{P}\).
5. Substitute the known values for \(d\), \(R\) (use \$0.0821\( L·atm/mol·K), \)T\( (in K), and \)P\( into the equation \)M = \frac{d R T}{P}\( to solve for the molar mass \)M$.