A 500. mL flask is filled with 2.00 g of an unknown gas at standard temperature and pressure (STP). What is the molar mass of the gas?

• A. 18.0 g/mol
• B. 44.0 g/mol
• C. 89.6 g/mol
• D. 32.0 g/mol

Answer: (C)

Verified step by step guidance

1. Identify the known values: volume (V) = 500. mL = 0.500 L, mass (m) = 2.00 g, and conditions are at STP (Standard Temperature and Pressure). At STP, the temperature is 273 K and pressure is 1 atm.
2. Recall that at STP, 1 mole of an ideal gas occupies 22.4 L. Use this to find the number of moles (n) of the gas in the 0.500 L flask by setting up a proportion: \(n = \frac{V}{22.4\ \text{L/mol}}\).
3. Calculate the number of moles using the volume of the gas: \(n = \frac{0.500\ \text{L}}{22.4\ \text{L/mol}}\) (do not compute the final value, just set up the expression).
4. Use the definition of molar mass, which is the mass of the gas divided by the number of moles: \(M = \frac{m}{n}\), where \(m\) is the mass in grams and \(n\) is the number of moles.
5. Substitute the values for mass and moles into the molar mass formula: \(M = \frac{2.00\ \text{g}}{\frac{0.500\ \text{L}}{22.4\ \text{L/mol}}}\), then simplify the expression to find the molar mass.