A 0.399 g sample of an unknown gas fills a 550. mL flask at standard temperature and pressure (STP). What is the molar mass of the gas?

• A. 28.0 g/mol
• B. 44.0 g/mol
• C. 32.6 g/mol
• D. 18.0 g/mol

Answer: (C)

Verified step by step guidance

1. Identify the known values: mass of the gas (m) = 0.399 g, volume (V) = 550. mL = 0.550 L, 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 0.550 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: \(n = \frac{0.550 \text{ L}}{22.4 \text{ L/mol}}\) (do not compute the final value yet).
4. Use the formula for molar mass (M): \(M = \frac{\text{mass}}{\text{moles}} = \frac{m}{n}\). Substitute the mass and the expression for moles from the previous step.
5. Express the molar mass as \(M = \frac{0.399 \text{ g}}{\frac{0.550 \text{ L}}{22.4 \text{ L/mol}}}\) and simplify the expression to find the molar mass of the gas.