A gas sample contains 4.0 g of CH_4 and 2.0 g of He. What is the total volume of the sample at STP (0°C, 1 atm)?

• A. 22.4 L
• B. 8.96 L
• C. 11.2 L
• D. 4.48 L

Answer: (C)

Verified step by step guidance

1. Calculate the number of moles of methane (CH_4) using its molar mass. The molar mass of CH_4 is calculated as: \(\text{Molar mass of CH}_4 = 12.0 + (4 \times 1.0) = 16.0\ \text{g/mol}\). Then, use the formula \(n = \frac{m}{M}\) where \(m\) is the mass and \(M\) is the molar mass.
2. Calculate the number of moles of helium (He) using its molar mass. The molar mass of He is approximately 4.0 g/mol. Use the same formula \(n = \frac{m}{M}\) to find the moles of helium.
3. Add the moles of CH_4 and He to find the total number of moles in the gas sample: \(n_{total} = n_{CH_4} + n_{He}\).
4. Use the ideal gas volume at STP to find the total volume. At STP (0°C and 1 atm), 1 mole of any ideal gas occupies 22.4 L. Calculate the total volume using \(V = n_{total} \times 22.4\ \text{L}\).
5. Summarize the steps and ensure units are consistent throughout the calculations to find the total volume of the gas mixture at STP.