What is the mass of propane, C3H8, in a 50.0 L container of the gas at STP?
The correct answer and explanation is:
Correct Answer:
The mass of propane, C₃H₈, in a 50.0 L container at STP is 98.1 grams.
Explanation:
To calculate the mass of a gas at standard temperature and pressure (STP), you need to understand how gases behave under these conditions. STP is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atm. At STP, one mole of any ideal gas occupies 22.4 liters.
Start by calculating how many moles of propane are present in the 50.0-liter container. Using the molar volume of a gas at STP: Moles of propane=Volume of gas at STPMolar volume at STP=50.0 L22.4 L/mol≈2.23 mol\text{Moles of propane} = \frac{\text{Volume of gas at STP}}{\text{Molar volume at STP}} = \frac{50.0 \, \text{L}}{22.4 \, \text{L/mol}} \approx 2.23 \, \text{mol}
Next, determine the molar mass of propane, C₃H₈. This requires summing the atomic masses of all atoms in one molecule of propane:
- Carbon (C): 12.01 g/mol × 3 = 36.03 g/mol
- Hydrogen (H): 1.008 g/mol × 8 = 8.064 g/mol
- Total molar mass = 36.03 + 8.064 = 44.094 g/mol
Now, multiply the number of moles by the molar mass to find the mass of propane: Mass=moles×molar mass=2.23 mol×44.094 g/mol≈98.1 g\text{Mass} = \text{moles} \times \text{molar mass} = 2.23 \, \text{mol} \times 44.094 \, \text{g/mol} \approx 98.1 \, \text{g}
This calculation uses dimensional analysis and gas law principles to convert the volume at STP into mass. Understanding the relationship between gas volume and moles at STP is key to solving this type of problem.