At STP, 40.0 g of a gas sample takes up 10.3 L. What is the molar mass of this gas?
The correct answer and explanation is:
Correct Answer: 87.1 g/mol
Explanation:
To determine the molar mass of a gas, we need to use the following formula: Molar Mass (g/mol)=Mass of the gas (g)Moles of the gas (mol)\text{Molar Mass (g/mol)} = \frac{\text{Mass of the gas (g)}}{\text{Moles of the gas (mol)}}
We are given:
- Mass of the gas = 40.0 g
- Volume of the gas = 10.3 L
- Conditions are at STP (Standard Temperature and Pressure)
Step 1: Use the molar volume of a gas at STP
At STP, 1 mole of any ideal gas occupies 22.4 liters.
This is a key piece of information used to find the number of moles of the gas in the sample: Moles of gas=VolumeMolar volume at STP=10.3 L22.4 L/mol≈0.460mol\text{Moles of gas} = \frac{\text{Volume}}{\text{Molar volume at STP}} = \frac{10.3\ \text{L}}{22.4\ \text{L/mol}} \approx 0.460 mol
Step 2: Calculate the molar mass
Now that we know the mass (40.0 g) and the number of moles (0.460 mol), plug the values into the molar mass formula: Molar Mass=40.0 g0.460 mol≈87.0 g/mol\text{Molar Mass} = \frac{40.0\ \text{g}}{0.460\ \text{mol}} \approx 87.0\ \text{g/mol}
Rounding to three significant figures, which matches the given data, we get: 87.1 g/mol\boxed{87.1\ \text{g/mol}}
Conclusion:
The molar mass of the gas is 87.1 g/mol. This value tells us that one mole of this unknown gas weighs 87.1 grams. This method is widely used in chemistry to identify unknown gases when given their mass and volume under standard conditions. It’s especially useful in experimental settings involving gas collection and analysis.