Determine the mass of 33.6 L of O2 at STP.
Understand the Problem
The question is asking to calculate the mass of 33.6 liters of oxygen gas (O2) at standard temperature and pressure (STP). At STP, one mole of an ideal gas occupies 22.4 liters. We need to first determine how many moles of O2 are in 33.6 L and then convert that to mass using the molar mass of O2.
Answer
48 g
Answer for screen readers
The mass of 33.6 liters of oxygen gas (O2) at standard temperature and pressure (STP) is 48 grams.
Steps to Solve
- Determine the number of moles of O2
To find the number of moles of oxygen gas (O2), use the formula:
$$ n = \frac{V}{V_m} $$
where ( n ) is the number of moles, ( V ) is the volume of the gas (33.6 L), and ( V_m ) is the molar volume of a gas at STP (22.4 L/mol).
Substituting the values:
$$ n = \frac{33.6 , \text{L}}{22.4 , \text{L/mol}} = 1.5 , \text{mol} $$
- Calculate the molar mass of O2
The molar mass of oxygen gas (O2) can be calculated by summing the atomic masses of its elements. The atomic mass of oxygen (O) is approximately 16 g/mol. Therefore, $$ \text{Molar Mass of } O2 = 2 \times 16 , \text{g/mol} = 32 , \text{g/mol} $$
- Calculate the mass of O2
Now that we have the number of moles and the molar mass, we can find the mass using the formula:
$$ \text{mass} = n \times \text{molar mass} $$
Substituting the values:
$$ \text{mass} = 1.5 , \text{mol} \times 32 , \text{g/mol} = 48 , \text{g} $$
The mass of 33.6 liters of oxygen gas (O2) at standard temperature and pressure (STP) is 48 grams.
More Information
At standard temperature and pressure (STP), the behavior of gases can often be approximated using the ideal gas law, which establishes a relationship between pressure, volume, temperature, and number of moles. This calculation shows how to relate volume to mass for a gas using its molar properties.
Tips
- Miscalculating the number of moles by not dividing the volume correctly by the molar volume.
- Forgetting to multiply the number of moles by the correct molar mass of O2.
- Using the wrong units: ensure that volume is in liters and mass is in grams.
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