Concept:At Standard Temperature and Pressure (STP), one mole of any ideal gas occupies a specific constant volume. To find the volume of a sample, convert its mass to moles and multiply by this constant.
Formula:$$ \text{Volume} = n \times 22.414 \text{ dm}^3 $$
Solution:- Oxygen gas is diatomic (\( \text{O}_2 \)). Its molar mass is \( 16 \times 2 = 32 \text{ g/mol} \).
- Calculate moles: \( n = 3.2 \text{ g} / 32 \text{ g/mol} = 0.1 \text{ moles} \).
- At STP, 1 mole of gas occupies \( 22.414 \text{ dm}^3 \).
- Volume = \( 0.1 \times 22.414 = 2.2414 \text{ dm}^3 \).
- Rounding to standard significant figures gives \( 2.24 \text{ dm}^3 \).
Why other options are incorrect:- \( 22.4 \text{ dm}^3 \): This is the volume of a full 1.0 mole of gas (which would be 32g of oxygen).
- \( 1.12 \text{ dm}^3 \): This would be the volume if the gas was only 0.05 moles.
- \( 24 \text{ dm}^3 \): This is the molar volume at RTP (Room Temperature and Pressure), not STP.
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