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Difficulty: HardThe Mole Concept, Avogadro's Constant, and Molar Mass

A sample of sulfur(IV) oxide gas (SO2\text{SO}_2) occupies a volume of 1.20 dm31.20\text{ dm}^3 at room temperature and pressure (RTP\text{RTP}). What is the total number of oxygen atoms present in this sample? [Molar volume of gas at RTP=24.0 dm3 mol−1,Avogadro’s constant NA=6.02×1023 mol−1][\text{Molar volume of gas at RTP} = 24.0\text{ dm}^3\text{ mol}^{-1}, \text{Avogadro's constant } N_A = 6.02 \times 10^{23}\text{ mol}^{-1}]

  1. 6.02×10226.02 \times 10^{22}Answer
  2. B
    6.45×10226.45 \times 10^{22}
  3. C
    3.01×10223.01 \times 10^{22}
  4. D
    3.23×10223.23 \times 10^{22}

Answer

6.02×10226.02 \times 10^{22} oxygen atoms
The correct answer is 6.02×10226.02 \times 10^{22}. Dividing the gas volume (1.20 dm31.20\text{ dm}^3) by the molar volume at RTP (24.0 dm3 mol−124.0\text{ dm}^3\text{ mol}^{-1}) gives 0.05 mol0.05\text{ mol} of SO2\text{SO}_2 gas. Since each molecule of SO2\text{SO}_2 contains 2 atoms of oxygen, the sample contains 0.10 mol0.10\text{ mol} of oxygen atoms. Multiplying 0.10 mol0.10\text{ mol} by Avogadro's constant (6.02×1023 mol−16.02 \times 10^{23}\text{ mol}^{-1}) yields 6.02×10226.02 \times 10^{22} oxygen atoms.

Step-by-Step Solution

1
Calculate the number of moles of SO2\text{SO}_2 gas at RTP
n(SO2)=1.20 dm324.0 dm3 mol−1=0.050 moln(\text{SO}_2) = \frac{1.20\text{ dm}^3}{24.0\text{ dm}^3\text{ mol}^{-1}} = 0.050\text{ mol}
Molar volume at room temperature and pressure is 24.0 dm3 mol−124.0\text{ dm}^3\text{ mol}^{-1}.
2
Determine the number of moles of oxygen atoms present
n(O)=2×0.050 mol=0.100 moln(\text{O}) = 2 \times 0.050\text{ mol} = 0.100\text{ mol}
Each molecule of SO2\text{SO}_2 contains 2 oxygen atoms.
3
Calculate the total number of oxygen atoms using Avogadro's constant
N(O)=0.100 mol×6.02×1023 mol−1=6.02×1022 atomsN(\text{O}) = 0.100\text{ mol} \times 6.02 \times 10^{23}\text{ mol}^{-1} = 6.02 \times 10^{22}\text{ atoms}
Multiplying moles of atoms by Avogadro's constant gives the exact atom count.

Key Concept

Molar volume of gases at RTP and stoichometric atom counting within polyatomic molecules.
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Topics

The Mole Concept, Avogadro's Constant, and Molar Mass

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