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Difficulty: Very hardOxygen, Ozone, and Classification of Oxides

A sample of 90 cm390\text{ cm}^3 of pure oxygen gas (O2\text{O}_2) is passed through an ozonizer where 20%20\% by volume of the oxygen is converted into ozone (O3\text{O}_3). If the resulting gas mixture is reacted completely with excess carbon(II) oxide (CO\text{CO}) to yield carbon(IV) oxide (CO2\text{CO}_2), what is the total volume of carbon(IV) oxide gas produced under the same conditions of temperature and pressure?

  1. A
    90 cm390\text{ cm}^3
  2. B
    168 cm3168\text{ cm}^3
  3. 180 cm3180\text{ cm}^3Answer
  4. D
    216 cm3216\text{ cm}^3

Answer

The total volume of carbon(IV) oxide gas produced is 180 cm3180\text{ cm}^3.
The total volume of carbon(IV) oxide produced is 180 cm3180\text{ cm}^3 because the total number of oxygen atoms available for reaction remains conserved regardless of the conversion into ozone. 72 cm372\text{ cm}^3 of diatomic oxygen yields 144 cm3144\text{ cm}^3 of carbon(IV) oxide and 12 cm312\text{ cm}^3 of triatomic ozone yields 36 cm336\text{ cm}^3 of carbon(IV) oxide.

Step-by-Step Solution

1
Calculate the volume of oxygen converted to ozone and the volume of ozone formed.
Volume of O2\text{O}_2 converted = 20%×90 cm3=18 cm320\% \times 90\text{ cm}^3 = 18\text{ cm}^3. Remaining unreacted O2=90−18=72 cm3\text{O}_2 = 90 - 18 = 72\text{ cm}^3. According to 3O2(g)→2O3(g)3\text{O}_2(g) \rightarrow 2\text{O}_3(g), 18 cm318\text{ cm}^3 of O2\text{O}_2 produces 23×18 cm3=12 cm3\frac{2}{3} \times 18\text{ cm}^3 = 12\text{ cm}^3 of O3\text{O}_3.
Ozonolysis causes a volume contraction where 3 volumes of O2\text{O}_2 yield 2 volumes of O3\text{O}_3.
2
Calculate the volume of CO2\text{CO}_2 produced by the unreacted O2\text{O}_2.
Reaction equation: 2CO(g)+O2(g)→2CO2(g)2\text{CO}(g) + \text{O}_2(g) \rightarrow 2\text{CO}_2(g). Volume of CO2\text{CO}_2 from O2=2×72 cm3=144 cm3\text{O}_2 = 2 \times 72\text{ cm}^3 = 144\text{ cm}^3.
By Gay-Lussac's Law of Combining Volumes, 1 volume of O2\text{O}_2 produces 2 volumes of CO2\text{CO}_2.
3
Calculate the volume of CO2\text{CO}_2 produced by the O3\text{O}_3.
Reaction equation: 3CO(g)+O3(g)→3CO2(g)3\text{CO}(g) + \text{O}_3(g) \rightarrow 3\text{CO}_2(g). Volume of CO2\text{CO}_2 from O3=3×12 cm3=36 cm3\text{O}_3 = 3 \times 12\text{ cm}^3 = 36\text{ cm}^3.
Each molecule of O3\text{O}_3 contains 3 oxygen atoms, reacting with 3 molecules of CO\text{CO} to yield 3 molecules of CO2\text{CO}_2.
4
Sum the total volume of CO2\text{CO}_2 produced.
Total volume of CO2=144 cm3+36 cm3=180 cm3\text{CO}_2 = 144\text{ cm}^3 + 36\text{ cm}^3 = 180\text{ cm}^3.
The total volume of carbon(IV) oxide formed is the sum of the volumes produced by both oxygen allotropes in the mixture.

Key Concept

Gay-Lussac's Law of Combining Volumes and Allotropic Conversion of Oxygen to Ozone
Estimated Time:2m 0s
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Topics

Oxygen, Ozone, and Classification of Oxides

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