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Difficulty: MediumOxygen, Ozone, and Classification of Oxides

During a laboratory demonstration, a sample containing 100 cm3100\text{ cm}^3 of ozone gas (O3\text{O}_3) undergoes complete thermal decomposition into oxygen gas (O2\text{O}_2) under constant temperature and pressure. What is the total volume of oxygen gas produced?

  1. 150 cm3150\text{ cm}^3Answer
  2. B
    100 cm3100\text{ cm}^3
  3. C
    66.7 cm366.7\text{ cm}^3
  4. D
    200 cm3200\text{ cm}^3

Answer

The total volume of oxygen gas produced is 150 cm3150\text{ cm}^3.
The thermal decomposition of ozone to oxygen is represented by the balanced equation 2O3(g)→3O2(g)2\text{O}_3(\text{g}) \rightarrow 3\text{O}_2(\text{g}). According to Gay-Lussac's law, gas volumes at constant temperature and pressure react in simple stoichiometric ratios. Here, 2 units of volume of ozone yield 3 units of volume of oxygen gas. Therefore, 100 cm3100\text{ cm}^3 of ozone gas yields 32×100 cm3=150 cm3\frac{3}{2} \times 100\text{ cm}^3 = 150\text{ cm}^3 of oxygen gas.

Step-by-Step Solution

1
Write the balanced chemical equation for the decomposition of ozone to oxygen.
2O3(g)→3O2(g)2\text{O}_3(\text{g}) \rightarrow 3\text{O}_2(\text{g})
Establishing the balanced chemical equation determines the mole and volume ratios of the gaseous species involved.
2
Apply Gay-Lussac's Law of Combining Volumes to determine the volume ratio.
2 volumes of O3 produce 3 volumes of O22\text{ volumes of }\text{O}_3 \text{ produce } 3\text{ volumes of }\text{O}_2
At constant temperature and pressure, the volumes of reacting gases and their products are in simple whole-number ratios given by their stoichiometric coefficients.
3
Calculate the volume of oxygen gas obtained from 100 cm3100\text{ cm}^3 of ozone.
Volume of O2=100 cm3×32=150 cm3\text{Volume of }\text{O}_2 = 100\text{ cm}^3 \times \frac{3}{2} = 150\text{ cm}^3
Multiplying the initial volume of ozone by the stoichiometric ratio 32\frac{3}{2} yields the final volume of oxygen produced.

Key Concept

Stoichiometry of Gas Reactions and Allotropic Conversion of Ozone
Estimated Time:1m 0s
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Topics

Oxygen, Ozone, and Classification of Oxides

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