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Difficulty: MediumGay-Lussac's Law of Combining Volumes and Avogadro's Law

A mixture of 30 cm330\text{ cm}^3 of carbon(II) oxide and 25 cm325\text{ cm}^3 of oxygen was sparked at constant temperature and pressure to form carbon(IV) oxide. What is the total volume of the resulting gaseous mixture?

  1. A
    30 cm330\text{ cm}^3
  2. 40 cm340\text{ cm}^3Answer
  3. C
    55 cm355\text{ cm}^3
  4. D
    10 cm310\text{ cm}^3

Answer

The total volume of the resulting gaseous mixture is 40 cm340\text{ cm}^3.
According to the balanced equation 2CO(g)+O2(g)→2CO2(g)2\text{CO}_{(g)} + \text{O}_{2(g)} \rightarrow 2\text{CO}_{2(g)}, two volumes of carbon(II) oxide react with one volume of oxygen to yield two volumes of carbon(IV) oxide. 30 cm330\text{ cm}^3 of carbon(II) oxide consumes 15 cm315\text{ cm}^3 of oxygen, leaving 10 cm310\text{ cm}^3 of excess oxygen unreacted. The reaction produces 30 cm330\text{ cm}^3 of carbon(IV) oxide gas. Adding the volume of carbon(IV) oxide produced to the remaining unreacted oxygen gives a total residual gaseous volume of 30 cm3+10 cm3=40 cm330\text{ cm}^3 + 10\text{ cm}^3 = 40\text{ cm}^3.

Step-by-Step Solution

1
Write and balance the stoichiometric chemical equation for the reaction.
2CO(g)+O2(g)→2CO2(g)2\text{CO}_{(g)} + \text{O}_{2(g)} \rightarrow 2\text{CO}_{2(g)}
To establish the mole and volume combining ratios according to Gay-Lussac's Law.
2
Determine combining volume ratios and identify the limiting reactant and unreacted gas.
By volume ratio, 2 cm32\text{ cm}^3 of CO\text{CO} reacts with 1 cm31\text{ cm}^3 of O2\text{O}_2. Therefore, 30 cm330\text{ cm}^3 of CO\text{CO} requires 12×30 cm3=15 cm3\frac{1}{2} \times 30\text{ cm}^3 = 15\text{ cm}^3 of O2\text{O}_2. Unreacted O2=25 cm3−15 cm3=10 cm3\text{O}_2 = 25\text{ cm}^3 - 15\text{ cm}^3 = 10\text{ cm}^3.
Carbon(II) oxide is completely consumed first, making it the limiting reactant.
3
Calculate the volume of gaseous product formed.
Since 2 cm32\text{ cm}^3 of CO\text{CO} produces 2 cm32\text{ cm}^3 of CO2\text{CO}_2 (a 1:11:1 ratio), 30 cm330\text{ cm}^3 of CO\text{CO} produces 30 cm330\text{ cm}^3 of CO2\text{CO}_2.
Gay-Lussac's Law applies directly to gaseous reactants and products under uniform conditions.
4
Sum the volumes of all gases present after the reaction completes.
Total residual volume = Unreacted O2\text{O}_2 + Produced CO2=10 cm3+30 cm3=40 cm3\text{CO}_2 = 10\text{ cm}^3 + 30\text{ cm}^3 = 40\text{ cm}^3.
The final mixture contains both the newly formed gaseous product and the remaining excess reactant.

Key Concept

Gay-Lussac's Law of Combining Volumes states that when gases react under constant temperature and pressure, their combining volumes and the volumes of any gaseous products bear a simple whole-number ratio to one another.
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Topics

Gay-Lussac's Law of Combining Volumes and Avogadro's Law

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