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Difficulty: Very hardCarbon: Allotropes, Coal Distillation, and Industrial Fuel Gases

An industrial fuel gas mixture derived from coal processing contains 40.0%40.0\% carbon(II) oxide (CO\text{CO}), 40.0%40.0\% hydrogen gas (H2\text{H}_2), and 20.0%20.0\% carbon(IV) oxide (CO2\text{CO}_2) by volume. Assuming air contains 20.0%20.0\% oxygen (O2\text{O}_2) by volume, what is the total volume of air required at s.t.p. for the complete combustion of 100.0 dm3100.0\text{ dm}^3 of this fuel gas mixture?

  1. 200.0 dm3200.0\text{ dm}^3Answer
  2. B
    40.0 dm340.0\text{ dm}^3
  3. C
    400.0 dm3400.0\text{ dm}^3
  4. D
    500.0 dm3500.0\text{ dm}^3

Answer

The total volume of air required at s.t.p. for complete combustion is 200.0 dm3200.0\text{ dm}^3.
In the 100.0 dm3100.0\text{ dm}^3 sample of fuel gas, the combustible gases are 40.0 dm340.0\text{ dm}^3 of CO\text{CO} and 40.0 dm340.0\text{ dm}^3 of H2\text{H}_2, while CO2\text{CO}_2 is already fully oxidized and non-combustible. According to reaction stoichiometry, 2CO+O2→2CO22\text{CO} + \text{O}_2 \rightarrow 2\text{CO}_2 and 2H2+O2→2H2O2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}, 40.0 dm340.0\text{ dm}^3 of CO\text{CO} requires 20.0 dm320.0\text{ dm}^3 of O2\text{O}_2 and 40.0 dm340.0\text{ dm}^3 of H2\text{H}_2 requires 20.0 dm320.0\text{ dm}^3 of O2\text{O}_2. The total pure oxygen needed is 40.0 dm340.0\text{ dm}^3. Since air is 20.0%20.0\% oxygen by volume, the required volume of air is 40.0 dm3÷0.20=200.0 dm340.0\text{ dm}^3 \div 0.20 = 200.0\text{ dm}^3.

Step-by-Step Solution

1
Determine the volumes of combustible and non-combustible components in the 100.0 dm3100.0\text{ dm}^3 fuel gas mixture.
Volume of CO=40.0 dm3\text{CO} = 40.0\text{ dm}^3, volume of H2=40.0 dm3\text{H}_2 = 40.0\text{ dm}^3, and volume of CO2=20.0 dm3\text{CO}_2 = 20.0\text{ dm}^3 (non-combustible).
By Gay-Lussac's Law of Combining Volumes, volume percentage corresponds directly to gas volume at s.t.p.
2
Write the balanced chemical equations and determine oxygen requirements for each combustible component.
2CO(g)+O2(g)→2CO2(g)2\text{CO}(g) + \text{O}_2(g) \rightarrow 2\text{CO}_2(g) requires 20.0 dm320.0\text{ dm}^3 of O2\text{O}_2; 2H2(g)+O2(g)→2H2O(l)2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(l) requires 20.0 dm320.0\text{ dm}^3 of O2\text{O}_2. Total pure O2=40.0 dm3\text{O}_2 = 40.0\text{ dm}^3.
Each combustible gas (CO\text{CO} and H2\text{H}_2) reacts with oxygen in a 2:12:1 mole (and volume) ratio.
3
Calculate the total volume of air needed to supply the required 40.0 dm340.0\text{ dm}^3 of pure oxygen.
Volume of air=40.0 dm30.20=200.0 dm3\text{Volume of air} = \frac{40.0\text{ dm}^3}{0.20} = 200.0\text{ dm}^3.
Air contains only 20.0%20.0\% oxygen by volume, so five times the volume of oxygen is needed in total air.

Key Concept

Industrial Fuel Gas Stoichiometry and Gas Volumetric Calculations
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Topics

Carbon: Allotropes, Coal Distillation, and Industrial Fuel Gases

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