Question:
In firedamp explosion, the methane concentration in the stoichiometric methane-air mixture, in % by volume, is
Assume the air contains 79% nitrogen and 21% oxygen, by volume.
In firedamp explosion, the methane concentration in the stoichiometric methane-air mixture, in % by volume, is
Assume the air contains 79% nitrogen and 21% oxygen, by volume.
Assume the air contains 79% nitrogen and 21% oxygen, by volume.
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Write the balanced combustion equation for methane in oxygen first, then use the fact that air is only 21% oxygen by volume to find how much air one volume of methane needs.
Updated On: Jul 27, 2026
- 5.4
- 9.5
- 10.8
- 14.8
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Question:
Firedamp is the methane gas found in coal mines, and it can explode when mixed with air in the right proportion. A stoichiometric mixture is the exact ratio of fuel to oxidiser at which the fuel burns completely, using up exactly all the oxygen supplied, with none left over. We need the volume percent of methane in air that gives this exact ratio.
Step 2: Key Formula or Approach:
Methane burns in oxygen by the reaction
\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \]
So one volume of methane needs exactly two volumes of oxygen to burn completely. Air is only 21% oxygen by volume, with the rest being nitrogen that does not take part in the burning but still occupies volume in the mixture. So the volume of air needed to supply 2 volumes of oxygen is
\[ V_{air} = \frac{V_{O_2}}{0.21} \]
Step 3: Detailed Explanation:
Take 1 volume of methane as the basis. It needs 2 volumes of oxygen, so the air needed is
\[ V_{air} = \frac{2}{0.21} = 9.524 \text{ volumes} \]
The total volume of the methane-air mixture is the methane plus this air:
\[ V_{total} = 1 + 9.524 = 10.524 \text{ volumes} \]
The percentage of methane by volume in the stoichiometric mixture is then
\[ \%CH_4 = \frac{1}{10.524} \times 100 = 9.5\% \]
Step 4: Final Answer:
Option (A), 5.4%, is close to the lower explosive limit of methane in air, not the stoichiometric value. Option (D), 14.8%, is close to the upper explosive limit of methane, again not the stoichiometric point. Option (C), 10.8%, does not come from the correct oxygen balance shown above, so it is also wrong. The stoichiometric methane concentration works out to 9.5% by volume.
\[ \boxed{9.5\%} \]
Firedamp is the methane gas found in coal mines, and it can explode when mixed with air in the right proportion. A stoichiometric mixture is the exact ratio of fuel to oxidiser at which the fuel burns completely, using up exactly all the oxygen supplied, with none left over. We need the volume percent of methane in air that gives this exact ratio.
Step 2: Key Formula or Approach:
Methane burns in oxygen by the reaction
\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \]
So one volume of methane needs exactly two volumes of oxygen to burn completely. Air is only 21% oxygen by volume, with the rest being nitrogen that does not take part in the burning but still occupies volume in the mixture. So the volume of air needed to supply 2 volumes of oxygen is
\[ V_{air} = \frac{V_{O_2}}{0.21} \]
Step 3: Detailed Explanation:
Take 1 volume of methane as the basis. It needs 2 volumes of oxygen, so the air needed is
\[ V_{air} = \frac{2}{0.21} = 9.524 \text{ volumes} \]
The total volume of the methane-air mixture is the methane plus this air:
\[ V_{total} = 1 + 9.524 = 10.524 \text{ volumes} \]
The percentage of methane by volume in the stoichiometric mixture is then
\[ \%CH_4 = \frac{1}{10.524} \times 100 = 9.5\% \]
Step 4: Final Answer:
Option (A), 5.4%, is close to the lower explosive limit of methane in air, not the stoichiometric value. Option (D), 14.8%, is close to the upper explosive limit of methane, again not the stoichiometric point. Option (C), 10.8%, does not come from the correct oxygen balance shown above, so it is also wrong. The stoichiometric methane concentration works out to 9.5% by volume.
\[ \boxed{9.5\%} \]
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