Answer & Solution
Answer: Option
D
Solution:
Let's break down this question step by step to understand how to solve it.
First, we need to know what happens when CH₄ (Methane) burns completely. This process is called complete combustion.
The chemical reaction for the complete combustion of methane is:
CH₄ + O₂ → CO₂ + H₂O
This equation isn't balanced yet. We need to make sure the number of atoms of each element is the same on both sides of the arrow. Let's balance it:
CH₄ + 2O₂ → CO₂ + 2H₂O
This balanced equation tells us that 1 molecule of Methane (CH₄) reacts with 2 molecules of Oxygen (O₂) to produce 1 molecule of Carbon Dioxide (CO₂) and 2 molecules of Water (H₂O).
Since the volumes are given at STP (Standard Temperature and Pressure), a very important principle applies: equal volumes of all gases contain the same number of molecules at STP. This means we can directly use the volume ratios from the balanced chemical equation.
So, the balanced equation tells us: 1 volume of CH₄ needs 2 volumes of O₂.
The question states we have 100 m³ of pure CH₄.
Therefore, the amount of Oxygen needed for its complete combustion will be:
Oxygen needed = 100 m³ CH₄ * (2 volumes O₂ / 1 volume CH₄)
Oxygen needed = 200 m³ O₂.
Now, we need to find out how much air is required to supply this 200 m³ of oxygen.
The question tells us that air contains 21 vol.% of oxygen. This means that out of every 100 m³ of air, only 21 m³ is oxygen.
We need 200 m³ of oxygen. Let's set up a proportion to find the total volume of air needed:
If 21 m³ O₂ is present in 100 m³ Air,
Then 1 m³ O₂ is present in (100 / 21) m³ Air.
So, 200 m³ O₂ will be present in (100 / 21) * 200 m³ Air.
Let's calculate the total air required:
Air needed = (200 * 100) / 21
Air needed = 20000 / 21
Air needed ≈ 952.38 m³
Comparing this calculated value with the given options, the closest and correct answer is 952 m³.
Therefore, the correct option is Option D: 952.
