Biogas can be generated as a by-product of many farming activities - VCE - SSCE Chemistry - Question 10 - 2011 - Paper 1

To find the ratio of the volume of methane produced to the volume of carbon dioxide produced, we need to analyze the reactions step by step and determine how much of each gas is generated in the process.

1. Step 1: Fermentation produces 2 moles of ethanol and 2 moles of carbon dioxide from 1 mole of glucose. Thus, from 1 mole of glucose, we get:

   • Volume of CO₂ = 2 moles
   • Volume of CH₄ = 0 moles

2. Step 2: Oxidation does not produce methane but converts ethanol to acetic acid and water. The balance of gases remains unchanged.

   • Volume of CO₂ remains = 2 moles
   • Volume of CH₄ remains = 0 moles

3. Step 3: Neutralization produces 1 mole of carbon dioxide for every 2 moles of acetic acid:

   • Therefore, from 2 moles of acetic acid, we get an additional 1 mole of CO₂. New total volume of CO₂ = 2 + 1 = 3 moles
   • Volume of CH₄ remains = 0 moles

4. Step 4: Bacterial Conversion converts the calcium acetate into methane and carbon dioxide:

   • This step produces 2 moles of methane (CH₄) and 1 mole of carbon dioxide (CO₂).
   • Final volume of CH₄ = 2 moles
   • Final volume of CO₂ = 3 moles

Putting all this together, we have:

• Volume of CH₄ = 2 moles
• Volume of CO₂ = 3 moles

The ratio of methane to carbon dioxide is therefore: $\text{Ratio} = \frac{\text{Volume of } CH₄}{\text{Volume of } CO₂} = \frac{2}{3}$

Thus, the answer is C. 2:3.