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 ($CH_4$) produced to the volume of carbon dioxide ($CO_2$) produced throughout the steps:

1. From Step 1: The fermentation of glucose produces 2 moles of ethanol ($C_2H_5OH$) and 2 moles of $CO_2$ for every 1 mole of glucose; therefore, 2 moles of $CO_2$ are produced.

2. From Step 2: The oxidation step generates 1 mole of acetic acid ($CH_3COOH$), which does not produce additional $CO_2$, so the count remains at 2 moles of $CO_2$.

3. From Step 3: In the neutralisation step, 2 moles of acetic acid produce 1 mole of $CO_2$. So, the total $CO_2$ produced becomes 2 + 1 = 3 moles.

4. From Step 4: In this final step, 1 mole of Calcium Acetate reacts with water to produce 2 moles of $CH_4$ and 1 mole of $CO_2$; thus, the total volume of $CO_2$ becomes 3 + 1 = 4 moles of $CO_2$.

5. Final Ratio: Now, we have 2 moles of $CH_4$ and 4 moles of $CO_2$. The ratio of the volume of $CH_4$ to $CO_2$ is: rac{2}{4} = rac{1}{2} This indicates a ratio of 2:1 when simplified in terms of $CH_4$ to $CO_2$.