11. A litre of 18% glucose solution is converted anaerobically into methane and carbon dioxide. The theoretical
maximum volume of gases at NTP assuming ideality, produced on complete conversion of the entire glucose
would be:
1. 112 L
2. 67.2 L
3. 134.4 L
4. 22.4 L

Theoretical Gas Volume Production from Glucose Fermentation

In the process of anaerobic fermentation (such as in methane production), glucose is converted into gases like methane (CH₄) and carbon dioxide (CO₂). To calculate the theoretical maximum volume of gases produced, we need to consider the chemical reaction and stoichiometry involved.

The Chemical Reaction for Anaerobic Glucose Fermentation

The process of anaerobic fermentation of glucose (C₆H₁₂O₆) to methane and carbon dioxide can be represented by the following simplified equation:

C6H12O6→3CH4+3CO2C_6H_{12}O_6 \rightarrow 3CH_4 + 3CO_2C6​H12​O6​→3CH4​+3CO2​

This equation shows that 1 mole of glucose produces 3 moles of methane and 3 moles of carbon dioxide.

Step-by-Step Calculation:

1. Determine the amount of glucose in moles:
   The molecular weight of glucose (C₆H₁₂O₆) is:

   $$6\times 12+12\times 1+6\times 16=180\text{ g/mol}$$

   We are given a 1-liter solution of 18% glucose. This means:

   $$\text{Mass of glucose}=1\text{ L}\times 0.18\times 1000\text{ g/L}=180\text{ g of glucose}$$

   The number of moles of glucose is:

   180 g180 g/mol=1 mol of glucose\frac{180 \text{ g}}{180 \text{ g/mol}} = 1 \text{ mol of glucose}180 g/mol180 g​=1 mol of glucose

2. Calculate the total moles of gases produced:
   From the reaction equation, 1 mole of glucose produces 3 moles of methane and 3 moles of carbon dioxide, which totals:

   3 mol CH4+3 mol CO2=6 moles of gas3 \text{ mol CH}_4 + 3 \text{ mol CO}_2 = 6 \text{ moles of gas}3 mol CH4​+3 mol CO2​=6 moles of gas

3. Calculate the volume of gases at NTP (Normal Temperature and Pressure):
   At NTP (0°C and 1 atm), 1 mole of gas occupies 22.4 liters. Therefore, the total volume of gases produced will be:

   $$6\text{ moles}\times 22.4\text{ L/mol}=134.4\text{ L of gas}$$

✅ Correct Answer:

(3) 134.4 L

Conclusion:

By applying stoichiometry and gas laws, we can calculate that the theoretical maximum volume of gases (methane and carbon dioxide) produced from the complete anaerobic fermentation of 1 liter of 18% glucose solution is 134.4 liters. This volume assumes ideal gas behavior and complete conversion of glucose.

Understanding such calculations is crucial in fields like bioengineering, waste management, and renewable energy, especially in processes involving biogas production.