Final answer:
To calculate the volume of methane produced by the bacterial breakdown of a simple sugar, use stoichiometry and the ideal gas law. First, convert the mass of sugar to moles. Then, calculate the moles of methane and use the ideal gas law to find the volume of methane. The volume of methane, CH₄ is 6.884 L.
Step-by-step explanation:
To calculate the volume of methane produced by the bacterial breakdown of a simple sugar, we need to use the stoichiometry of the reaction and the ideal gas law. The balanced equation shows that 1 mole of sugar produces 3 moles of methane.
First, we convert the mass of sugar to moles using its molar mass. Then, we use the ideal gas law to calculate the volume of methane.
Step 1: Calculate the moles of sugar: 1.10 kg sugar * (1 mol / 180.16 g)
= 6.107 mol sugar
Step 2: Calculate the moles of methane: 6.107 mol sugar * (3 mol CH₄ / 1 mol sugar)
= 18.321 mol CH₄
Step 3: Calculate the volume of methane using the ideal gas law: V = (n * R * T) / P
V = (18.321 mol * 0.0821 L·atm/mol·K * 300 K) / 825 torr
V = 6.884 L