A butyl rubber bag of total volume 3.0 m3 is used as a biogas digester. Each day it is fed an input of 0.20 m3 of slurry, of which 4.0 kg is volatile solids, and a corresponding volume of digested slurry is removed. (This input corresponds roughly to the waste from 20 pigs.) Assuming that a typical reaction in the digestion process is
C12H22O11 + H2O → 6CH4+ 6CO2
and that the reaction takes 7 days to complete, calculate
(i) the volume of gas
(ii) the heat obtainable by combustion of this gas for each day of operation of the
digester
(iii) how much kerosene would have the same calorific value as one day’s biogas?
To calculate the answers to each part of the question, we can follow these steps:
(i) Calculate the volume of gas produced per day:
- We know that the digester is fed with 0.20 m³ of slurry daily.
- According to the reaction equation, 1 mole of C12H22O11 (sugar) produces 6 moles of CH4 (methane) gas.
- To determine the number of moles of sugar in the slurry, we need its molar mass.
- The molar mass of C12H22O11 is 342 g/mol. Therefore, 4.0 kg (4000 g) of sugar is equivalent to 4000 g / 342 g/mol = 11.70 mol.
- As 1 mole of sugar produces 6 moles of methane, the total volume of methane gas produced is 11.70 mol × 6 = 70.20 m³ of CH4.
(ii) Calculate the heat obtainable by combustion of the gas per day:
- The heat of combustion of methane is -890 kJ/mol.
- Multiplying the number of moles of methane (70.20 mol) by the heat of combustion (-890 kJ/mol), we get -62,418 kJ, which is the heat obtainable from the combustion of the gas per day.
(iii) Calculate the kerosene equivalent:
- To find how much kerosene has the same calorific value, we need to determine its calorific value per unit mass.
- The calorific value of kerosene is approximately 44 MJ/kg or 44,000 kJ/kg.
- Divide the heat obtainable per day (62,418 kJ) by the calorific value of kerosene per kilogram (44,000 kJ/kg) to find the mass of kerosene: 62,418 kJ / 44,000 kJ/kg = 1.42 kg.
Therefore, the answers to the questions are:
(i) The volume of gas produced per day is 70.20 m³ of CH4.
(ii) The heat obtainable by combustion of this gas per day is -62,418 kJ.
(iii) One day's biogas is equivalent to approximately 1.42 kg of kerosene.