We are asked to determine the mass of methane required to heat the air in a house by 15.0 ˚C.
Calculate mole air needed:
mol air = 175,000 mol air
q= 7.875 x 104 kJ
We'll use the thermochemical equation to calculate the mass of CH4.
Molar mass CH4 = 16.05 g/mol
CH4(g) + O2(g) → CO2(g) + H2O(g); ΔHrxn˚ = –802.3 kJ/mol
Combustion of natural gas (primarily methane) occurs in most household heaters. The heat given off in this reaction is used to raise the temperature of the air in the house. Assuming that all the energy given off in the reaction goes to heating up only the air in the house, determine the mass of methane required to heat the air in a house by 15.0 ˚C. Assume each of the following: house dimensions are 35.0m x 35.0m x 3.2 m; specific heat capacity of air is 30 J/K•mol; 1.00 mol of air occupies 22.4 L for all temperatures concerned.