What is the mass of methane in grams?

Question

The heater used in a 4.41 m×3.45 m×2.99 m dorm room uses the combustion of natural gas (primarily methane gas) to produce the heat required to increase the temperature of the air in the dorm room. Assuming that all of the energy produced in the reaction goes towards heating only the air in the dorm room, calculate the mass of methane required to increase the temperature of the air by 7.91 °C. Assume that the specific heat of air is 30.0 J/K·mol and that 1.00 mol of air occupies 22.4 Lat all temperatures. Enthalpy of formation values can be found in this table. Assume gaseous water is produced in the combustion of methane.

Answer 1

ΔH_C (neg. because it's exothermic) = 2ΔH_f,H20(g) + ΔH_f,CO2 - ΔH_f,CH4 (look up in table - I ignored ΔH_f,O2 because it is an element in its natural state)

Q into room = -(m_CH4/M_CH4) ΔH_C = n_airC_airΔT

n_air = V_room*(1000 liters/m³)(22.4 liters/mole)

Solve for m_CH4 in grams (M_CH4 = 16.026 g/mole) (Remember to express ΔH in Joule/mole)

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