Mass of methane

Question

The heater used in a 4.36m x 3.3m x 3.05 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 5.15 °C. Assume that the specific heat of air is 30.0 J/K mol and that 1.00 mol of air occupies 22.4 L at all temperatures. Assume gaseous water is produced in the combustion of methane.

Answer 1

First thing is to find out the volume of air in the room.

Volume of air in the room = 4.36 m x 3.3 m x 3.05 m = 43.88 m³

Converting this to volume in liters, we have 43.88 m³ x 1000 L / m³ = 43,880 L of air

Next, we'll convert this to moles of air in the room:

43,880 L x 1 mol / 22.4 L = 1959 moles of air

Next, we'll calculate amount of energy needed to raise the temperature of the air by 5.15º:

q = mC∆T

q = heat = ?

m = mass = 1959 moles

C = specific heat of air = 30.0 J/molº

∆T = change in temperature = 5.15º

q = (1959 mols)(30.0 J/molº)(5.15º)

q = 302,666 J

To find the mass of methane needed, we would need to know the molar enthalpy of combustion for methane, which is not provided in the question. Wikipedia provides a value of -891 kJ/mole.

Mass methane required = 302,666 J x 1 kJ/1000 J = 302.7 kJ x 1 mol methane / 891 kJ = 0.340 mols

0.340 mols x 16 g / mole = 5.44 g methane