natural gas specific heat

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Chemistry homework question. Please help in any way you can. THANK YOU!?

1. You want to heat your house with natural gas CH4. The house has 275 sq. m of the floor area and the height of 2.5 m (between the floor and the ceiling). The air has a specific molar heat capacity of 29.1 j/mol*K. The molar mass of air is 28.9 and a density of 1.22 g/L at these temperatures. How much methane do you have to use in order to heat air from 15 to 22 oC in your house?

V = 275 x 2.5 = 687.5 m^3 =>687500 dm^3 =>

mass = 1.22 g/dm^3 x 687500 dm^3 =838750 g

moles air = 838750 g / 28.9 g/mol =29022

Q = mol x molar heat capacity x delta T=
= 29022 x 29.1 ( 22- 15) = 7943321 J required

I find ( on wikipedia) that 1 mole of methane gives 890000 J

moles methane needed = 7943321 / 890000 =8.9

mass CH4 = 8.9 mol x 16 g/mol =142.4 g

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