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 10.0 ∘C. Assume each of the following: house dimensions are 35.0 m × 35.0 m × 3.2 m ; specific heat capacity of air is 30 J/K⋅mol; 1.00 mol of air occupies 22.4L for all temperatures concerned.

Answer :

dsdrajlin

Answer:

0.92 kg

Explanation:

The volume occupied by the air is:

[tex]35.0m\times 35.0m \times 3.2m \times \frac{10^{3}L }{1m^{3} } =3.9 \times 10^{6} L[/tex]

The moles of air are:

[tex]3.9 \times 10^{6} L \times \frac{1.00mol}{22.4L} =1.7 \times 10^{5}mol[/tex]

The heat required to heat the air by 10.0 °C (or 10.0 K) is:

[tex]1.7 \times 10^{5}mol \times \frac{30J}{K.mol} \times 10.0 K = 5.1 \times 10^{7}J[/tex]

Methane's heat of combustion is 55.5 MJ/kg. The mass of methane required to heat the air is:

[tex]5.1 \times 10^{7}J \times \frac{1kgCH_{4}}{55.5 \times 10^{6} J } =0.92kgCH_{4}[/tex]

Combustion is a type of chemical reaction in which a compound reacts in the presence of air to form the product. The mass of methane required in the reaction is 0.92 kg.

What is mass?

Mass is the amount of the weight or the matter that depicts the quantity in grams, kilograms etc.

The volume occupied by the air in the house is calculated as:

[tex]35 \times 35 \times 3.2 \times \dfrac{10^{3}\;\rm L}{1\;\rm m^{3}} = 3.9\times 10^{6}\;\rm L[/tex]

The number of moles of air is:

[tex]3.9\times 10^{6}\;\rm L\times \dfrac{1\;\rm mol}{22.4\;\rm L}= 1.7\times 10^{5}\;\rm mol[/tex]

The heat needed to heat the air of the room is:

[tex]1.7\times 10^{5}\;\rm mol \times \dfrac{30\;\rm J}{\rm K.mol}\times 10\;\rm K= 5.1\times 10^{7}\;\rm J[/tex]

The heat of combustion of methane is 55.5 MJ/kg so the mass of methane will be:

[tex]5.1\times 10^{7}\;\rm J \times \dfrac{1}{55.5\times 10^{6}}= 0.92\;\rm kg[/tex]

Therefore, 0.92 kg is the mass required of methane.

Learn more about combustion and mass here:

https://brainly.com/question/18704325

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