Concept explainers
9.91 You want to heat the air in your house with natural gas (CH4). Assume your house has 275 m2(ahout 2800 ft2) of floor area and that the ceilings are 2.50 m from the floors. The air in the house has a molar heat capacity of 29.1 J mol-l K-l. (The number of moles of air in the house may he found by assuming that the average molar mass of air is 28.9 g/mol and that the density of air at these temperatures is 1.22 g/L.) What mass of methane do you have to burn to heat the air from 15.0 to 22.0°C?
Interpretation:
The mass of methane required to raise the temperature of air in the house from
Concept Introduction:
- Chemical reactions proceed through absorption (endothermic) or evolution (exothermic) of heat.
- The quantity of heat absorbed or released depends on the amount of the substance, its specific heat capacity and the change in temperature.
- Specific heat capacity is the amount of heat required to raise a unit mass of a given substance through a unit degree increase in temperature.
Answer to Problem 9.91PAE
Solution: Mass of methane required = 4.25 kg
Explanation of Solution
Given: Initial temperature of air (T1) =
Final temperature of air (T2) =
Change in temperature (
Dimensions (volume) of the house =
Specific heat capacity of air, cair = 29.1 J/K-mol
Formula:
1. Enthalpy of combustion:
nproducts and nreactants are the number of moles of products and reactants respectively
2. Heat required to raise the temperature of air:
mair = mass of air
cair = specific heat capacity of air
Calculation:
Step I: Find enthalpy of combustion of methane
Based on equation 1 we have:
Substituting for the respective enthalpies formation:
Step II: Calculate the heat required to raise the temperature of air
Volume of air = volume of the room = 687.5 m3 = 687500 L
Now, the density of air = 1.22 g/L
Therefore, the mass of air occupied in the room =
The number of moles of air (nair) =
Based on equation 2:
Step III: Calculate the mass of methane
From Step II, 1 mole of methane releases an energy = 890.2 kJ
The number of moles of methane required corresponding to 236475.3 kJ energy =
=
1 mole of methane (CH4) = 16 g
The mass corresponding to 265.64 moles =
The mass of methane required to raise the temperature of air in the house from
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Chapter 9 Solutions
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