# 9.91 You want to heat the air in your house with natural gas (CH 4 ). Assume your house has 275 m 2 (ahout 2800 ft 2 ) 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?

### Chemistry for Engineering Students

3rd Edition
Lawrence S. Brown + 1 other
Publisher: Cengage Learning
ISBN: 9781285199023

### Chemistry for Engineering Students

3rd Edition
Lawrence S. Brown + 1 other
Publisher: Cengage Learning
ISBN: 9781285199023
Chapter 9, Problem 9.85PAE
Textbook Problem
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## 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 Introduction

Interpretation:

The mass of methane required to raise the temperature of air in the house from 150C to 220C should be calculated.

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.

### Explanation of Solution

Given: Initial temperature of air (T1) = 150C

Final temperature of air (T2) = 220C

Change in temperature ( ΔT ) = T2-T1=22-15=7.00C = (7 + 273) K = 280 K

Dimensions (volume) of the house = 275 m2×2.50 m = 687.5 m3

Specific heat capacity of air, cair = 29.1 J/K-mol

Formula:

1. Enthalpy of combustion:

ΔHrxn=nproductsΔHf0(products) - n reactantsΔHf0 (reactants) -------(1)

nproducts and nreactants are the number of moles of products and reactants respectively

ΔHf (products)0 and ΔHf (reactants)0 are the standard heats of formation of the products and reactants respectively

2. Heat required to raise the temperature of air:

q = mair×cair×ΔT--------(2)

mair = mass of air

cair = specific heat capacity of air

ΔT = change in temperature

Calculation:

Step I: Find enthalpy of combustion of methane

CH4(g) + 2O2(g)CO2(g) + 2H2O(g)

Based on equation 1 we have:

Δ

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