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MSJ2e_Ch06_ISM2_June26_p279

MSJ2e_Ch06_ISM2_June26_p279 - Chapter 6 Energy and Chemical...

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Chapter 6: Energy and Chemical Reactions Now, we’ll start the calculation with the specific sample give: 2.70 γ Αλ 1 μολ Αλ 26.9815 γ Αλ 1675.7 κϑεωολωεδ 2 μολ Αλ = 83.8 κϑεωολωε Check your answer: The sample is a tenth of a mole, and the equation shows that two moles of Al are needed. So, the resulting heat is half of a tenth of the original molar enthalpy. Chemical Fuels 101 . Define the problem : Determine the mass of fuel required to generate the heat to melt a mass of ice and raise its temperature to a specified value. Develop a plan : Use Equation 6.2 and the molar enthalpy of fusion to calculate the heat needed. Then balance the equation describing the combustion of the fuel. Use Equation 6.9, a table of molar enthalpies of formation, and the stoichiometry of the balanced equations to determine the molar enthalpy change for each combustion reaction. Then use that enthalpy and the molar mass as conversion factors to determine the mass of fuel needed. Execute the plan : To change a phase in the system, use q = m × H fus ; to change the temperature of the water, use q = c × m × T. q total = (m ice × H fus,ice ) + (c water × m water × T water ) To simplify the calculation, factor out the common mass term m ice = m water = m: q total = (m ice × H fus,ice ) + (c water × m water × T water ) To simplify the calculation, factor out the common mass term m ice = m water = m: q total = m × [( H fus,ice ) + (c water × T water )] Table 6.1 gives the specific heat capacity of water to be 4.184 J g –1 °C –1 . Question 46 gives the molar enthalpy of fusion of ice as 333 J/g. q total = 56.0 g × [(333 J/g) + (4.184 J g –1 °C –1 ) × (75.0 °C – 0. °C)] = 3.6 × 10 4 J The reaction describing the combustion of propane is similar to those described in Section 6.11. The fuel reacts with oxygen and making gaseous carbon dioxide and water: C 3 H 8 (g) + O 2 (g) CO 2 (g) + H 2 O(g) Balance the chemical equation: C 3 H 8 (g) + 5 O 2 (g) 3 CO 2 (g) + 4 H 2 O(g) H° = (3 mol) × H φ ο (CO 2 ) + (4 mol) × H φ ο (H 2 O(g)) – (1 mol) × H φ ο (C 3 H 8 ) – (5 mol) × H φ ο (O 2 ) Look up the H φ ο value in Table 6.9. H° = (3 mol) × (–393.509 kJ/mol) + (4 mol) × (–241.818 kJ/mol) – (1 mol) × (–103.8 kJ/mol) – (5 mol) × (0 kJ/mol) = –2044.0 kJ Now, we’ll figure out the mass needed for the melting and warming of the water sample: 3.6 10 4 ϑ 1 κϑ 1000 ϑ 1 μολ Χ 3 Η 8 2044.0 κϑ 44.0953 γ Χ 3 Η 8 1 μολ Χ 3 Η 8 = 0.78 γ Χ 3 Η 8 Check your answer : The molar enthalpy of C 3 H 8 is large and negative because propane is a good fuel. The energy needed for the sample is relatively small, so the mass of fuel is also small. 3
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Chapter 6: Energy and Chemical Reactions 102. Define the problem : Determine the mass of fuel required to raise the temperature of the air in a house to a specified value, given the dimensions of rooms in the house, the molar heat capacity of air, the average molar mass of air and the density of the air.
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