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Solutions to Problems 57 41. (a) Divide by the molecular weight: (kcal ÷ (g = kcal g⁻¹. Methane: = 16 g -212.8 mol⁻¹ kcal (MW mol⁻¹ of = 13.3 kcal Ethane: = 12.4 kcal g⁻¹ Propane: = 12.0 kcal g⁻¹ Pentane: = 11.7 kcal g⁻¹ (b) Ethanol (gas): = -7.3 kcal (c) Qualitatively, the observation is quite consistent with the much lower heat production by weight from the combustion of ethanol alkanes; oxygen-containing molecules are indeed poorer sources of energy as fuels. 42. (a) 2 + 3 O₂ 2 CO₂ + 4 H₂O Except for liquid H₂O, all substances are in the gas phase. 2 (CH₃)₃COCH₃ + 15 O₂ 10 CO₂ + 12 H₂O (b) The molecular weight of methanol (32) is close to that of ethane (30), but the value for ethane (-372.8 kcal is much greater in magnitude than that of methanol. Similarly, (CH₃)₃COCH₃ has a molecular weight of 88, close to that of hexane (86). The for the latter is -995.0 kcal mol⁻¹, again considerably more than that for 2-methoxy-2-methylpropane. Although addition of oxygenated compounds to the fuel mixtures of internal combustion engines reduces the heat yield per mass of fuel upon combustion, it accomplishes two other goals. First, the oxygen supplied in these additives contributes to permit more complete oxidation of the components of the fuel mix, reducing emission of partly oxidized byproducts such as CO. Second, the fuel mix is less susceptible to so-called pre-ignition, in which the fuel ignites before the piston has had a chance to reach the endpoint of its com- pression stroke in the cylinder. Pre-ignition results in "knocking" noises in an engine and wastes energy. 43. (a) Calculate for both the primary and the secondary hydrogen abstraction reactions first. Data: DH° for primary C-H = 101 kcal mol⁻¹; for secondary C-H, 98.5 kcal mol⁻¹; for HBr, 87 kcal mol⁻¹. Therefore, (primary C-H abstraction) = 101 - 87 = +14 kcal mol⁻¹ (secondary C-H abstraction) = 98.5 - 87 = +11.5 kcal mol⁻¹ So, we have the following energy diagram as a result: + HBr = 15 kcal = +14 kcal mol⁻¹ = 13 kcal mol⁻¹ E = +11.5 kcal mol⁻¹ CH₃CH₂CH₃ + Br. Reaction coordinate