Page 107 - Physical chemistry eng

84 CHAPTER 4 Thermochemistry

b. Using the data tables and your answer to (a), calculate P4.30 Use the average bond energies in Table 4.3 to esti-
¢H° f for sucrose. mate ¢ U for the reaction C H (g) + H (g) ¡ C H (g).
2
2 6
2 4
c. The rise in temperature of the calorimeter and its contents Also calculate ¢U° R from the tabulated values of ¢H° f for
as a result of the reaction is 1.743 K. Calculate the heat reactant and products (Appendix B, Data Tables). Calculate
capacity of the calorimeter and its contents. the percent error in estimating ¢U° R from the average bond
energies for this reaction.
P4.23 Calculate ¢H° R at 675 K for the reaction 4 NH (g) +
3
6 NO(g) ¡ 5 N (g) + 6 H O(g) using the temperature P4.31 Use the tabulated values of the enthalpy of combus-
2
2
dependence of the heat capacities from the data tables. tion of benzene and the enthalpies of formation of CO (g) and
2
Compare your result with ¢H° R at 298.15. Is the difference H O(l) to determine ¢H° f for benzene.
2
large or small? Why? P4.32 Compare the heat evolved at constant pressure per
P4.24 From the following data at 298.15 K as well as data mole of oxygen in the combustion of sucrose (C H O )
12 22 11
in Table 4.1 (Appendix B, Data Tables), calculate the standard and palmitic acid (C H O ) with the combustion of a typi-
16 32 2
enthalpy of formation of H S(g) and of FeS (s): cal protein, for which the empirical formula is C H NO.
4.3 6.6
2
2
Assume for the protein that the combustion yields N (g),
2
–1
≤H° R (kJ mol ) CO (g), and H O(l). Assume that the enthalpies for com-
2
2
Fe(s) + 2 H S(g) ¡ FeS (s) + 2 H (g) –137.0 bustion of sucrose, palmitic acid, and a typical protein are
2
2
2
-1
-1
-1
>
H S(g) + 32 O (g) ¡ H O(l) + SO (g) –562.0 5647 kJ mol , 10,035 kJ mol , and 22.0 kJ g , respectively.
2
2
2
2
Based on these calculations, determine the average heat
P4.25 Using the protein DSC data in Problem P4.10, calcu- evolved per mole of oxygen consumed, assuming combustion
late the enthalpy change between T = 288 K and T = 318 K. of equal moles of sucrose, palmitic acid, and protein.
Give your answer in units of kJ per mole. Assume the molec- P4.33 A camper stranded in snowy weather loses heat by
ular weight of the protein is 14,000. grams. [Hint: You can wind convection. The camper is packing emergency rations
perform the integration of the heat capacity by estimating the consisting of 58% sucrose, 31% fat, and 11% protein by
area under the DSC curve and above the dotted baseline in weight. Using the data provided in Problem P4.32 and assum-
Problem P4.10. This can be done by dividing the area up into ing the fat content of the rations can be treated with palmitic
small rectangles and summing the areas of the rectangles. acid data and the protein content similarly by the protein data
Comment on the accuracy of this method.] in Problem P4.32, how much emergency rations must the
P4.26 Given the following heat capacity data at 298 K, cal- camper consume in order to compensate for a reduction in
culate ¢H° f of CO (g) at 525 K. Assume that the heat capaci- body temperature of 3.5 K? Assume the heat capacity of the
2
ties are independent of temperature. body equals that of water. Assume the camper weighs 67 kg.
State any additional assumptions.
Substance C(graphite) O (g) CO (g)
2
2
P4.34 In order to get in shape for mountain climbing,
>
-1 -1
C , J mol K 8.52 28.8 37.1 an avid hiker with a mass of 60. kg ascends the stairs in
P m
the world’s tallest structure, the 828 m tall Burj Khalifa in
P4.27 Calculate ¢H for the process in which Cl (g) initially
2
at 298.15 K at 1 bar is heated to 690. K at 1 bar. Use the tem- Dubai, United Arab Emirates. Assume that she eats
energy bars on the way up and that her body is 25%
perature-dependent heat capacities in the data tables. How large
efficient in converting the energy content of the bars into the
is the relative error if the molar heat capacity is assumed to be
work of climbing. How many energy bars does she have to
constant at its value of 298.15 K over the temperature interval?
3
eat if a single bar produces 1.08 * 10 kJ of energy upon
P4.28 From the following data at 298.15 K C, calculate the
metabolizing?
standard enthalpy of formation of FeO(s) and of Fe O (s):
2 3
P4.35 We return to the 60. kg hiker of P4.34, who is
–1
≤H° R (kJ mol ) climbing the 828 m tall Burj Khalifa in Dubai. If the
Fe O (s) + 3 C(graphite) ¡ 2 Fe(s) + 3 CO(g) 492.6 efficiency of converting the energy content of the bars into
2 3
the work of climbing is 25%, the remaining 75% of the
FeO(s) + C(graphite) ¡ Fe(s) + CO(g) 155.8
energy released through metabolism is heat released to her
C(graphite) + O (g) ¡ CO (g) -393.51 body. She eats two energy bars and a single bar produces
2
2
3
CO(g) + 1>2 O (g) ¡ CO (g) -282.98 1.08 * 10 kJ of energy upon metabolizing. Assume that
2
2
the heat capacity of her body is equal to that for water.
P4.29 Calculate the average C—H bond enthalpy in Calculate the increase in her temperature at the top of the
methane using the data tables. Calculate the percent error in structure. Is your result reasonable? Can you think of a
equating the average C—H bond energy in Table 4.3 with the mechanism by which her body might release energy to avoid
bond enthalpy. a temperature increase?