Page 192 - Physical Chemistry

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General 5.61 Without using tables, state which of each of the follow-
5.56 Give the SI units of (a) pressure; (b) enthalpy; (c) molar ing pairs has the greater S° m,298 : (a) C H (g) or n-C H (g);
4
2
10
6
entropy; (d) Gibbs energy; (e) molar volume; (f) temperature. (b) H O(l) or H O(g); (c) H(g) or H (g); (d) C H (s) or
2
2
10
8
2
C H (g).
10
8
5.57 If H° for a reaction is independent of T, prove that the
reaction’s S° is independent of T. [Hint: Use Eq. (5.18).] 5.62 Without using thermodynamics tables, predict the sign
of S° 298 and H° 298 for each of the following. You can use
5.58 (a) Show that for any substance lim a 0. (Hint:
T→0 Table 19.1. (a)(C H ) O(l) → (C H ) O(g); (b)Cl (g) → 2Cl(g);
Use one of the Maxwell relations.) (b) Verify that a for an ideal 2 5 2 2 5 2 2
(c) C H (g) → C H (s); (d) combustion of (COOH) (s) to
2
8
8
10
10
gas does not obey the result in (a). Hence, (classical) ideal
CO (g) and H O(l); (e) C H (g) H (g) → C H (g).
6
2
2
2
4
2
2
gases do not obey the third law (as noted in Sec. 5.7).
5.63 The Tennessee Valley Authority’s coal-burning Paradise
5.59 Without consulting tables, state whether or not each of the power plant (by no means the world’s largest) produces 1000
following must be equal to zero. (Note: S is the conventional MW of power and has an overall thermal efficiency of 39%.
entropy.) (a) H° (N O , g); (b) H° (Cl, g); (c) H° (Cl , The overall thermal efficiency is defined as the work output di-
f
298
2
298
f
2
298
f
5
g); (d) S° m,298 (Cl , g); (e) S° (N O , c); (f) S° (N , g); vided by the absolute value of the heat of combustion of the
f
350
2
5
2
2
m,0
(g) G° (N , g); (h) C° P,m,0 (NaCl, c); (i) C° P,m,298 (O , g). fuel. [Since only 85 to 90% of the heat of combustion is trans-
400
f
2
2
5.60 The adiabatic flame temperature is the temperature that ferred to the steam, the overall thermal efficiency is not the
would be reached in a flame if no heating of the surroundings same as the efficiency defined by Eq. (3.1).] The typical en-
occurred during the combustion, so that U of the reaction is thalpy of combustion of coal is 10000 British thermal units
used entirely to raise the temperature of the reaction products (Btu) per pound, where 1 Btu equals 1055 J. How many pounds
and to do expansion work. To estimate this temperature, use the of coal does the Paradise plant burn in (a) one minute; (b) one
scheme of Fig. 5.4b with the following changes. Since the com- day; (c) one year?
bustion is at constant P and is assumed adiabatic, we have
5.64 True or false? (a) When an exothermic reaction in a
H q 0, so step (a) has H 0 instead of U 0.
P closed system with P-V work only is run under isobaric and
Likewise, H replaces U in steps (b) and (c) . For combustion
adiabatic conditions, H 0. (b) When a substance is in its
in air, the calorimeter K is replaced by 3.76 moles of N (g) for
2 thermodynamic standard state, the substance must be at 25°C.
each mole of O (g). Estimate the adiabatic flame temperature
2 (c) G of an element in its stable form and in its standard state at
for combustion of methane, CH (g), in air initially at 25°C, as-
4 25°C is taken to be zero.
suming that O and CH are present in stoichiometric amounts.
2 4
Use Appendix data. Note that step (b) involves vaporization of 5.65 What experimental measurements are needed to deter-
water. Proper calculation of H requires integrating C of the mine H° , S° , and G° of a newly synthesized liquid
b P f 298 m,298 f 298
products. Instead, assume that an average C of the products hydrocarbon?
P
can be used over the temperature range involved and that this
5.66 Use Appendix H° 298 and S° m,298 data to calculate
f
average is found by combining the following 1000-K C° val-
P,m G° of C H OH(l). Compare with the value listed in the
ues, given in J/(mol K): 32.7 for N (g), 41.2 for H O(g), 54.3 f 298 2 5
2 2 Appendix.
for CO (g).
2