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NUMERICAL PROBLEMS 83

(s) + 2 C(graphite) + -1
P4.12 Consider the reaction TiO 2 constant is 330. J K . Calculate the enthalpy of solution of
2 Cl (g) ¡ 2 CO(g) + TiCl (l) for which ¢H° R,298K = Na SO in water at this concentration. Compare your result
2
4
4
2
-1
-80. kJ mol . Given the following data at 25°C, (a) calculate with that calculated using the data in Table 4.1 (Appendix B,
¢H° R at 135.8°C, the boiling point of TiCl , and (b) calculate Data Tables).
4
¢H° f for TiCl (l) at 25°C: P4.19 Nitrogen is a vital component of proteins and nucleic
4
Substance TiO (s) Cl (g) C(graphite) CO(g) TiCl (l) acids, and thus is necessary for life. The atmosphere is com-
4
2
2
-1
¢H° f (kJ mol ) –945 –110.5 posed of roughly 80% N , but most organisms cannot directly
2
utilize N for biosynthesis. Bacteria capable of “fixing” nitro-
2
-1
–1
C P,m (J K mol ) 55.06 33.91 8.53 29.12 145.2 gen (i.e., converting N to a chemical form, such as NH ,
2
3
which can be utilized in the biosynthesis of proteins and
Assume that the heat capacities are independent of temperature.
nucleic acids) are called diazotrophs. The ability of some
P4.13 Calculate ¢H° R and ¢U° R for the oxidation of plants like legumes to fix nitrogen is due to a symbiotic rela-
benzene. Also calculate
tionship between the plant and nitrogen-fixing bacteria that
¢H° -¢U° R live in the plant’s roots. Assume that the hypothetical reaction
R
¢H° R for fixing nitrogen biologically is
P4.14 Several reactions and their standard reaction N 2 (g) + 3 H 2 O(l) ¡ 2 NH 3 (aq) + 3 2 2 (g)
O
enthalpies at 298.15 K are given here:
a. Calculate the standard enthalpy change for the biosynthetic
–1
≤H° R (kJ mol ) fixation of nitrogen at T = 298 K. For NH (aq), ammonia
3
CaC (s) + 2 H O(l) ¡ Ca(OH) (s) + C H (g) -127.9 dissolved in aqueous solution, ¢H° =-80.3 kJmol -1 .
2
2
2
2 2
f
Ca(s) + 1>2 O (g) ¡ CaO(s) -635.1 b. In some bacteria, glycine is produced from ammonia by
2
CaO(s) + H O(l) ¡ Ca(OH) (s) –65.2 the reaction
2
2
NH 3 (g) + 2 CH 4 (g) + 5 O
The standard enthalpies of combustion of graphite and C H (g) 2 2 (g)
2 2
-1
are –393.51 and –1299.58 kJ mol , respectively. Calculate the ¡ NH 2 CH 2 COOH(s) + H 2 O(l)
standard enthalpy of formation of CaC (s) at 25°C.
2
Calculate the standard enthalpy change for the
P4.15 Benzoic acid, 1.35 g, is reacted with oxygen in a synthesis of glycine from ammonia. For glycine,
constant volume calorimeter to form H O(l) and CO (g) at ¢H° = -537.2 kJ mol -1 . Assume T = 298 K.
2
2
f
298 K. The mass of the water in the inner bath is 1.55 * c. Calculate the standard enthalpy change for the synthesis of
3
10 g. The temperature of the calorimeter and its contents
glycine from nitrogen, water, oxygen, and methane.
rises 2.76 K as a result of this reaction. Calculate the
calorimeter constant. P4.20 If 3.365 g of ethanol C H OH(l) is burned com-
2 5
pletely in a bomb calorimeter at 298.15 K, the heat produced
P4.16 The total surface area of Asia consisting of forest, is 99.472 kJ.
7
cultivated land, grass land, and desert is 4.46 * 10 km 2 .
a. Calculate ¢H° combustion for ethanol at 298.15 K.
Every year, the mass of carbon fixed by photosynthesis by
vegetation covering this land surface according to the reac- b. Calculate ¢H° f of ethanol at 298.15 K.
tion 6 CO (g) + 6 H O(l) ¡ C H O (s) + 6 O (g) is P4.21 From the following data, calculate ¢H° R,391.4 K for the
6 12 6
2
2
2
3
-2
about 455. * 10 kg km . Calculate the annual enthalpy reaction CH COOH(g) + 2 O (g) ¡ 2 H O(g) + 2 CO (g):
2
3
2
2
change resulting from photosynthetic carbon fixation over –1
the land surface given earlier. Assume P = 1 bar and ≤H° R (kJ mol )
T = 298 K. CH COOH(l) + 2 O (g) ¡ 2 H O(l) + 2 CO (g) –871.5
2
2
2
3
P4.17 Calculate ¢H° R and ¢U° R at 298.15 K for the follow- H O(l) ¡ H O(g) 40.656
2
2
ing reactions: CH COOH(l) ¡ CH COOH(g) 24.4
3
3
a. 4 NH (g) + 6 NO(g) ¡ 5 N (g) + 6 H O(g)
3
2
2
Values for ¢H° R for the first two reactions are at 298.15 K,
b. 2 NO(g) + O (g) ¡ 2 NO (g) and for the third reaction at 391.4 K.
2
2
c. TiCl (l) + 2 H O(l) ¡ TiO (s) + 4 HCl(g)
4
2
2
Substance CH COOH(l) O (g) CO (g) H O(l) H O(g)
2
2
2
2
3
d. 2NaOH(aq) + H SO (aq) ¡ Na SO (aq) + 2 H O(l)
2
2
4
2
4
C P,m > R 14.9 3.53 4.46 9.055 4.038
Assume complete dissociation of NaOH, H SO , and
2
4
Na SO 4
2
P4.22 A 0.1429 g sample of sucrose C H O is
12 22 11
e. CH (g) + H O(g) ¡ CO(g) + 3 H (g) burned in a bomb calorimeter. In order to produce the
2
2
4
f. CH OH(g) + CO(g) ¡ CH COOH(l) same temperature rise in the calorimeter as the reaction,
3
3
2353 J must be expended.
SO (s) is dissolved in 225 g of water
P4.18 A sample of Na 2 4
at 298 K such that the solution is 0.325 molar in Na SO . a. Calculate ¢ U and ¢ H for the combustion of 1 mole
4
2
A temperature rise of 0.146°C is observed. The calorimeter of sucrose.