Cairo University
Metallurgical Department
Faculty of Engineering
2nd Year Metallurgy
Department of Mining, Petroleum
Physical Chemistry
and Metallurgical Engineering
2011/2012 (1st term)
Sheet 7: Thermochemistry, Enthalpy and Entropy as Function of Pressure, and
the Third Law of Thermodynamics
1. One mole of gold is taken from state 1 ( p=1 atm. T=293K ) to state 2 ( p=1
atm. T=273K ). What pressure must be applied to gold at 273 K in order to
raise its enthalpy back to that of state 1 (call this state 3 )? Calculate the
entropy difference between states 1 and 3; given the following data: the
density of Au at 20 ̊C is 19.3 gm/cm3 ; the coefficient of thermal expansion
of Au is 1.344 x 10-5 (K)-1 which is independent of pressure; and the atomic
weight of Au is 197; given that:
CP (Au(S)) = 5.66 + 1.24 x 10-3 T – 6,82 x 105 T-2 cal/(deg.gm atom).
2. Calculate the standard heat change of the following reaction at 25 °C and 1
atmospheric pressure: 3FeO + 2Al  Al2O3 + 3Fe, per mole of Al2O3
formed, per mole of Fe formed, per mole of FeO reacted, per mole of Al
reacted and per gram of Fe formed; given that:
∆H𝑓° (FeO) at 298K = - 63.3 Kcal/mole
∆H𝑓° (Al2O3) at 298K= - 400 Kcal/mole, and The atomic weight of Fe = 56
3. Calculate the standard heat of formation of solid WO3 from solid W and O2
gas at 25 °C and 1 atmosphere pressure from the following data at 25° C
and 1 atm:
W(s)
+
O2(g)  WO2(s)
∆H𝑓° (R) at 298K = - 134 Kcal
1
O2(g)  W3O8(s)
ΔHf°(R) at 298K = - 131.5 Kcal
W3O8(s) + 0.5 O2(g)  3WO3(s)
ΔHf°(R) at 298K = - 66.5 Kcal
3WO2(s) +
4. Predict the heat of fusion for LiCl at 883K, given the followings:
Li(l) + 0.5 Cl2(g)  LiCl(l)
∆H𝑓° at 883K = - 92.347 Kcal/mole
Li(l) + 0.5 Cl2(g)  LiCl(s)
∆H𝑓° at 883K = - 97.105 Kcal/mole
5. Calculate the standard heat of formation of anhydrous aluminum chloride
from
the following data:
2Al(s) + 6HCl(aq.)  Al2Cl6(aq.) + 3H2(g)
H2(g)
+
∆H𝑓° (R) at 298K = - 240 Kcal
Cl2(g)  2HCl(g)
∆H𝑓° (R) at 298K = - 44 Kcal
∆H𝑓° (R) at 298K = - 17.5 Kcal
HCl(g) +
aq.
 HCl(aq.)
Al2Cl6 +
aq.
 Al2Cl6(aq.)
∆H𝑓° (R) at 298K = - 153.7 Kcal
6. The enthalpy changes for the following reactions are as follows:
2B + 3H2 + 3O2 + aq.  2H3BO3(aq.) ∆H𝑓° (R) at 298K = - 512.8 Kcal
∆H𝑓° (R) at 298K = - 4.12
B2O3 + 3H2O(l) + aq.  2H3BO3(aq.)
H2
Kcal
∆H𝑓° (R) at 298K = - 68.73 Kcal
+ 0.5 O2  H2O(l)
Calculate the standard heat of formation of B2O3 per mole of B2O3, and per
gram of B2O3. The atomic weight of B and O are 11 and 16, respectively.
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7. Calcium carbide is considered to be a potential fuel in the basic oxygen
converters and would be expected to burn into CaO and CO or CO 2,
depending
upon the conditions. If the heat required to raise the steel
scrap to 1600 °C is
333 kcal/Kg of scrap; assuming that the reactions
take place at 25 °C, calculate how many Kg of steel scrap can be charged
per 1000 Kg of CaC2, if:
a) all CaC2 is consumed to form CO,
b) all CaC2 is consumed to form CO2, or
c) 60% of CaC2 is utilized to produce CO2 and the rest produces CO.
Given that:
∆H𝑓° (CaC2) at 298K = - 14.1 Kcal/mole
∆H𝑓° (CaO) at 298K = - 151.8 Kcal/mole
∆H𝑓° (CO) at 298K
= - 26.42 Kcal/mole
∆H𝑓° (CO2) at 298K = - 94.05 Kcal/mole
The atomic weights of Ca and C are 40 and 12, respectively.
8. Eighteen grams of ice at 0 °C is heated to 100 °C until vapor is formed
against a external pressure of 1 atm. Calculate:
a) the thermal energy needed for the process,
b) the work done by the system on the surroundings, and
c) the internal energy change throughout the process.
You might use the following data for H2O:
ΔH°(fus) at 0 °C = 1.4 Kcal/mole
ΔH°(vap) at 100 °C = 9.7 Kcal/mole
Cp(H2O) = 18 Kcal/(deg.mole)
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9. Calculate the changes in heat content associated with the reduction
of the oxides of iron and aluminum, at 25 oC, according to the
following reactions:
Fe2O3 + 3C  2Fe + 3CO
Al2O3 + 3C  2Al + 3CO
You might use the following data:
2Fe + 1.5 O2  Fe2O3
ΔHf°(Fe2O3) at 298K = - 200,000 cal/mole
2Al + 1.5 O2  Al2O3
ΔHf°(Al2O3) at 298K = - 404,000 cal/mole
C(graphite) + 0.5 O2  CO ΔHf°(CO) at 298K = - 25,000 cal/mole
Entropies of CO, Al, Fe, Al2O3, Fe2O3: and C(graphite) at 25 oC are
74.3, 6.7, 6.5, 12.8, 21.8, and 1.39, cal/(deg-mole) for oxides or
Cal/(deg-gm atom) for elements, respectively.
10. Caluclate ∆H°(R) and ∆G°(R) at 298K for the following reaction:
4 CaO + Si → 2 Ca + Ca2SiO4
You might use the following data:
∆H𝑓° (CaO) at 298K = -151,600
cal/mole,
∆H𝑓° (Ca2SiO4) at 298K = -551,100
S ° (Ca) at 298K = 9.95 e.u.,
cal/mole,
S ° (Si) at 298K = 4.5 e.u. ,
S ° (CaO) at 298K = 9.5 e.u., and S ° (Ca2SiO4) at 298K = 30.5 e.u.
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11. The molar heats of formation and entropy change due to the formation of
various vanadium oxides from vanadium metal and oxygen gas at 298K are
listed after. From these information calculate ∆G°(R), ∆H°(R), and ∆S°(R)
at 298K for the following reactions:
a) 4 VO(s) + O2(g) → 2 V2O3(s)
b) 2 V2O3(s) + O2(g) → 4 VO2 (s)
c) 4 VO2(s) + O2(g) → 2 V2O5(s)
Oxide
∆H𝑓° (298K) , Kcal/mole
∆S ° (298K) , cal/(deg.mole)
VO
-103.2
-22.1
V2O3
-291.3
-85.6
VO2
-170.6
-43.9
V2O5
-370.6
-105.4
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