(c) How much heat is transferred to or from the reaction vessel when the products reach a temperature of 1263oC?
9.5 A mixture of CO and CO2, is passed over molybdenum dioxide (MoO2(s)) held in a furnace at a controlled temperature. Using Fig. 9.3 for the necessary data, determine:
(a) If the CO2/CO ratio in the flowing gas is 3, at what temperature T* does the solid oxide decompose to the metal? (i.e., the metal and oxide coexist at equilibrium)
For the following parts, draw a stability diagram like Fig. 9.2a with lines for the Mo/MoO2 equilibrium and for the CO2/CO equilibrium. Note that the latter depends on the CO2/CO ratio in the gas phase.
(b) If the CO2/CO ratio is held constant and the temperature is increased above T*, what is the stable phase?
(c) If the temperature is held constant at T* and the CO2/CO ratio is reduced, what phase is stable?
9.6 A gas mixture containing a CO2/CO ratio of 10-5 is passed over TiO2 at 1200oC. What is the stable form of titanium (metal, monoxide or dioxide)?
Hint: compare the O2 pressure established by the CO2/CO gas to that for the TiO/TiO2 equilibrium and for the Ti/TiO equilibrium.
9.7 In the melt/slag problem treated in Sect. 9.7, suppose that the oxygen pressure in a gas phase contacting the two condensed phases is specified.
(a) Derive the equations for the compositions of the melt and slag (i.e., x™' and xjj8) as functions of the equilibrium constants KM and KP and p .
(b) If the oxygen pressure is 10-11 atm, what are the equilibrium compositions of the melt and slag at 1000 K? Use the equilibrium constants given in the example at the end of Sect. 9.7.
(c) From the result obtained in part (a), over what range of oxygen pressure are solutions possible? Physically, what happens when pO is outside of this range?
9.8 In the melt-slag problem treated in Sect. 9.7, the dioxide PO2 replaced by the monoxide PO. The initial charge is 1 mole of M and 1 mole of PO. The system is closed, so oxygen is conserved during equilibration. Using the values of KM and KP given in the example in Sect. 9.7, calculate the compositions of the melt and slag.
9.9 In the melt-slag example in Sect. 9.7, the slag phase is ideal but M and P in the melt form a regular solution with Q = 5 kcal/mole. What are the equilibrium compositions of the two phases?
9.10 At high temperatures, diatomic molecules dissociate according to A2(g) = 2A(g).
(a) At temperature T and total pressure p, derive the expression for the degree of dissociation P, defined as the fraction of the total quantity of the element that exists in atomic form, in terms of the equilibrium constant KP.
(b) For I2 , the thermochemical parameters of the dissociation reaction are
AH° = 157 kJ/mole and AS° = 113 J/mole-K. What is the degree of dissociation in pure iodine vapor at 700 K and 0.1 atm total pressure?
(c) At very high temperatures, dissociation of diatomic molecules contributes to the heat capacity of the gas: CP = CP0 + CPdiss where CP0 is the heat capacity in the absence of dissociation. How large is CPdiss for the conditions of part (b)?
9.11 If methane is burned in oxygen, the principal reaction products are carbon dioxide and water (see Eq(9.1)). However, when methane is reacted with steam, the main reaction products are CO2 and H2.
(a) Write the equilibrium reaction (per mole of methane)
(b) The standard free energy change of the reaction (as written in part(a)) is -7.1 kJ/mole at 900 K. The total pressure is 1 atm and the steam-to-methane ratio of the feed gas is 50. Assuming that the reaction of part (a) is the only one occurring, what percentage of the input methane is converted to carbon dioxide at equilibrium?
(c) What is the oxygen pressure in this gas at equilibrium?
(d) Is carbon monoxide a significant component of the equilibrium gas?
9.12 The reaction XO + Y = YO + X can be broken into two couples. The stability diagram for this system is sketched below.
(a) What are the two couples?
(b) What equations are represented by the two lines?
(c) Identify the stable phases in the numbered regions and at point P.
9.13 A graduate student research project involves measuring the hydrogen content of zirconium specimens by "outgassing" at elevated temperature. The original hydrogen content is expressed as the atomic ratio (H/Zr). The specimen is contained in a vessel of known volume that is initially pumped out of all gas. When the specimen is inserted into the hot vessel, the hydrogen in the metal is partially released and causes the pressure in the apparatus to rise. The pressure rise is measured. However, not all of the hydrogen is released from the metal because at equilibrium, Sieverts' law requires that some hydrogen remain dissolved in the metal. The following information is given:
- the temperature of the specimen and the vessel, T
- The vessel volume V
- The moles of zirconium in the specimen, nZr
- The Sieverts' law constant for hydrogen dissolution in Zr, KSH
Derive the equation from which the H/Zr ratio of the original specimen could be calculated from the measured pressure increase when the specimen is heated. The quantity of H remaining in the metal can be assumed to be much less than nZr.
9.14 Consider the system at temperature T and total pressure p in which the following reactions occur:
(a) Neglecting dissociative dissolution of A2 in the metal M, derive the equations giving the composition (in mole fraction units) of the equilibrium gas if the equilibrium constants KP1 and KP2 are given.
(b) If the Sieverts' law constant for dissociative dissolution of A2 in the metal is KSA, how are the results of part (a) changed? What is the mole fraction of A dissolved in the metal? The activity of the solid metal M is not affected by dissolved A and the total gas pressure
9.15 When oxygen gas at 1 atm is passed over solid ruthenium metal at 2000 K, the metal reacts to form gaseous oxides. However, it is not possible to determine experimentally whether the dominant oxide is RuO(g), RuO2(g) or RuO3(g). Only the enthalpies of formation of these species are known. They are, respectively, 102, 37, and 30 kcal/mole of O2.Estimate which of the three possible vapor species is dominant and its equilibrium pressure. Use the entropy "rule of thumb"
9.16 Consider formation of Ag2S by the reaction: S2(g) +4Ag(S or L) = 2Ag2S(L). When silver is liquid (T > 1235 K), the thermochemical properties of this reaction are given in Table 9.3.
(a) Calculate the equilibrium sulfur pressure over the two-phase Ag/Ag2S liquid mixture at 1300 K.
(b) At 1200 K, Ag is solid but Ag2S is liquid. Calculate the standard free energy change for the reaction at 1200 K. Use the enthalpy of melting of silver of 11.3 kJ/mole to correct for the change in phase of silver. What is the equilibrium sulfur pressure at this temperature?
9.17 Prove that Eq (9.25) is valid even when AHo and ASo are temperature dependent, but ACP is constant.
9.18 At 2257 K and 1 atm total pressure, 1.77%. of initially pure water is dissociated by the equilibrium reaction 2H2O(g) = 2H2(g) + O2(g). At this temperature,
(a) What is the equilibrium constant KP?
(b) What is the standard Gibbs free energy of the reaction?
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Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.