The values of the 02 pressure required for coexistence of M and M02 are usually quite small, because, except for the noble metals, oxides are much more stable than the elemental metals. Reaction (9.3) releases substantial heat, so AHo is large and negative. This term dominates AGo, which is also large and negative. For instance, if AGo = -200 kJ/mole at 1000 K, Eq (9.33a) gives p0 = 3.6x10-11 atm. From practical considerations, such a low pressure of 02 is difficult to produce and control in a process or an experiment. However, oxygen pressures in this range can be reliably established by exploiting the equilibria of gas mixtures that exchange 02 in a reaction. Gas-phase equilibria of this type include 2C0 + 02 = 2C02 and 2H2 + 02 = 2H20. Mixtures with a preset C02/C0 ratio or H20/H2 ratio generate oxygen pressures in the desired range (Sect. 9.7). How this 02 pressure affects the oxidation of a metal is explained below.
By "reactive gas" is meant a mixture of two gases that fix the partial pressure of a third species by an equilibrium reaction. The Co/Co2 combination that establishes an oxygen partial pressure by reaction 9.26 is an example of a reactive gas.
A "reactive metal" in the present discussion is one that, together with one of its oxides, fixes an equilibrium partial pressure of oxygen by reaction 9.3.
When the reactive gas contacts the reactive metal, a common equilibrium may be established. This equilibrium can be expressed iin one of two ways.
The first way is by the overall reaction:
This reaction is reaction (9.3) minus reaction (9.26). The law of mass action for reaction (9.36)
The implication of this is that only a single CO/CO2 ratio permits equilibrium to be established between the reactive gas and the reactive metal.
The second way of expressing the equilibrium of the gas-solid reaction is to equate the oxygen pressure generated by each:
That the equilibrium expressions of Eqs (9.36) and (9.37) are equivalent is demonstrated as follows. Assume that the mixed CO/CO2 gas flows over the solid in a furnace, as in Fig.9.5. The equilibrium oxygen pressure in the gas phase is given by Eq ( 9.27a) (for 2000 K), or in general, by:
(PO2 )CO/CO2 = (PCO2 /PCO)2 exp(AGC°/CO2 /RT) (9.39)
The equilibrium O2 pressure generated by the MO2/M couple is a function of temperature only:
Reaction (9.36) is simply reaction (9.3) minus reaction (9.26). This algebraic relation of the overall reaction to its component reactions also applies to the free-energy changes. This equivalence demonstrates That the standard approach of Eq (9.37) is no different from equating oxygen partial pressures, as in Eq (9.38).
Example: Powdered nickel metal is contacted with a flowing mixture of CO2 and CO at 1 atm total pressure in a furnace at 2000 K. The quantity of metal is limited, but because of continual flow, the quantity of the gas mixture is unlimited. Therefore, the oxygen pressure established in the gas phase is imposed on the metal, and determines whether or not it oxidizes.
At what CO2/CO ratio do both Ni and NiO coexist? The O2 pressure established by the gas mixture is given by:
The nickel/nickel oxide equilibrium reaction is: 2Ni + O2 = 2NiO, for which AGo = -46 kJ/mole at 2000 K. According to Eq (9.33a), for coexisting Ni and NiO in the solid phase, the oxygen pressure must be:
Kp with KP = 4.4x105
The mixed solid and the mixed gas are in equilibrium when ( p0 )gas = (po )solid. From the above equations, this condition yields the required ratio of CO2 to CO in the gas:
What is the solid phase if the CO2/CO ratio is 1?
For this ratio in the gas, the gas-phase law of mass action gives:
Since ( p0 )gas < ( p0 )solid, the gas removes any oxygen from the solid and only Ni remains in the solid phase.
A number of problems involving reactions between gases and pure solids are provided at the end of this chapter. Most deal with metal/metal oxide couples in which the oxygen pressure is controlled by CO2/CO mixtures (problems 9.5, 9.6 and 9.20). In some applications, more than one solid oxide must be considered (problem 9.6). In other systems, one or more metal oxides are gaseous (problems 9.15 and 9.23).
In this class of reactions, the solid phases need not be metals and metal oxides for the theory to apply. In problem 9.16, sulfur replaces oxygen as the element combining with the metal. In problem 9.2, the solid is pure carbon and the gas phase is a mixture of hydrogen and methane. This problem is another example of coupling of a gas-phase reaction with a gas-solid reaction. It is analogous to the simultaneous gas-phase equilibrium involving CO and CO2 and the gas-solid equilibrium between oxygen and a metal/metal oxide couple.
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