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Metal Production: Ellingham Diagrams

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Metal Production: Ellingham Diagrams j l Metal Production: Ellingham Diagrams (a) for 2Fe(s) O# 2FeO(s) ∆Gmlk529 800j113.0 T J (b) for 1.5Fe(s)jO l Fe O (s) The change in Gibbs free energy caused by the ∆ mlk j # $ % oxidation of a pure metal to form the pure metal oxide G 553400 148.0 T J (c) for 4Fe O (s)jO l 6Fe O (s) is called the standard Gibbs free energy of formation ∆ mlk $ %j # # $ of the oxide, ∆Gm (where the pure metal and the pure G 498900 281.3 T J (d) for 6FeO(s)jO l 2Fe O (s) oxide are the designated standard states), and is given ∆ mlk j # $ % by G 624400 250.2 T J. The reactions given by Eqns. (a)–(d) above are ∆Gml∆HmkT∆Sm (1) written for the consumption of one mole of oxygen gas ∆ ml in order that G RTlnp(O#) for each reaction can where ∆Hm is the standard enthalpy change and ∆Sm is be plotted as a function of T on a single Ellingham the standard entropy change for the oxidation re- diagram. Wustite (‘‘FeO’’) and magnetite (Fe$O%) action. Oxidation reactions are exothermic which, by exhibit ranges of nonstoichiometry. Thus in reaction convention, makes ∆Hm a negative quantity and, as (a) iron-saturated wustite is chosen as the standard the formation of a condensed oxide from a condensed state for FeO and in reaction (d) oxygen-saturated metal involves the consumption of oxygen gas, ∆Sm is wustite is chosen as the standard state for FeO. a negative quantity. If the oxidation reaction does not Similarly, in reaction (b), iron-saturated magnetite is involve a change in the heat capacity of the system chosen as the standard state for Fe$O% and in reaction then ∆Hm and ∆Sm are independent of temperature, in (c) oxygen-saturated magnetite is the standard state ∆ m which case G is a linear function of temperature and for Fe$O%. The Ellingham lines for the equilibria given a plot of ∆Gm vs. temperature gives the standard by Eqns. (a)–(d) are shown in Fig. 1. Every point in an Ellingham line on an Ellingham diagram. In an Ellingham diagram represents a unique thermodyn- Ellingham diagram the value of ∆Hm is given by the amic state (combination of temperature and partial intersection of the Ellingham line with the T l 0K pressure of oxygen). Any point is a pair of values of T ∆ m axis and the value of S is the negative of the slope of and RT ln p(O#) and substitution of the value of T into the line. the value of RT ln p(O#) gives the corresponding value The equilibrium constant, Kp, is obtained from the of the partial pressure of oxygen. Isotherms in an standard Gibbs free energy of formation of the oxide Ellingham diagram are vertical lines and Eqn. (5) as shows that oxygen isobars are straight lines which radiate from the origin of the diagram (∆Gml0, T l ∆GmlkRT ln K (2) p 0K) with a slope of Rlnp(O#). This allows a nomographic scale for oxygen pressure to be placed where, for an oxidation reaction along the right-hand edge of the diagram and the l V) xMjO (g) l M O (3) oxygen isobar for p(O#) 10 atm is shown as a # x # broken line in Fig. 1. The oxygen pressure at any point the equilibrium constant gives the required combi- in the diagram is read from the scale as being colinear nation of the activities of the metal and the oxide and with a line drawn from the origin of the diagram the partial pressure of oxygen gas required for the through the point of interest to the nomographic scale. three-phase metal–oxide–gas equilibrium as For example, the state identified as ch in Fig. 1 is the l m l V) state T 1635 C and p(O#) 10 atm. aM O A three-phase equilibrium (metal–oxide–gas) in a K l x # (4) binary system (Fe–O) has one degree of freedom, ax [p M (O#) which can be selected as temperature or partial The choice of the pure metal and the pure oxide a pressure of oxygen. Thus line C in Fig. 1 represents the variation of oxygen pressure with temperature re- standard states makes the activities of M and MxO# have values of unity in Eqn. (4), in which case the quired to maintain phase equilibrium between the combination of Eqns. (1), (2), and (4) gives condensed phases magnetite and hematite (Fe#O$) and the gas phase. This is the equilibrium oxygen pressure. ∆Gml∆HmkT∆SmlRT ln p(O (eq)) (5) If the state of the system is moved off the Ellingham # line the equilibrium is destroyed and one of the Equation (5) gives the variation of the partial pressure condensed phase disappears. For example, moving the of oxygen, p(O#(eq)), with temperature required for thermodynamic state from a point on the Ellingham equilibrium between the pure metal, the pure oxide, line C to a less negative value of ∆Gm at constant and the gaseous phase containing oxygen. The ap- temperature increases the partial pressure of oxygen to plication of Eqn. (5) to the Ellingham diagram creates a value higher than that required for the equilibrium at a phase stability diagram. that temperature and thus the magnetite becomes The standard Gibbs free energies of formation of unstable. Similarly, moving the thermodynamic state the various oxides of iron are as follows: from a point on line C to a state of more negative free 1 Metal Production: Ellingham Diagrams Figure 1 ∆ m Phase stability in the system Fe–Fe#O$ as a function of G and temperature. energy at constant temperature decreases the partial liquid oxide. Line A at temperatures higher than pressure of oxygen to a value less than that required 1371mC is for equilibrium between solid iron, and for equilibrium at that temperature and thus the liquid iron oxide. The increase in the entropy when hematite phase disappears. Line C is thus the bound- wustite melts to form liquid oxide causes a decrease in ary between the phase stability fields of magnetite and the standard entropy change for the reaction, which hematite. Similarly line B is the variation, with produces an ‘‘elbow’’ in the Ellingham line. The four temperature, of the oxygen pressure required to Ellingham lines define the phase stability fields of iron, maintain equilibrium between iron and magnetite. In wustite, magnetite, and hematite. states above the line the oxygen pressure is higher than The Ellingham diagram shows that the production that required for the equilibrium and thus magnetite is of a metal from its oxide requires that the ther- stable relative to iron. Conversely, iron is the stable modynamic state be moved from a point within the state below the line. Thus in any reduction–oxidation phase stability field of the oxide to a point within the equilibrium the oxidized state is stable above the phase stability field of the metal. Figure 1 shows that Ellingham line and the reduced state is stable below this change of state can be accomplished by: (i) the line. Line D is the boundary between the phase decreasing the oxygen pressure at constant tempera- stability fields of magnetite and wustite and line A is ture; (ii) increasing the temperature at constant oxygen the boundary between the phase stability fields of iron pressure; or (iii) a combination of increasing the and wustite. Lines A, B, and D meet at the invariant temperature and decreasing the oxygen pressure. state (T l 560mC, p(O ) l 4i10V#%atm) at which the Consider the vertical broken line at 1300mC in Fig. 1. # ∆ ml l eutectoid equilibrium iron–wustite–magnetite equilib- At G 0(p(O#) 1atm) the system exists as rium occurs in the system. The change in the slope of hematite. Decreasing the oxygen pressure at constant line A occurs at the eutectic point (1371mC) at which temperature moves the thermodynamic state to the l i V# equilibrium exists between solid iron, wustite and point a on line C at p(O#) 1.3 10 atm in which 2 Metal Production: Ellingham Diagrams Figure 2 The carbon line in the Ellingham diagram. state magnetite is in equilibrium with hematite. consequence that the standard entropy change is Further decrease in the oxygen pressure moves the virtually zero. In contrast, the line CD has a negative j l system through the magnetite phase field to the state b slope because the reaction 2C O# 2CO involves l i V) at p(O#) 2.2 10 atm in which state magnetite is the consumption of one mole of gas (O#) and the in equilibrium with wustite. Decreasing the oxygen production of two moles of gas (CO) with the pressure below 2.2i10V) moves the system into the consequence that the standard entropy change is a l i V"# wustite phase field and at p(O#) 2 10 atm, the positive quantity. A gaseous atmosphere containing state c, iron is produced in equilibrium with wustite. oxygen gas in equilibrium with carbon thus contains m Iron is the stable phase at 1300 C and an oxygen both CO and CO#, but the different thermodynamic i V"# \ pressure of less than 2 10 atm. The influence of stabilities of two gases causes the ratio p(CO) p(CO#) increasing the temperature at a constant partial in the gas in equilibrium with carbon to be a significant V) pressure of 10 atm is shown as the broken line.
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