1. Equilib Slide 48 Fixing the activity of a species O 2 (g) in the product equilibrium FeS and O 2 : Results window O 2 i.e. FeS + 1.83709 O 2 as reactants O 2 final equilibrium partial pressureO 2 0.03709 mol O 2 must be added to the reactants in order to have the final equilibrium partial pressure for O 2 O 2 = 0.01 atm P O 2 = 0.01 atm

2. Equilib Slide 49 liquidCuCr Setting up of an ideal liquid solution of Cu and Cr No liquid phases species are selected. In order to select the components of an ideal solution, proceed as follows: 1. Press the « List Window » button Cr 2. Click the mouse right button in the first column (+) of the line containing Cr (liq) species – an extended menu appears. Ideal Solution Cr 3. Click on « Ideal Solution #1 » in sub-menu « Ideal Solution » to select Cr (liq) as first component. Cu Ideal Solution #1 4. Repeat steps 2 and 3 to select Cu (liq) as second component of Ideal Solution #1.

3. Equilib Slide 50 Cu Cr CuCr Oxidation of a liquid Cu -Cr alloy assuming ideal mixing of Cu and Cr Cr (liq) Cu (liq) Ideal Solution #1 5. Cr (liq) and Cu (liq) are the components of «Ideal Solution #1» menu Window Custom solutions 1 ideal solution Details 6. Return to menu Window The «Custom solutions» label box indicates: 1 ideal solution … For more information, press « Details » 7. Set Final Conditions and press « Calculate »

4. Equilib Slide 51 Results window – assumption of Cr (liq) - Cu (liq) ideal mixing. Ideal solution phase: liquid#1. X Cr X Cu Ideal solution phase: liquid#1. Numbers are mole fractions, X Cr (liq) = 0.25 X Cu (liq) = 0.75 Cr 2 O 3 Pure solid Cr 2 O 3

5. Equilib Slide 52 CrCu List window – assumption of Cr (liq) - Cu (liq) ideal mixing. Ideal solution X Cu X Cr Ideal solution, hence X Cu (liq) = a Cu (liq) = 0.75 X Cr (liq) = a Cr (liq) = 0.25 According to the phase diagram (next page): X Cr (liq) = 0.01837 at 1373 K (1100°C). assumption not very good Hence, the assumption of an ideal solution is not very good in this example. Option Show properties selected

6. Equilib Slide 53 Tie-lines in the Cu- Cr phase diagram (ref. D.J. Chakrabarti and D.E. Laughlin, Bull. Alloy Phase Diagrams, p. 100, 1984) 1076.6°C 1100°C (1373 K) 1200°C (1473 K) 1300°C (1573 K) 1084.87°C 1860°C This is the experimental X Cr (liq) = 0.01837 or wt.% Cr (liq) = 1.508

7. Equilib Slide 54 Cr Cr Input to program Reaction to calculate activity of Cr liquid in equilibrium with pure solid Cr. Cr Pure Cr (s) a Cr(solid) = 1 (from phase diagram) Cr ? Cr (liq) in solution a Cr(liquid) = ? Isothermal reaction, hence equilibrium when  G = 0. Output of interest

8. Equilib Slide 55 Cr CuCuCr Estimation of the Henrian activity coefficient of Cr (liq) in Cu (liq) from the Cu-Cr phase diagram We find that: log 10 [    Cr (liq) ] (T -1 ) = 5983.29 T -1 - 2.9522 For dilute solutions we can express the activity a Cr (liq) as a function of the molar fraction X Cr (liq), by applying Henry’s law: a Cr (liq) =   Cr (liq) X Cr (liq) where   Cr (l) is the temperature dependant Henrian activity coefficient. The solution is fairly dilute, hence Henry’s law is fairly applicable..

9. Equilib Slide 56 CrCu Specifying the temperature dependant Henrian activity coefficient for Cr in Cu (liq) Cr 1. Click the mouse right button in the first column (+) of the line containing Cr (liq) species and an extended menu appears. Activity dialog box Cr 2. Click on « activity coefficient » in « Activity » sub-menu to open the dialog box for Cr (liq).   Cr (liq) T (K) 3. Enter the values of the activity coefficient   Cr (liq) log 10 [    ] = A / T (K) + B Note: T is in Kelvin. From the previous page, we have: log 10 [    Cr (liq) ] (T -1 ) = 5983.29 T -1 - 2.9522

10. Equilib Slide 57 CrCu Setting the Final Conditions for the Cr - Cu oxidation calculation – T= 1373, 1473 and 1573 K. Menu Window Custom Solutions 1 activity coefficient 1 ideal solution Details 4. Return to Menu Window The «Custom Solutions» label box indicates:1 activity coefficient 1 ideal solution For more informations, press « Details » 5. Set Final Conditions and press « Calculate »

11. Equilib Slide 58 CuCrLiquid alloy Results for oxidation of Cu-Cr alloy at 1373 K. Liquid alloy coexists with solid Cr and Cr 2 O 3 – the composition agrees with the phase diagram. P cu = 0.766 × 10 -6 atm 0 mol i.e. no gas phase. However, these mole fractions give equilibrium partial pressures. For example, P cu = 0.766 × 10 -6 atm Cr Pure solid Cr Cr 2 O 3 Pure solid Cr 2 O 3 X Cr(l) = 0.01837 X Cr(l) = 0.01837 same value as phase diagram Flag to a custom solution

12. Equilib Slide 59 CuCr More results for oxidation of Cu -Cr alloy – T=1473 K and 1573 K. X Cr(l) =0.041914 X Cr(l) = 0.041914, same value as phase diagram. Cr Pure solid Cr Cr 2 O 3 Pure solid Cr 2 O 3 Cr Pure solid Cr XCr(l) = 0.086069 XCr(l) = 0.086069 same value as phase diagram Cr 2 O 3 Pure solid Cr 2 O 3

13. Equilib Slide 60 CrCu List window – a summary of activities of Cr and Cu in liquid alloy at 1373 K, 1473 K and 1573 K. Crliquidus Cu - Cr Compare Cr concentration in liquid alloy with liquidus in the binary phase diagram Cu - Cr (see earlier page 41). 1373 K 1473 K 1573 K

14. Equilib Slide 61 Input for the leaching of an arsenic-bearing copper concentrate by HCl and HNO 3 acids at elevated temperature and pressure. Elevated T and P Two ideal solutions: gasaqueous gas and aqueous; and pure solids. Arsenic-bearing copper concentrate Leaching agent

15. Equilib Slide 62 Results Window standard output for the leaching of an arsenic-bearing copper concentrate by HCl and HNO 3 acids at elevated temperature and pressure. +…+… +…+… +…+… X(H 2 O) = 0.80331 P total = 5.0 atm P(H 2 O) = X(H 2 O) × P total = 4.01655 atm Important: in aqueous solutions the solutes are given with respect to 55.5 mol(1000 g or 1L) of water. Hence, the values are molalities. For example: mH[+] = 0.59929 mH[+] = 0.59929 hence pH0.222 pH = -log 10 (0.59929) = 0.22236 Note the potential with respect to the standard H 2 (g) electrode. Three pure solids aqueous Three pure solids at equilibrium with the aqueous and gas gas solutions.

16. Equilib Slide 63 FACT Non-Ideal Solutions - FACT-FELQ Changing the units of the data And change: temperature, from Kelvin to Celsius mass, from mole to gram Conversion equations and factors appear when the arrow points to a parameter box Select “Units” from the Menu bar

17. Equilib Slide 64 Selection of FACT Non-Ideal Solutions - FACT-FELQ. Calculation of the solubility of C in liquid cast iron. Note the change of units More information gives: full title namefull title name short description of the complete solution phaseshort description of the complete solution phase list of possible components for the current systemlist of possible components for the current system

18. Equilib Slide 65 FACT Non-Ideal Solutions - FACT-FELQ, Results Window standard output showing the solubility of C in liquid cast iron. Graphite saturation +…+… Compositions in the liquid solution phase are given in weight percent (wt. %). The amount of: Fe is 100.00 g = 94.854 % × 105.43 g Mn is 1.00 g = 0.94854 % × 105.43 g Si is 1.00 g = 0.94854 % × 105.43 g C is 3.4253 g = 3.2490 % × 105.43 g

19. Equilib Slide 66 FACT Non-Ideal Solutions: Selection of the slag solution phase for the decarburisation of pig iron by oxygen injection. 1. Select “Show all”. 2. Scroll through the list. 3. For more information: select “ more info ” and point the phase line, or point to the phase name or info box and click the right mouse button, or press on the “List Window” button to see a complete list of the possible components. «solutions» Possible «solutions» for our problem. 4.

20. Equilib Slide 67 FACT Non-Ideal Solutions: more information about the available slag and liquid iron solution phases. There are 3 subsets of the solution phase SOLN-SLAG: SOLN-SLAG?; SOLN-SLAGB; SOLN-SLAGA. Only one can be selected. The reason why there are solution subsets is because not all the binary, ternary systems, etc…, in the complete solution have been optimised yet. «?» indicates that not all the species have been optimised together and is not recommended. In the present example, we select SOLN-SLAGA (the complete oxide phase) rather than SOLN-SLAGB (a limited carbonate phase). Possible liquid steel phase

21. Equilib Slide 68 solution pure solidsfinal conditions FACT Non-Ideal Solutions: Selection of the solution phases, pure solids and final conditions for the decarburisation of pig iron by oxygen injection. SOLN-SLAGASOLN-FELQ gas Selection of 2 solutions: SOLN-SLAGA, SOLN-FELQ; gas and pure solids pure solids. Enter the Final Conditions and Calculate>>

22. Equilib Slide 69 FACT Non-Ideal Solutions: additional ways to have more information about available solution phases. List Window For more details on the solutions, go to the List Window 1.Point the arrow to the “+” column 2.Click on the right mouse button; an extended menu appears. custom select species… 3.Select “custom select species…” to examine and modify your selection but…

23. Equilib Slide 70 FACT Non-Ideal Solutions - FACT-SLAGA & FACT-FELQ. Decarburisation of pig-iron by oxygen injection. +…+… +…+… CO (g) Almost 100 % CO (g) CaO slag CaO addition promotes slag formation. gas phaseLess C in liquid steel because C has mostly gone into the gas phase. slagLess Si in liquid steel because of its oxidation into the slag.

24. Equilib Slide 71 FACT Non-ideal Solutions: FACT-SLAGA & FACT-FELQ. Desulfurizing a steel by CaSi addition. Data entry. Note the use of the variable amount “A” for the slag. Starting composition of the steel melt Calcium silicide addition These are the defaults values for the reactant species when the “Initial Conditions” box has been checked. Specifying initial conditions is only useful if you want to calculate or constrain changes in the extensive properties (  V,  H, etc…). You have to select, for each reactant species, the phase, the temperature, the total pressure and the stream number. streamAll reactants in a given stream are grouped together, they have the same temperature and total pressure. If you change the temperature (or pressure) of any one member of the stream, then the temperature (or pressure) of all the other members of the stream will be changed to the same common value.

25. Equilib Slide 72 FACT Non-ideal Solutions: FACT-SLAGA & FACT-FELQ. CaSi solution phases final conditions FACT Non-ideal Solutions: FACT-SLAGA & FACT-FELQ. Desulfurizing a steel by CaSi addition. Selection of solution phases and final conditions. Final conditions Final conditions: = 0.015 T = 1627°C P = 1 atm and Calculate>>

26. Equilib Slide 73 CaSi FACT Non-ideal Solutions: FACT-SLAGA & FACT-FELQ. Desulfurizing a steel by CaSi addition. Standard output. +…+… +…+… Gas phase, mainly Ar No solid phases (activity<1) Two liquid solutions: slag containing sulfurslag containing sulfur liquid steelliquid steel The value of “A”

27. Equilib Slide 74 CaSi FACT Non-ideal Solutions: FACT-SLAGA & FACT-FELQ. Desulfurizing a steel by CaSi addition. ChemSage output. … …… … …… Final Conditions Stream constituents or Amount of reactants Product gas phase, mainly Ar Product solution slag (SLAGA or Aslag-liq) phase Product solution steel (FELQ or Fe-liq) phase No pure solids phases Mass fractions of system components Equilibrium thermodynamic values System densities (g/cm 3 ) with and without gas phase