Preamble :

● In steelmaking, the impurities like carbon, silico, manganese, phosphorus and sulphur are removed fromhot metal through a combinatio of gas/metal, gas/slag and gas/metal/slag reactions so as to producesteel of desired chemistry and cleanliness (cleanliness refers to the inclusions). Science of steelmaking involves equilibrium concentration of an impurity between the phases and the rate of
transfe of an impurity from the hot metal.

Equilibrium between the phases :

● The phases in steelmaking are hot metal, molten slag and gas. Hot metal is a multi-component solution inwhich impurities like carbon, silicon, manganese, phosphorus and sulphur are dissolved in very low amoun(total concentration of all the impurities is approximately 5% to 6%) in iron. Slag is a solution of predominantlyoxides with small amounts of sulphides, phosphides, silicates etc. Composition of the solutionin steelmaking is conveniently expressed either as weight (Wt%) or mole fraction(N). The molefraction of the ith component in a solution of n components is

Ni = Xi/∑Xi, 1)

● where Xi is the number of moles of with component. The equilibrium of a component between the liquid phase is expressed in terms of integral molar free energy Free energy. Integral molar free energy of solution

Gm = ∑GimNi = ∑ Gi Ni − ∑Gi oNi = RT∑ Ni ln ai,

● GiNi represents free energy of solution and GioNi is the free energy of pure components before entering into the solution. The quantity Gim is the partial molar free energy of mixing of component i and representthe change of energy or work which a mole of pure component i can make available.

● Chemical potential is a useful concept to describe chemical equilibrium between liquid phases. At chemical equilibrium the chemical potential of any component is identical in all phases. Knowledge of chemical potential is important in steelmaking because an impurity can transfer in the gaseous or slag phase only when its chemical potential is lower than in hot metal.

● The criterion for equilibrium at constant temperature and pressure is the change in the integral molar free energy of the solution (dG)T,P, i.e.

(dG)T,P = 0 for an infinitesimal process and
(∆G)T,P = 0 for a finite process

Where (dG)P is change in integral molar free energy

● At constant temperature and pressure when (dG)T,P < 0, a process occurs spontaneously. For an isothermalchemical reaction say A + B = C + D, (∆G) = ∆Go + RT lnJ, where J is activity
quotient and ∆Go is the standard free energy change.

● At equilibrium
∆Go = − RT ln (J)eq = −RTln K, where K is equilibrium constant. 4)

Activity of solution :

● In dealing with chemical reactions in solution it is important to define the activity of a component. Activityof a component denotes its effective concentration. It is related to fugacity as

ai = fi/fio

● fi is the fugacity of component i in solution and fio is the fugacity of a component in its standard state(standard state could be either pure element or compound at 1 atmospheric pressure) So at standard state activity equals 1. In an ideal gas activity of a component i is equal to its partial pressure.

Raoults’s Law :

● An ideal solution obeys Raoult’s law, in which activity of a component ai equals to its mole fraction Ni
ai = Ni

● Real solutions exhibit either positive or negative deviation from Raoult’s law for a binary solution. Deviationfrom Raoult’ law is taken care by activity coefficient γi
γi = ai/ Ni,

● The Fe-Mn forms an ideal solution, whereas the Fe-Cu exhibits strong positive deviation and the Fe-Si strong negative from Raoult’s law. Physically it implies that in Fe-Cu solution copper has a strong tendencyto segregate, and in Fe-Si solution silicon has a strong tendency to form chemical compound with iron.

● In binary liquid oxides, FeO-MnO behaves ideally, whereas most binary silicates i.e. CaO − SiO2, FeO − SiO2, MgO − SiO2 show negative deviation from Raoult’s law.

Henry’s law :

● Liquid steel, and to a reasonable extent hot metal primarily fall in the category of dilute solution. In a dilute binary solution activity of a solute obeys Henry’s law, which is stated as
ai = γioNi,

● where γio is a constant (activity coefficient for the solute in dilute binary) and Ni is the mole fraction of the specie i. Solutes in all infinite dilute solutions obey Henry’s law. Deviation from Henry’s law occurs
when the solute concentration increases.

● In steelmaking the concentration of solute in molten steel is expressed in weight percent. It is frequently most convenient to choose the infinitely dilute solution expressed in terms of weight percent as the standard state. This is defined as

hi /(Wt% i) = 1 when wt% i →0
For weight percent i other than zero
hi = fi Wt% i

Interaction parameter:

● Molten steel contains several dissolved solutes in dilute scale. For example, molten steel contains C, S, P, Si, M etc. This steel is a multi-component solution. In multi-component solution solutes interact with one another and thus influence activities of other solutes. If Fe is the solvent, and 1, 2….k are solutes in dilute state, then

● The term eij is known as interaction parameter describing the influence of solute j on the activity coefficient of solute i. The value of interaction parameter can be found in any book on thermodynamics.

● The concept of interaction parameter is very important in estimating the activity of a solute element in present of the solute elements. For example we want to calculate the activity of sulphur in hot metal of composition C = 4%, Si = 1.5%, Mn =1% and S = 0.04% at 1600 ℃ .

● By assuming infinite dilute solution
as the standard state, the activity of sulphur is given by

 Substitutingthe value of eS S= − 0.028, eS C= 0.24, eSSi = 0.066 and eSMn = −0.025, we get
fS = 10.78 and activity of sulphur is 0.43.

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