Solutes in dilute binary solutions obey Henry's law, which is stated as follows: a¡= γ¡0 Xi where, γ¡0 is a constant, known as the Hemy's law constant. Deviation from Henry's law occurs when the solute concentration increases. Therefore, activities of dissolved elements in liquid steel are expressed with reference to Henry's law, and not Raoult's law. Raultian standard state Región de disoluciones diluidas SE CUMPLE LA LEY DE HENRY Henrian standard state a=N Escala actividades de Henry a=kN (SOLUTE) In non ideal cases and in very dilute solutions the activity is, as shown by the straight-line relationship, proportional to the mole fraction though they are not equal. This is the region of Henry's law as shown by the Henry's line in Fig. 2.1(a) for which a standard state has been defined,i.e., the activity coefficient of a solute, γ0, is unity in aninfinitely dilute solution. In ironmaking, as in the making of other metals, we deal with impurities in the metal whose concentrations are small. Therefore, a more convenient standard state can be defined where the activity is equal to unity at one weight per cent concentration of the solute, as shown schematically in Fig 2.1(b), which is an enlarged version of Fig. 2.1(a) in the dilute region. The choice of this standard state is rendered mathematically feasible because at low concentrations the weight per cent of any solute in solution ,is approximately proportional to its mole fraction . (1,1) Mole fraction vs wt % 1 wt % standard Henrian vs. 1 wt % standards Nj j% Therefore, activities of dissolved elements in liquid steel are expressed with reference to Henry's law, and not Raoult's law. Since it is the intention to find values directly in weight percent, the composition scale is weight percent. With these modifications, i is in solution with Fe as solvent in the binary Fe-i solution. If: 1.- Henry's law is obeyed by the solute in the binary Fe-i solution, then: h¡ = aH,i = W¡ = [% i] 2.- Henry's law is not obeyed by the solute i, then h¡ = aH,i = fiW¡ = fi[% i] where, hi is activity, W¡ is weight percent and f¡ is activity coefficient in the so-called one weight percent standard state. This is because, at 1 wt. %, hi = 1, if Henry's law is obeyed. Interacciones soluto-soluto en soluciones diluidas de múltiples componentes El acero fundido y el hierro, así como otros metales impuros (Cu, Pb, etc) en el estado diluido tienen varios solutos disueltos. Por ejemplo, el acero tiene C, Mn, S, P, etc. Se ha encontrado que los solutos en una solución de múltiples componentes interactúan entre sí y, por lo tanto, influyen en las actividades de otros solutos. Si Fe es el disolvente, y 1, 2, ..., i,… j, ..., k son solutos en estado diluido, se tiene que: k log fi T 1873 K ( 1600 oC ) eijW j ei1W j ei2W2 ..... eiiWi .. eijW j .... eikWk j 1 eij = Coefficient describing the influence of solute j on the activity coefficient of solute i. log fi T 1873 K 1873 k j 1873 j 1 2 i k e W e W e W ..... e W .. e W .... e W i j i 2 i i i j i k T j 1 i j T eij = Coefficient describing the influence of solute j on the activity coefficient of solute i.