Preamble:

Phosphorus removal from hot metal is the most important refining reaction. Phosphorus has atomic number 15 and it can give up all 5 electrons from its outermost shell to become  or accept 3 electrons to become  to attain stable configuration. This means that phosphorus can be removed both under oxidizing as well as reducing conditions.But removal of phosphorus under reducing conditions is not practical since its removal is highly hazardous. Thus P removal is practised mostly under oxidizing conditions..

Equilibrium Considerations:

Phosphorus removal reaction

At T > 1382K,   becomes positive which results in decomposition of to
P and O.Thus removal of phosphrous requires that   must be reduced.

                                              (2)
Now

and                               (3)

                            (4) 
      
By equation 2 and 3 and replacing by using Raoult’s Law and after rearrangement

                                   (5)

is activity coefficient of  in slag. The LHS of equation 5 is index of
dephosphorization and denotes distribution of phosphorus between slag and
metal. Higher value of LHS demands low in a slag of a given composition.