Explain with appropriate diagrams the lever rule and Tie-line rule.

Compositions of two coexisting phases of a binary system are given by tie-line rule. For overall composition which lies on the tie line, composition of the two phases remains the same, c_s and c_i.  A  little  reflection  would show  that  this  would be  possible  only  if  relative amounts of the co-existing phases change, as overall composition is varied along the tie line. It's a horizontal line drawn temperature of intersects within the two-phase region. If for instance a liquid phase and a solid phase co-exist at a temperature T, intersection of the tie-line drawn at that temperature with liquids gives the composition of liquid, and intersection with the solids gives composition of the solid. It can be applied only in two-phase region. For overall compositions which lie on the tie line composition of the two co-existing phases remain same. There is change only in their relative amounts.