In regards to electrochemical reactions, two main types of reactions can be visualized using the Frost diagram. Comproportionation is when two equivalents of an element, differing in oxidation number, combine to form a product with an intermediate oxidation number. Disproportionation is the opposite reaction, in which two equivalents of an element, identical in oxidation number, react to form two products of differing oxidation numbers.
Disproportionation: 2 M → M + M.
Comproportionation: M + M → 2 M.
2 n = m + p in both examples.
Using a Frost diagram, one can predict whether one oxidation number would undergo disproportionation or two oxidation numbers would undergo comproportionation. Looking at two slopes among a set of three oxidation numbers on the diagram, assuming the two standard potentials (slopes) are not equal, the middle oxidation will either be in a “hill” or “valley” form. A hill is formed when the left slope is steeper than the right, and a valley is formed when the right slope is steeper than the left. An oxidation number that is on “top of the hill” tends to favor disproportionation into the adjacent oxidation states. The adjacent oxidation states, however, will favor comproportionation if the middle oxidation state is in the “bottom of a valley”.
By Jensen's inequality, drawing the line between the oxidation state to the left and the one to the right and seeing if the species lies above or below this line is a quick way to determine concavity/convexity (concavity would indicate comproportionation, for example)