In this talk we show how the small object argument, familiar in the study of model categories, is an useful tool to produce cotorsion pairs in exact categories (in the sense of Quillen). We then particularize to the case of a Frobenius exact category, showing that there is a one-to-one correspondence between (complete) cotorsion pairs in it and Hom-orthogonal pairs in its stable category (giving rise to distinguished triangles).