Necessary and sufficient criteria for reaction spontaneity in a given direction and for spontaneity of finite transformations in single-reaction, closed systems are developed. The criteria are general in that they hold for reactions conducted under either conditions of constant T and p or constant T and V. These results are illustrated using a simple, liquid-to-vapor phase transition as an example. Following this development, the paper investigates the source of the mathematical and logical errors contained in textbooks ca. 1950 to the present that led to the fallacious statements still present in most introductory chemistry textbooks and some more advanced texts that the conditions for spontaneity are ?G < 0 at constant T and p and ?A < 0 at constant T and V, whereas the corresponding conditions for equilibrium are ?G = 0 or ?A = 0. This investigation shows the principal errors to be (i) incorrect evaluation of definite integrals; (ii) failure to determine whether the results of such integrations produce criteria for spontaneity and equilibrium that are necessary conditions, sufficient conditions, both, or neither; and (iii) incorrect logical arguments related to equilibrium. The question of why such errors have been perpetuated in textbooks for over 50 years is also addressed. Some recommendations for revision of textbooks, for more frequent use of the concept of chemical force in discussing spontaneity and equilibrium, and for revision of the notation and nomenclature related to spontaneity and equilibrium are made. [See additional series articles: Spontaneity and Equilibrium, Part I at EJ1031144, and Part 11 at EJ1032433.]