A detailed study was made of the rates of hydrolysis of trans-[Co(en)₂ (NO₂)₂] NO₃ as a function of acid concentration in perchloric, hydrochloric, hydrobromic, sulfuric, and nitric acids up to high concentrations of acid. All the data could be fitted 1 to the equations proposed by Bunnett¹.

(1) [log k₁ - log (H +)] = w*log a_w + Ratio

and

(2) [log k₁ - log Hₒ] = wlog a_w + Constant.

In these equations, k₁ is the first-order rate constant, (H+) is the hydrogen-ion concentration, a_w is the activity of water in the solution, and Hₒ is the Hammett acidity function. The w and w* are the slopes"Ratio" and"Constant" are the intercepts, of plots of the left side of eq. 1 or eq. 2 versus the log a_w. Bunnett proposed that for the hydrolysis of organic compounds, wand w* values are indicative of mechanism.

From the constant values of w* obtained in hydrobromic, hydrochloric, sulfuric, and perchloric acids, a mechanism involving water acting as a nucleophile was indicated. The different value of w* obtained in nitric acid was consistent with the known difference in hydration in nitric acid. Values of w also were consistent with nucleophilic attack by water.

Rates of hydrolysis of trans-[Co(en)₂ (NO₂)₂] NO₃ were also measured as a function of temperature. In perchloric acid, good linear Arrhenius plots were obtained from which the energy of activation was 23.6 + 0.8 kcal. and the activation entropy was 2.9 + 2.3 eu. at the 95% confidence level.

Arrhenius plots in hydrochloric, hydrobromic, sulfuric, and nitric acids were curved, the amount of curvature increasing with acid concentration and temperature. At lower temperatures, the activation energy was 23-24 kcal. but decreased to as low as 12 kcal. at high acid concentrations and higher temperatures. This behavior is consistent with two consecutive reactions, the second reaction having the lower activation energy; the latter reaction was identified with addition of an anion to the intermediate nitroaquo complex.

A series of dinitro complexes with"inert" ligand size varying from ammonia to 1, 10-phenanthroline was made; these complexes were studied in hydrochloric and perchloric acids. The first-order rate constant decreased as the size of the ligand increased, indicating direct participation of water in an SN₂ reaction. The values of w* in both acids were consistent with nucleophilic participation of water; for the bipyridine and orthophenanthroline complexes a lower value of w was observed. This observation could be related to the expectation that these large complexes would not be hydrated as much as the smaller compounds.

A mechanism for the hydrolysis reaction consistent with the observed behavior was given. According to this mechanism, the complex is first protonated in an equilibrium step; the protonated species reacts with water to give the nitroaquo complex as the rate determaining step for all compounds· in all acids. Finally, the nitroaquo complex reacts with an anion Z⁻ (except when Z⁻ is ClO₄⁻) to give the final product of reaction.

This investigation shows that Bunnett's equations are useful for correlating data, but some caution in accepting Bunnett's mechanistic interpretations from the values of w and w* is necessary. It is satisfying that application of these ideas to a totally different system (inorganic complexes) lead to a mechanism consistent with current ideas about the reactivity of coordination compounds of cobalt(III).