Proton-Transfer Studies by Nuclear Magnetic Resonance. I. Diffusion Control in the Reaction of Ammonium Ion in Aqueous Acid

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Abstract
Rate constants were determined by precise nuclear‐magnetic‐resonance techniques for the reactions: NH 4 + + H 2 O −→ lim k 4 NH 3 + H 3 O + ; NH 3 + H 3 O + −→ lim k ‐4 NH 4 + + H 2 O ; and N lim − H 4 + + NH 3 −→ lim k 6 N lim − H 3 + NH 4 + in aqueous acid at 25°C. For 0.25–3.00M NH4Cl, k —4 and k 6 were 4.3×1010 sec—1 M —1 and 1.17×109 sec—1 M —1 respectively, independent of NH4Cl concentration. Both rate constants increase on addition of KCl. The rate constant,k 4, was 24.6 sec—1 at zero ionic strength and decreased sharply with NH4Cl concentration. The values of KA needed in the kinetic analysis were measured also. The reaction of NH4 + with H2O was investigated also in 50–60 wt % H2SO4‐H2O mixtures, where the half‐life for isotopic exchange was between two and 20 minutes. The data allowed us to estimate the rate constant (1/τ D +1/τ R ) for the rupture of the H3N···HOH hydrogen bond, by diffusion (D) or rotation (R). The value obtained was 51×1010 sec—1. Using Einstein's theory of Brownian motion, the value of 1/τ D was estimated to be 34×1010 sec—1, leaving 17×1010 sec—1 for 1/τ R , of which 12×1010 and 5×1010 sec—1 are the contributions due to the rotation of H2O and NH3, respectively. The probability that NH3 rotates during an encounter is therefore fairly small. The order of magnitude of k —4 and k 6 suggests that these reactions are diffusion controlled. Upon applying the Debye‐Smoluchowski theory to calculate the frequency of encounters, we found that k —4 is consistent with reaction occurring whenever H3O+ and NH3 are next‐nearest neighbors. The steric factor for this reaction appears to be unity. Since the data in strong acid suggest that rotation of a molecule during an encounter is improbable, we conclude that the reactants are oriented during their approach so that the unshared electrons of the NH3 face an acidic hydrogen. To interpret k 6, we assume a mechanism in which NH3 and NH4 + become next‐nearest neighbors by simple diffusion; the jump to a nearest‐neighbor site then requires a somewhat higher activation energy than simple diffusion because NH3 must displace a tightly bonded water molecule. The reaction with rate constantk 4 is activation controlled. The negative salt effect on k 4 suggests diffusion of charge in the transition state.