Thermodynamic study of proton-bond dimers formation in atmospheric pressure: An experimental and theoretical study

• Thermodynamics of a complex reaction of MH+(H2O)n + M ↔ MH+M(H2O)m + (n − m)H2O has been studied.
• Effective thermodynamics parameters of Keq, and ΔHeff were defined for the reaction.
• The experimental values of the ΔHeff change from positive to negative upon raising temperature.
• The behavior of the Keq, and ΔHeff, as a function of temperature, are predicted by DFT calculation.

Proton bonding is responsible for many important phenomena in physics, chemistry and biology. Simple proton-bound dimers of the type MHM+ are often used as model systems to investigate the nature of intermolecular interactions such as proton bonding. In this work, the thermochemistry of formation of symmetric proton bond dimmers at atmospheric pressure, in an ion mobility spectrometry (IMS) cell, was studied experimentally and theoretically. To establish equilibrium in the ionization region, the sample concentration was increased until the reaction quotient was independent of the sample concentration. The relative abundances of the monomer and dimer were obtained from the intensity of their corresponding peaks to use them in obtaining the equilibrium constant, Keq = [MHM+]/[MH+][M]. Van’t Hoff plot was then used to extract the enthalpy change of reaction. It was found that the experimental enthalpy is much smaller than expected and it was strongly temperature dependent. These were attributed to hydration of protonated ions. Parallel to experimental study, density functional theory (DFT) calculations at the B3LYP/6-311++G(d,p) level of theory were performed to obtain the enthalpy of the reactions MH+(H2O)n + M ↔ MH+M(H2O)m + (n − m)H2O with different n and m values. The theoretical values of equilibrium constant and enthalpy led to the fact that a mixture of protonated monomers, MH+(H2O)n with different hydration numbers, is in equilibrium with their un-hydrated dimer. For such a complex reaction, an effective equilibrium constant and an effective enthalpy were defined as Keff = 1/Σ(pn/Kn) and ΔHeff = ΣYnΔH°n, respectively. p is the partial pressure of water, and Kn and ΔH°n are the equilibrium constant and the enthalpy of the reaction MH+(H2O)n + M ↔ MH+M + nH2O, respectively. Yn = (pn/Kn)/Σ(pn/Kn), is the contribution of the nth reaction in the whole reaction, being dependent on the water partial pressure and temperature. Using this model, we predicted the experimental behavior of enthalpy of dimer formation reaction in IMS by the calculation.