PAC determination of bond dissociation enthalpies
As described in the PAC Determination of Reaction Enthalpies and Volume Changes section, and like any calorimeter, PAC is used to determine reaction enthalpies. To investigate the energetics of a specific bond, a suitable reaction must be devised so that the desired bond dissociation enthalpy (BDE) can be derived from the reaction enthalpy, using a thermodynamic cycle. In the simplest cases, the chosen reaction is simply the homolysis of the bond of interest and therefore the reaction enthalpy coincides with the BDE. This was the case, for instance, in the determination of the Co—C BDE in methylcobalamin (MeCbl, a member of the vitamin B12 family) [1], reaction 7, or the O—O BDE in di-tert-butyl peroxide (t-BuOOBu-t) [2], reaction 8.
| Me—Cbl (sln) → Me• (sln) + Cbl• (sln) | (7) | |
| t-BuOOBu-t (sln) → 2 t-BuO• (sln) | (8) |
Reaction 7 represents a typical example of the application of PAC to the study of enzymatic activity [3]. The metal-ligand homolysis corresponds to the rate determining step. Since the Co—C is the weakest bond in the molecule, it can be selectively broken by tuning down the laser frequency, usually to the green region of the spectrum. The metal-ligand BDE, fundamental to understand the mechanism of enzymatic action, coincides with the measured enthalpy of the homolysis.
Reaction 8 is part of a general strategy to determine BDEs in organic molecules [4-6]. The generated tert-butoxyl radicals can selectively abstract an hydrogen from several types of molecules, such as phenols, amines, tiophenols, and various hydrocarbons, enabling the determination of the corresponding R—H BDE. The mechanism is depicted below:
t-BuOOBu-t (sln)  2 t-BuO• (sln) |
(8) | |
| 2 RH (sln) + 2 t-BuO• (sln) → 2 R• (sln) + 2 t-BuOH (sln) | (9) | |
| Net: | t-BuOOBu-t (sln) + 2 RH (sln) → 2 R• (sln) + 2 t-BuOH (sln) | (10) |
The enthalpy of the overall reaction 10 (ΔrH) is related to the R—H BDE through eq 11, obtained from a thermodynamic cycle and involving several auxiliary terms: standard enthalpies of formation (ΔfH°) and solution (ΔslnH°) of liquid di-tert-butyl peroxide, liquid tert-butyl alcohol, and gaseous hydrogen atom [7].
The auxiliary enthalpies of formation in this equation are well known. The solution enthalpy terms are also available for several solvents, with the exception of the solvation enthalpy of the hydrogen atom. If necessary, solution enthalpies of di-tert-butyl peroxide and liquid tert-butyl alcohol can be determined for a given solvent, e.g. using reaction-solution calorimetry [2].
One of the most widely used solvents in PAC studies is benzene. In this case, introducing all the relevant values, the above equation assumes the much simpler look of eq 12:
 |
(12) |
The solvation enthalpy of the hydrogen atom was intentionally left out because an experimental value is not available. However, a value of 5±1 kJ.mol-1 for organic solvents can be predicted by using the hydrogen molecule as a suitable model [8], in keeping with results from theoretical calculations [9,10]. Note, however, that the solvation enthalpy of the hydrogen atom is only relevant for the calculation of the solution-phase BDE. When deriving the gas-phase BDE, it will cancel out [11,12]. In other words, even if that estimate is dead wrong, it will only affect the accuracy of the solution-phase bond dissociation enthalpy.