Protons absolute entropies

Q Calculate the value of the absolute entropy of hydration of the proton. 

Note 4.5.- Up until now, we have defined an entropy known as the absolute entropy, because it is characterized by a number of complexions equal to 1. In fact, in that number, we have only taken account of the states of the nucleus, the electrons and the atoms. There is nothing to suggest that, were we to take account of the states of the particles internal to the nucleus such as protons, neutrons or other nuclear subatomic particles, we would actually obtain the same absolute entropy. In fact, our absolute entropy can be qualified as chemical, strictly speaking, it remains a relative entropy value that calculated by taking the number of complexions at the scale of the atom as equal to 1. 

BGt(M) = gas-phase basicity of species M at temperature T Cp = molar heat capacity at constant pressure k = reaction rate constant = equilibrium constant PAj(M) = proton affinity of species M at temperature T S (M) = absolute entropy of... 

In the case of non-HBD solvents, such as DMSO, the measured pK values are absolute (that is, free from ion pairing) and can be directly compared with gas-phase acidities6 in addition, knowledge of the heats of ionization in DMSO7 allows the evaluation of a possible entropy effect when the two phases are compared. The mechanism of proton transfer between oxygen and nitrogen acids and bases in aqueous solution has been reviewed8. 

The Absolute Standard Molar Entropy of Hydration of the Proton... 

In what sense is this potential absolute It refers back, eventually, to the free energy of a hypothetical stationaiy electron and a hypothetical stationaiy proton in the gas phase. In this sense, it is reasonable to call the quantity given by Eq. (9.2) absolute, for a stationaiy electron or proton has no entropy and the potential energy of a stationaiy isolated particle must be zero. 

The proton affinities, PA (equation 44), are not determined directly from ICR (ion cyclotron resonance) spectrometry, but entropy terms were instead evaluated in SCF ab initio calculations209. These absolute PA values and those relative to ammonia, APA, are summarized in Table 27209, which also contains the theoretical proton affinities obtained at different levels of theory. 

Ion-trapping and flow reactor mass spectrometry permit gas-phase ions and neutral molecules to be confined and attain equilibrium after a sufficient number of collisions. The equilibrium constant can then be deduced by measurement of gas partial pressures (for Bj and B2) and mass spectrometric ion intensities (for gaseous BiH and B2H ). The resulting AG provides the difference in gas-phase basicity between Bj and B2. If the absolute gas-phase basicity of either base is known, then the GB value of the other can be determined. Proton affinities are subsequently determined via AG = AH — TAS, with the entropy of basicity approximated via quantum chemical approaches. Table 6.6 lists proton affinity and gas-phase basicities for nitrogen bases, with the bases ranked in order of descending gas-phase basicity. The majority of organic bases exhibit GB values between 700 and 1000 kJ/mol. Compilations of PA and GB values are available. " ... 

Finally, let us point out that the absolute standard electrode potential value of the couple H+w/H2(g) is actually about 4.5 V. This value cannot be verified since we cannot measure an absolute potential. It was obtained by using thermodynamic cycles, taking into account some thermodynamic data such as the proton hydration enthalpy and entropy. These last ones have been approached by considering the quadrupole model of water (see Chap. 1). It is quite evident that the value of 4.5 V differs considerably from the conventional one (0.00 V). However, it does not change the redox phenomena provision since only the standard electrode potential differences are taken into account. 

The evaluation of such a body of interrelated thermodynamic data involves first an evaluation of the thermochemical scales for internal consistency in the three parameters, AG° (at different temperatures), AH° and AS°. Final values assigned for the proton affinities and entropy changes must be consistent with what is known about the thermochemistry of M and MFI+. The lengths of segments of the scale linking different primary standards (compounds for which Eqn [2] can be used to derive an absolute proton affinity value) must of course match the known interval between the known proton affinity values. 

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