Protonation, free energies

The similarity between this table and a table of proton free energies is striking just as the pH defines the average proton free energy in a solution and thus controls the ratio of conjugate acid and base, so does the ° control the ratio of conjugate oxidant and reductant concentrations. 

Use the search engine Google to locate the Web document The Fall of the Proton Why Acids React with Bases by Stephen Lower. This document explains acid/base behavior in terms of the concept of proton free energy. How is an acid/base titration described in this view In a titration of strong acid with strong base, what is the free energy sink In a complex mixture of weak acid/base systems, such as serum, what happens to protons ... 

Much less information is available for the proton free energy of solvation, most certainly because of problems related to the determination of the entropic contribution TAS i. From a theoretical point of view, this contribution is much more sensitive than the enthalpic term for the choice of a model for the solvated proton and also to the level of theory employed in the calculations. Table VII.9 summarizes the results for the proton solvation free energy reported in the literature. 

Belieres, J.P. and Angell, C.A., Protonic ionic liquids Preparation, characterization, and proton free energy level representation, J. Phys. Chem. B 111 (18), 4926 937 (2007). 

BeUeres J-P, Angell CA (2007) Protic ionic liquids preparation, characterization, and proton free energy level representation. JPhys Chem B 111(18) 4926—4937. doi 10.1021/jp067589u... 

Fig. 6 a Protonation on O and on N of S-SPl conformer, b protonation on O and on N of R-SP2 conformer, as for the neutral case, both enantiomers of a given conformer react in the same way (see Fig. 7). The protonation free energies (kJ mol ) for the reaction SP - -H30 — > SPH + H2O are computed at the CAM-B3LYP/6-311-1- G(d,p) level at room temperature. Note that while protonation on the O leads to the open cir-TCCOH conformer (see Table S7), protonation on the N atom leads to a stable close SP conformer (see Table S8)...

Belieres J. -P. Angell, C. A. (2007). Protic Ionic Liquids Preparation, Characterization, and Proton Free Energy Level Preparation. /. Phys. Chem., B, 111, 4926-4937. 

Figure A3.8.3 Quantum activation free energy curves calculated for the model A-H-A proton transfer reaction described 45. The frill line is for the classical limit of the proton transfer solute in isolation, while the other curves are for different fully quantized cases. The rigid curves were calculated by keeping the A-A distance fixed. An important feature here is the direct effect of the solvent activation process on both the solvated rigid and flexible solute curves. Another feature is the effect of a fluctuating A-A distance which both lowers the activation free energy and reduces the influence of the solvent. The latter feature enliances the rate by a factor of 20 over the rigid case.

It is possible to detemiine the equilibrium constant, K, for the bimolecular reaction involving gas-phase ions and neutral molecules in the ion source of a mass spectrometer [18]. These measurements have generally focused on tln-ee properties, proton affinity (or gas-phase basicity) [19, 20], gas-phase acidity [H] and solvation enthalpies (and free energies) [22, 23] ... 

Let us define the respective basicity by — AG in the gas phase and — AG" in aqueous solution. For discussions concerning the relative strength in basicity of a series of methyl-amines, only the relative magnitudes of these quantities are needed. Thus the free energy changes associated with the protonation of the methylamines relative to those of ammonia are defined as... 

Free energy changes of methylamines m aqueous solution upon protonation refeiTed to... 

Procedures to compute acidities are essentially similar to those for the basicities discussed in the previous section. The acidities in the gas phase and in solution can be calculated as the free energy changes AG and AG" upon proton release of the isolated and solvated molecules, respectively. To discuss the relative strengths of acidity in the gas and aqueous solution phases, we only need the magnitude of —AG and — AG" for haloacetic acids relative to those for acetic acids. Thus the free energy calculations for acetic acid, haloacetic acids, and each conjugate base are carried out in the gas phase and in aqueous solution. 

The relative stabilities of 1-phenylvinyl cations can be measured by determining the gas-phase basicity of the corresponding alkynes. The table below gives some data on free energy of protonation for substituted phenylethynes and 1-phenylpropynes. These give rise to the corresponding Yukawa-Tsuno relationships. 

Outer sphere electron transfer (e.g., [11-19,107,160-162]), ion transfer [10,109,163,164] and proton transfer [165] are among the reactions near electrodes and the hquid/liquid interface which have been studied by computer simulation. Much of this work has been reviewed recently [64,111,125,126] and will not be repeated here. All studies involve the calculation of a free energy profile as a function of a spatial or a collective solvent coordinate. 

Through all these calculations of the effect of pH and metal ions on the ATP hydrolysis equilibrium, we have assumed standard conditions with respect to concentrations of all species except for protons. The levels of ATP, ADP, and other high-energy metabolites never even begin to approach the standard state of 1 M. In most cells, the concentrations of these species are more typically 1 to 5 mM or even less. Earlier, we described the effect of concentration on equilibrium constants and free energies in the form of Equation (3.12). For the present case, we can rewrite this as... 

As we have seen, the metabolic energy from oxidation of food materials—sugars, fats, and amino acids—is funneled into formation of reduced coenzymes (NADH) and reduced flavoproteins ([FADHg]). The electron transport chain reoxidizes the coenzymes, and channels the free energy obtained from these reactions into the synthesis of ATP. This reoxidation process involves the removal of both protons and electrons from the coenzymes. Electrons move from NADH and [FADHg] to molecular oxygen, Og, which is the terminal acceptor of electrons in the chain. The reoxidation of NADH,... 

The free energy difference for protons across the inner mitochondrial membrane includes a term for the concentration difference and a term for the electrical potential. This is expressed as... 

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