Free energy proton

See also Gibbs free energy proton affinity. 

Fig. 16 Schematic representation of the free energy proton transfer path from neutral to zwitterionic glycine or vice versa in 53 waters. The QM/MM-MFEP results are presented in red, compared with experimental values in black [205, 206] and CPMD calculations in blue [201]...

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] ... 

Gamma radiation produces free carriers much as does visible light (36). High energy protons and electrons produce defects that reduce minority carrier lifetime according to equation 8 ... 

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... 

Reported values for A and ApH vary, but the membrane potential is always found to be positive outside and negative inside, and the pH is always more acidic outside and more basic inside. Taking typical values of A F = 0.18 V and ApH = 1 unit, the free energy change associated with the movement of one mole of protons from inside to outside is... 

Assume that the free energy change, AG, associated with the movement of one mole of protons from the outside to the inside of a bacterial cell is —23 kJ/mol and 3 must cross the bacterial plasma membrane per ATP formed by the bacterial FjEo-ATP synthase. ATP synthesis thus takes place by the coupled process ... 

A proton-motive force of approximately —250 mV is needed to achieve ATP synthesis. This proton-motive force, A, is composed of a membrane potential, A P, and a pH gradient, ApH (Chapter 21). The proton-motive force is defined as the free energy difference, AG, divided by S, Paraday s constant ... 

The critical hydrogen content for the ductility loss increased with increasing hydrogen solubility in the alloy. The fracture surfaces were not characteristic of those found under conditions of SCC. In terms of hydrogen and deuterium solubility in a similar series of bcc alloys, the equilibrium constants were determined at infinite dilution as a function of temperature The free energy function was expressed in terms of the bound-proton model. 

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