Energy equilibrium constant

Calculated Rate Constants, Activation Energies, Equilibrium Constants, and Related Experimental Data, for Addition of CO and H2 to 3Fe(CO)4 at 300 K... 

Standard-state Free Energies, Equilibrium Constants, and Concentrations... 

In treating the various topics in this book the particular method employed has been determined in each case by considerations of simplicity, usefulness and logical development. In some instances the classical, historical approach has been preferred, but in others the discussion follows more modern lines. Whenever feasible the generalized procedures, involving reduced temperatures and pressures, which have been evolved in recent years chiefly by chemical engineers, are introduced. As regards statistical methods, the author feels that the time has come for them to take then-place as an essential part of chemical thermodynamics. Consequently, the applications of partition functions to the determination of heat capacities, entropies, free energies, equilibrium constants, etc., have been introduced into the text in the appropriate places where it is hoped their value will be appreciated. 

As previonsly discussed, for any redox couple, the ratio of reductant/oxidant is a function of the two variables Eh and pH of the system. We have already defined Eh in terms of free energy, equilibrium constant, and electron activity. pH is defined in terms of proton activity. These two master variables regulate many biogeochemical reactions and determine the stability of minerals and nutrient regeneration in soils and sediments. Thus, the activities or concentrations of reductant and oxidant can be depicted as... 

Cell Potentials and Free Energy Equilibrium Constants... 

The nature of the datum, e.g., Gibbs energy , Equilibrium constant, etc. 

To proceed fiirther, to evaluate the standard free energy AG , we need infonnation (experimental or theoretical) about the particular reaction. One source of infonnation is the equilibrium constant for a chemical reaction involving gases. Previous sections have shown how the chemical potential for a species in a gaseous mixture or in a dilute solution (and the corresponding activities) can be defined and measured. Thus, if one can detennine (by some kind of analysis)... 

The value of the standard free energy AG depends on the choice of reference state, as does the equilibrium constant. Thus it would be safer to write the equilibrium constant K for a gaseous reaction as... 

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] ... 

The most important themiodynamic property of a substance is the standard Gibbs energy of fomiation as a fimetion of temperature as this infomiation allows equilibrium constants for chemical reactions to be calculated. The standard Gibbs energy of fomiation A G° at 298.15 K can be derived from the enthalpy of fomiation AfT° at 298.15 K and the standard entropy AS° at 298.15 K from... 

The solubilization of diverse solutes in micelles is most often examined in tenns of partitioning equilibria, where an equilibrium constant K defines the ratio of the mole fraction of solute in the micelle (X and the mole fraction of solute in the aqueous pseudophase. This ratio serves to define the free energy of solubilization -RT In K). 

The equilibrium constant at constant temperature is directly related to the maximum energy, called the free energy AG. which is obtainable from a reaction, the relationship being... 

Equilibria in Solution The stability of a protein-ligand complex in solution is measured in terms of the equilibrium constant and the standard free energy of association based on it. For association of species P and L in solution to form a complex PL, i.e., for... 

Equilibrium constants for protein-small molecule association usually are easily measured with good accuracy it is normal for standard free energies to be known to within 0.5 kcal/mol. Standard conditions define temperature, pressure and unit concentration of each of the three reacting species. It is to be expected that the standard free energy difference depends on temperature, pressure and solvent composition AA°a also depends on an arbitrary choice of standard unit concentrations. 

Conformational free energy simulations are being widely used in modeling of complex molecular systems [1]. Recent examples of applications include study of torsions in n-butane [2] and peptide sidechains [3, 4], as well as aggregation of methane [5] and a helix bundle protein in water [6]. Calculating free energy differences between molecular states is valuable because they are observable thermodynamic quantities, related to equilibrium constants and... 

Thermodynamics shows that equilibrium constants can be related to Gibbs free energies, AG, by Eq. (3). 

Ihe allure of methods for calculating free energies and their associated thermod)mai values such as equilibrium constants has resulted in considerable interest in free ene calculations. A number of decisions must be made about the way that the calculatior performed. One obvious choice concerns the simulation method. In principle, eit Monte Carlo or molecular dynamics can be used in practice, molecular dynamics almost always used for systems where there is a significant degree of conformatio flexibility, whereas Monte Carlo can give very good results for small molecules which either rigid or have limited conformational freedom. 

Having calculated the standai d values AyW and S" foi the participants in a chemical reaction, the obvious next step is to calculate the standard Gibbs free energy change of reaction A G and the equilibrium constant from... 

P)(]uation (3-34) makes clear a difficulty that will bedevil us throughout computational chemistry Although the accuracy of compi.itatknial chemistry is extremely high, the demands placed on our results ntay he even higher. In the present case, the equilibrium constant is dependent on the exponential of the standard free energy... 

See the box entitled Enthalpy Free Energy and Equilibrium Constant accompanying this section for a discussion of these relationships... 

One of the fundamental equations of thermo dynamics concerns systems at equilibrium and relates the equilibrium constant K to the dif ference in standard free energy (A6°) between the products and the reactants... 

This experiment describes a characterization analysis in which the degree of association, equilibrium constant, and hydrogen bond energy are measured for benzyl alcohol and phenol in CCI4. 

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