Free energy equilibrium constant

Know the effect of temperature on equilibrium constants, free energy, and entropy and enthalpy changes. 

The value of a pe-pH diagram consists primarily in providing an aid for the interpretation of equilibrium constants (free energy data) by permitting the simultaneous representation of many reactions. Of course, such a diagram, like all other equilibrium diagrams, represents only the information used in its construction. 

In the field of radioactive waste management, the hazardous material consists, to a large extent, of actinides and fission products from nuclear reactors. Due to differences in scientific approaches and assumptions, there is a great deal of contradictory and unreliable thermodynamic data concerning aqueous speciation of these elements in the scientific literature, in the form of equilibrium constants, free energies and enthalpies. To fulfil the requirements of a proper modelling of the behaviour of the actinide and fission products in the environment, it is essential to establish a reliable thermochemical database by critically and comprehensively reviewing all available data in the literature. 

Gas chromatographic retention data in some instances can be used in the determination of equilibrium constants, free energies, heats and entropies for the interactions between column liquids containing metal complexes and a great variety of volatile ligands that may be passed through the column. Stability constants have been determined for sixteen silver-... 

For a system at equilibrium, the free energy change, AG, at constant temperature and pressure is zero. Let two phases, a and (3, of the same substance, in equilibrium at a temperature T and pressure P, be considered. If the two phases are reversibly converted into one another (a (3) by withdrawing or supplying heat, the system is always in equilibrium, and AG is zero. It readily follows that the molar free energy of the substance in the two phases in equilibrium is the same... 

At equilibrium the free energy changes associated with the second and third stages are zero. For the first stage at, constant temperature T ... 

Therefore there is no overall chemical reaction. Assuming that conditions such as pH and ionic strength are the same on both sides of the membrane, the equilibrium constant for the transport reaction is KGlut = 1 and the equilibrium Gibbs free energy is AG°glut = 0. 

For non-standard conditions we can find the free energy of a reaction using AG = AG° RT InQ. For the special case of equilibrium, the free energy is zero, so AG° = -RT InK, AG° = -5700 log K (in joules). Thus free energy is related to the equilibrium constant, K. 

Here we have divided both sides of the equation by nF to isolate the cell potential in the equation. This equation also resembles the Nernst equation (Equation 13.4), and it is easy to see how it arises. At equilibrium, the free energy change is zero and the reaction quotient, Q, is equal to the equilibrium constant, K. 

You can derive the equation relating AG° to the equilibrium constant K from the preceding equation. In the previous section, you saw that as a chemical reaction approaches equilibrium, the free energy decreases and continues to decrease until equilibrium is reached. At equilibrium, the free energy ceases to change then AG = 0. Also, the reaction quotient Q becomes equal to the equilibrimn constant K. If you substitute AG = 0 and Q = K into the preceding equation, you obtain... 

The solution is based on a modified version of White, Johnson, and Dantzig s minimization of free energy technique. The technique minimizes the Gibbs free energy at constant temperature and pressure subject to the conservation of mass constraint since at chemical equilibrium the free energy is at a minimum. 

F is known as the free energy. When the film is in equilibrium, or more correctly thermodynamic equilibrium, the free energy will be minimized. This is analogous to the minimization of the potential energy of a system of particles in classical mechanics. From Eq. (3.1) the area. A, of the film will have a minimum value when the film has reached equilibrium as a/ remains constant. The film tension, a/, is a function of temperature only. 

It is useful to summarise the assumptions considered for the thermodynamic analysis discussed above, and the main results obtained. Based on the stress strain relationship for the glassy system in the form of equation 3, the chemical potential of a solute component in the polymeric mixture may be calculated as the derivative of the specific non-equilibrium Helmholtz free energy with respect to the moles of solute per polymer mass Yi at constant temperature, pressure and specific volume, as expressed in eqaution 12. On the other side, under the same assumption, the nonequilibrium Helmholtz free energy has a unique value at given temperature, specific volume and composition, whatever is the pressure of the system, as stated in equation 13. 

In completely separate investigations, early osmometry studies of the association of the nucleic acid bases and nucleosides in solution indicated that the molecules were also aggregating in columns [42]. Sedimentation equilibrium studies showed that this process is reversible and that there is a near constant free energy increment when each additional molecule is added, irrespective of the existing length of the column. Such behavior was termed isodesmic . For purine and pyrimidine nucleosides, the association constants indicate weak associations where both. H and. S are negative (i.e., the aggregation process is enthalpically rather than entropically driven). The standard free... 

Assume that the system has a constant number of molecules N — M and is at constant temperature and constant volume. It follows that at equilibrium the free energy A is minimum, or... 

Thus, for spontaneous processes at constant temperature and volume a new quantity, the Helmholtz free energy A, decreases. At equilibrium under such restrictions cL4 = 0. 

For spontaneous processes at constant temperature and pressure it is the Gibbs free energy G that decreases, while at equilibrium under such conditions dG = 0. 

We have seen that equilibrium in an isolated system (dt/= 0, dF= 0) requires that the entropy Sbe a maximum, i.e. tliat dS di )jjy = 0. Examination of the first equation above shows that this can only be true if. p. vanishes. Exactly the same conclusion applies for equilibrium under the other constraints. Thus, for constant teinperamre and pressure, minimization of the Gibbs free energy requires that dGId Qj, =. p. =... 

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... 

Having separated the dynamical from equilibrium (or, more accurately, quasi-equilibrium) effects, one can readily discover the origin of the activation free energy and define the concept of the potential of mean force by analysis of the expression for the TST rate constant, k in (A3.8.3). The latter can be written as [7]... 

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 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... 

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