Equilibrium constant Gibbs free energy and

The units of AG are joules (or kilojoules), with a value that depends not only on E, but also on the amount n (in moles) of electrons transferred in the reaction. Thus, in reaction A, n = 2 mol. As in the discussion of the relation between Gibbs free energy and equilibrium constants (Section 9.3), we shall sometimes need to use this relation in its molar form, with n interpreted as a pure number (its value with the unit mol struck out). Then we write... 

Relation between standard reaction Gibbs free energy and equilibrium constant van t Hoff equation ... 

Because the chemical potential is a thermodynamic property of species i, it must have the same value irrespective of the particular convention chosen for a,. It follows that the value of the standard chemical potential h% and consequently the values of he standard Gibbs free energy and equilibrium constant should depend on that choice. As Hi is the value of Hi for unit activity, the state having such activity in the scale chosen is the standard state. There are lUPAC recommendations for most common situations (Cox et al. 1982). Eor the solutes in the solution phase activities af in all cases collected in Table 5.1, the recommended and commonly anployed Henry law convention is used... 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

FIGURE 7.24 At constant temperature and pressure, the direction of spontaneous change is toward lower Gibbs free energy. The equilibrium state of a system corresponds to the lowest point on the curve. 

AU,) - the differences between the depths of different minima so going down from a shallower to a deeper minimum of the molecular PES means decreasing the Gibbs free energy and such a process generally has an equilibrium constant larger than unity. However, for precise calculations, the terms coming from translations, rotations and vibrations also must be taken into account. 

A system at constant temperature, pressure, and mole numbers tries to decrease its Gibbs free energy. At equilibrium, the Gibbs free energy of the system is minimized. 

Skill 26.1 Recognize the relationships among enthalpy, entropy, Gibbs free energy, and the equilibrium constant. 

Since equilibrium constants are related to Gibbs free energy, and the latter in turn is related to H and S, it is apparent that in some sense, heat capacities are the fundamental quantities from which all the others can be derived. 

We leam to determine the standard reduction potentials based on the standard hydrogen electrode reference and use them to calculate the emf of a cell and hence the spontaneity of a cell reaction. A relationship exists between a cell s emf, the change in the standard Gibbs free energy, and the equilibrium constant for the ceU reaction. (19.3 and 19.4)... 

Quantities in brackets refer to equilibrium solution concentrations of the indicated species. Stability constants are related to standard thermodynamic parameters such as entropy, enthalpy, Gibbs free energy, and temperature, through well-known relationships. The expression in Equation 9.3 can be manipulated using a series of mass balance expressions to relate the equilibrium concentrations of species to the initial concentrations (co) of species used to set up the experiment ... 

Complexing behavior can be checked for via a thorough literature review. Consulting the extensive compilations by the National Bureau of Standards (1) and the Russian Academy of Science (2) is a good first step. Other sources to check are the Smith and Martell (3) and SUlen (4) compilations. These references provide vcdues for the Gibbs free energies and heats of formation for precipitate, ionic, vapor, aqueous molecule and complex species which can be used to calculate the various equilibrium constants needed for modeling aqueous solutions. There are also values for some of the cation hydrolysis complexes. 

Here, is the water-gas shift reaction s equilibrium constant dependent on Gibbs free energy and stack temperature, where and E2 are constants related to Gibbs free energy change. The assumption that this reaction is in equilibrium allows us to remove its reaction rate from the equation set. 

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. =... 

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... 

The equilibrium constant of a reaction can be related to the changes in Gibbs Free Energy (AG), enthalpy (AH) and entropy (AS) which occur during the reaction by the mathematical expressions ... 

The decrease in Gibbs free energy as a signpost of spontaneous change and AG = 0 as a criterion of equilibrium are applicable to any kind of process, provided that it is occurring at constant temperature and pressure. Because chemical reactions are our principal interest in chemistry, we now concentrate on them and look for a way to calculate AG for a reaction. 

What Are the Key Ideas Instead of going tu cumpletiun, reactions proceed until the composition of a reaction mixture corresponds to minimum Gibbs free energy. This composition is described by an equilibrium constant that is characteristic of the reaction and depends on the temperature. 

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