Standard Gibbs energy change relationship

Calculation of equilibrium conversions is based on the fundamental equations of chemical-reaction equilibrium, which in application require data for the standard Gibbs energy of reaction. The basic equations are developed in Secs. 15.1 through 15.4. These provide the relationship between the standard Gibbs energy change of reaction and the equilibrium constant. Evaluation of the equilibrium constant from thermodynamic data is considered in Sec. 15.5. Application of this information to the calculation of equilibrium conversions for single reactions is taken up in Sec. 15.7. In Sec. 15.8, the phase role is reconsidered finally, multireaction equilibrium is treated in Sec. I5.9.t... 

Although the Bronsted relation was first discussed with respect to proton transfer reactions, it has been found to apply to other types of reactions including electron and atom transfer reactions. Equation (7.11.1) implies that there is also a linear relationship between the Gibbs activation energy for the reaction and the standard Gibbs energy change for the associated equilibrium. Thus, one may also write... 

Now let us consider some examples of the relationship between the standard Gibbs energy change, AG , and the equilibrium constant K, making the assumption that the behavior is ideal... 

Here the C are the coefficients of the descriptors Xj in the equation. The form (4.1) follows from the basic thermodynamic relationship between the standard Gibbs energy change AG° for a reaction and the reaction s equilibrium constant... 

By starting with the relationship between standard Gibbs energy change and the equilibrium constant, the van t Hoff equation—relating the equilibrium constant and temperature—can be written (equation 13.25). With this equation, tabulated data at 25 °C can be used to determine equilibrium constants not just at 25 °C but at other temperatures as well. 

The Van t Hoff isotherm establishes the relationship between the standard free energy change and the equilibrium constant. It is of interest to know how the equilibrium constant of a reaction varies with temperature. The Varft Hoff isochore allows one to calculate the effect of temperature on the equilibrium constant. It can be readily obtained by combining the Gibbs-Helmholtz equation with the Varft Hoffisotherm. The relationship that is obtained is... 

Practically in every general chemistry textbook, one can find a table presenting the Standard (Reduction) Potentials in aqueous solution at 25 °C, sometimes in two parts, indicating the reaction condition acidic solution and basic solution. In most cases, there is another table titled Standard Chemical Thermodynamic Properties (or Selected Thermodynamic Values). The former table is referred to in a chapter devoted to Electrochemistry (or Oxidation - Reduction Reactions), while a reference to the latter one can be found in a chapter dealing with Chemical Thermodynamics (or Chemical Equilibria). It is seldom indicated that the two types of tables contain redundant information since the standard potential values of a cell reaction ( n) can be calculated from the standard molar free (Gibbs) energy change (AG" for the same reaction with a simple relationship... 

Here, AfG° is the change of the standard Gibbs energy for the reaction i in the forward direction. As a result, k derivative is mathematically invalid at fixed ki in equation (1.48). Thus, equation (1.48) cannot be apphed directly for finding the rate determining steps, since the preceding thermo dynamic relationships of some rate constants are necessary to consider for mathematical reasons. 

The apparent equilibrium constant K and the standard transformed Gibbs energy change A G ° for a biochemical reaction can be calculated from the A G ° values by using the relationship... 

In several reports, Lamy et al. have developed in detail the different relationships that allow us to calculate several important thermodynamic parameters of DEFCs [13, 14]. The Gibbs energy change of ethanol (under standard conditions) is — 1,326.7 kJ/mol. Therefore, the electromotive force (EMF) of a DEFC is ... 

In order to illustrate the relationship of polarity measurements and photochemical charge separation, let us estimate the non-Coulomb component of the change of the standard Gibbs energy AG for the transfer of a singly-charged ion with a radius r = 5 A from the micellar phase into the aqueous phase [9] ... 

The standard potential of a cell reaction (E n) values can be calculated from the standard molar free (Gibbs) energy change (AG" ") for the same reaction with a simple relationship ... 

The standard enthalpy and Gibbs free energy changes for a chemical reaction can be calculated from A./H° and A/G° data using the relationships... 

The standard electrode potential E° of a redox reaction is a measure of the potential that would be developed if both reductants and oxidants were in their standard states at equal concentrations and with unit activities. The units of E° are volts and ° can be calculated from the Gibbs free energy change (AG ) of the redox reaction from the relationships... 

The standard Gibbs free energy change, AG°, is most commonly used. The symbol0 designates a reaction involving reactants and products in their standard states (pure substances in their most stable states at 25 °C and 1 atm pressure). The relationship between A G° and Kcq is given by the expression... 

Calculate AG° and Kfor each independent reaction. This may be done as in the relevant examples earlier in this section, with determination of AG° as a function of temperature. An easier route, however, is to use the standard Gibbs free-energy change of formation A Gy for each compound at the temperature of interest in the relationship... 

The numerical values of the equilibrium constants can of course be converted to standard Gibbs free-energy changes through the relationship ln(K) = —AG°/RT and it is frequently of interest to attempt interpretations of these free energies in terms of contributions of various individual interactions to the overall value. There... 

The Daniell cell is an example of a galvanic cell, in this type of electrochemical cell, electrical work is done by the system. The potential difference, between the two half-cells can be measured (in volts, V) on a voltmeter in the circuit (Figure 7.1) and the value of is related to the change in Gibbs energy for the cell reaction. Equation 7.9 gives this relationship under standard conditions, where is°ceu is the standard cell potential. 

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