Thermodynamic standard state

Equation 7.15 implies that, for an electrochemical reaction involving a redox reaction, there exists an electrode potential that is related to the chemical potentials of the reactants and the reaction products and is calculated by this equation. This electrochemical potential is called the redox potential . This potential is positive for an oxidation reaction, where a constituent involved will gain in valency, while it is negative for a reduction reaction, where the valency is reduced for the constituent. In the standard thermodynamic state (i.e., for an ideal condition where each of the species is 1 mol at standard temperature and pressure), the standard redox potential is... 

Experimental standard thermodynamic state functions for this ion in the gas phase can be obtained from the following sources the GB of cyclopentene, an ICR... 

Shortcomings of the choice of the equilibrium state as the electrical reference point in the evaluation of the temperature effect on the rate of electrode reactions, and consequently of the overpotential as an experimental substitute for A(A0) in the WE-RE cell at various temperatures, have been discussed in the previous section. Hence, another reference point should be sought. From a theoretical point of view, the choice is unambiguous—it is the zero point on the relative electrode potential scale, defined by the SHE convention. Basically, this is also an equilibrium state, but of a single reaction selected by convention, namely, the reduction of two hydrogen ions to molecular hydrogen. The value of A0 at the interface when this reaction is held at equilibrium, assuming all species involved are in standard thermodynamic states, is fixed by the SHE convention as zero. The same convention associates additional properties with this reference state temperature, solvent, and solute Independence. Formally, the properties of the SHE satisfy the principal theoretical requirements for the electrical reference point in the evaluation of the effect of temperature on the rate of electrode reactions. 

The free energy differences obtained from our constrained simulations refer to strictly specified states, defined by single points in the 14-dimensional dihedral space. Standard concepts of a molecular conformation include some region, or volume in that space, explored by thermal fluctuations around a transient equilibrium structure. To obtain the free energy differences between conformers of the unconstrained peptide, a correction for the thermodynamic state is needed. The volume of explored conformational space may be estimated from the covariance matrix of the coordinates of interest, = ((Ci [13, lOj. For each of the four selected conform-... 

We now know the energy of the propene thermodynamic state (propene(g)) relative to the state 3 C(g) and 6 11(g) and the energy of the therrnodynarnie standard state of the elements relative to the same state 3 C(g) and 6 11(g)). which is opposite in sign to the summed energies of formation of 3 C(g) and (i IKg). The energy differenee between these thennodynamie states is... 

The values of fH° and Ay.G° that are given in the tables represent the change in the appropriate thermodynamic quantity when one mole of the substance in its standard state is formed, isothermally at the indicated temperature, from the elements, each in its appropriate standard reference state. The standard reference state at 25°C for each element has been chosen to be the standard state that is thermodynamically stable at 25°C and 1 atm pressure. The standard reference states are indicated in the tables by the fact that the values of fH° and Ay.G° are exactly zero. 

First, we shall explore a conceptual relation between kinetics and thermodynamics that allows one to draw certain conclusions about the kinetics of the reverse reaction, even when it has itself not been studied. Second, we shall show how the thermodynamic state functions for the transition state can be defined from kinetic data. These are the previously mentioned activation parameters. If their values for the reaction in one direction have been determined, then the values in the other can be calculated from them as well as the standard thermodynamic functions. The implications of this calculation will be explored. Third, we shall consider a fundamental principle that requires that the... 

The NPT + test particle method [8, 9] aims to determine phase coexistence points based on calculations of the chemical potentials for a number of state points. A phase coexistence point is determined at the intersection of the vapor and liquid branches of the chemical potential versus pressure diagram. The Widom test particle method [7] of the previous paragraph or any other suitable method [10] can be used to obtain the chemical potentials. Corrections to the chemical potential of the liquid and vapor phases can be made, using standard thermodynamic relationships, for deviations... 

Since AG° can be calculated from the values of the chemical potentials of A, B, C, D, in the standard reference state (given in tables), the stoichiometric equilibrium constant Kc can be calculated. (More accurately we ought to use activities instead of concentrations to take into account the ionic strength of the solution this can be done introducing the corresponding correction factors, but in dilute solutions this correction is normally not necessary - the activities are practically equal to the concentrations and Kc is then a true thermodynamic constant). 

The standard state (and thus any standard thermodynamic property) of a pure solid refers to the pure substance in the solid phase under the pressure p of 1 bar (0.1 MPa). The standard state of a pure liquid refers to the pure substance in the liquid phase at p = 1 bar. When the substance is a pure gas, its standard state is that of an ideal gas at p = 1 bar (or, which is equivalent, that of a real gas at P = o). 

Equation A1.3 shows that isotope effects calculated from standard state free energy differences, and this includes theoretical calculations of isotope effects from the partition functions, are not directly proportional to the measured (or predicted) isotope effects on the logarithm of the isotopic pressure ratios. Rather they must be corrected by the isotopic ratio of activity coefficients. At elevated pressures the correction term can be significant, and in the critical region it may even predominate. Similar considerations apply in the condensed phase except the fugacity ratios which define Kf are replaced by activity ratios, a = Y X and a = y C , for the mole fraction or molar concentration scales respectively. In either case corrections for nonideality, II (Yi)Vi, arising from isotope effects on the activity coefficients can be considerable. Further details are found in standard thermodynamic texts and in Chapter 5. 

The ion level in condensed phases has been represented by the real potential, a, referred to the standard gaseous state of the ion at the outer potential of the condensed phases. The reference level, then, is not common to all ions but differs with different ions. In chemical thermodynamics, the conventional energy scale is based on the assumption that all atoms in the stable form in the standard state are at the zero energy level, which is the thermodynamic reference level of energy for chemical substances. In the following, we discuss the relationship between the scale of the ion level represented by the real potential of ions and the conventional energy scale of particles in chemical thermodynamics. 

In transition-state theory, the absolute rate of a reaction is directly proportional to the concentration of the activated complex at a given temperature and pressure. The rate of the reaction is equal to the concentration of the activated complex times the average frequency with which a complex moves across the potential energy surface to the product side. If one assumes that the activated complex is in equilibrium with the unactivated reactants, the calculation of the concentration of this complex is greatly simplified. Except in the cases of extremely fast reactions, this equilibrium can be treated with standard thermodynamics or statistical mechanics . The case of... 

Similar transfer functions can be defined for other thermodynamic state functions, e.g. H. However, if these functions are to be combined to yield other state functions, e.g. S, then care must be exercised to ensure that, as in the use of equation (15), the same standard state is always used. 

The standard thermodynamic functions of solvation defined as above indicated by superscript differ from the generally tabulated standard thermodynamic functions indicated by superscript0 due to the constraints of fixed positions. They therefore lack the changes in the translational degrees of freedom, due to the compression from the volume of the gaseous state to that in the solution, not relevant to the solvation of the solute. Thus, AH = AH0 + RT (1 - ap7), where ap is the isobaric expansibility of the solvent, AS = AS0 + R( - ap7), AV = AV° - (RT/P°) -1 + ktP°), where kt is the isothermal compressibility of the solvent, and so on. 

Above all, thermodynamics is a useful subject. Its usefulness is largely dependent on the tabulation of thermodynamic quantities in an efficient and convenient form. Because it takes at least two variables to determine the state of a pure material, tables could get rather unwieldy. To avoid this, properties are tabulated at a standard (pressure) state and then converted to the pressure that is desired. For hquids and sohds, the standard state is just that of the pure material at 1.0 bar pressure. 

A standard thermodynamic value occurs with all components at 25 °C and 100 kPa. This thermodynamic standard state is slightly different from the standard temperature and pressure (STP) often used for gas law problems ( 0 °C and 1 atm=101.325 kPa). Standard properties of common chemicals are listed in tables. 

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