Standard value chemical potential

For a substance in a given system the chemical potential gi has a definite value however, the standard potentials and activity coefficients have different values in these three equations. Therefore, the selection of a concentration scale in effect determines the standard state. 

In the case of ions in solution, and of gases, the chemical potential will depend upon concentration and pressure, respectively. For ions in solution the standard chemical potential of the hydrogen ion, at the temperature and pressure under consideration, is given an arbitrary value of zero at a specified concentration... 

For ions in solution the standard reference state is the hydrogen ion whose standard chemical potential at = 1 is given an arbitrary value of zero. Similarly for pure hydrogen at Phj = = 0- Thus for the... 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

The activity coefficient of the solvent remains close to unity up to quite high electrolyte concentrations e.g. the activity coefficient for water in an aqueous solution of 2 m KC1 at 25°C equals y0x = 1.004, while the value for potassium chloride in this solution is y tX = 0.614, indicating a quite large deviation from the ideal behaviour. Thus, the activity coefficient of the solvent is not a suitable characteristic of the real behaviour of solutions of electrolytes. If the deviation from ideal behaviour is to be expressed in terms of quantities connected with the solvent, then the osmotic coefficient is employed. The osmotic pressure of the system is denoted as jz and the hypothetical osmotic pressure of a solution with the same composition that would behave ideally as jt. The equations for the osmotic pressures jt and jt are obtained from the equilibrium condition of the pure solvent and of the solution. Under equilibrium conditions the chemical potential of the pure solvent, which is equal to the standard chemical potential at the pressure p, is equal to the chemical potential of the solvent in the solution under the osmotic pressure jt,... 

The relationships of the type (3.1.54) and (3.1.57) imply that the standard electrode potentials can be derived directly from the thermodynamic data (and vice versa). The values of the standard chemical potentials are identified with the values of the standard Gibbs energies of formation, tabulated, for example, by the US National Bureau of Standards. On the other hand, the experimental approach to the determination of standard electrode potentials is based on the cells of the type (3.1.41) whose EMFs are extrapolated to zero ionic strength. 

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). 

Note, in using Equations 50 and 53 above, that tabulations of thermodynamic data for electrolytes tend to employ a 1 molar ess concentration for all species in solution. For situations defined to have a standard-state pH value different from 0 (which corresponds to a 1 molar concentration of solvated protons), the standard-state chemical potentials for anions and cations are determined as... 

The problem of standard states as well as a comparison of AG° values obtained from different isotherms was discussed by Torrent et Using the Guggenheim model of the interphase,they derived a relation between the chemical potentials of all components in the interphase and in the bulk that are required to describe the equilibrium state. 

The Gibbs energy of adsorption is a measure of adsorbate-metal interactions. Its values depend, however, on the choice of standard states for the chemical potentials of the components involved in the process. Therefore AG° values determined for different systems can only be compared if they refer to the same standard-state conditions. AG° values of adsorption of thiourea (TU) on several metallic electrodes, calculated for the most often used standard states, are presented in Table 1. 

It follows from Eqn. 6-22 that the standard chemical potential of hydrated ions determined from the standard equilibrium potential of the ion transfer reaction is a relative value that is to the standard chemical potential of hydrated protons at unit activity, which, by convention in aqueous electrochemistry, is assigned a value of zero on the electrodiemical scale of ion levels. 

If we set at a value of zero according to the conventional chemical thermodynamic energy scale, the standard chemical potential of a hydrated proton,, is given by Eqn. 6-24 ... 

The value of k is constant because the standard chemical potentials in the two solvents are constants at a fixed temperature. Nemst s distribution law also can be stated in terms of molality. 

Although we cannot determine its absolute value, the chemical potential of acomponent of a solution has a value that is independent of the choice of concentration scale and standard state. The standard chemical potential, the activity, and the activity coefficient have values that do depend on the choice of concentration scale and standard state. To complete the definitions we have given, we must define the standard states we wish to use. 

Equations (4.7) and (4.8) are both very useful when analysing surfactant aggregation behaviour and experimental cmc values. The difference in standard chemical potentials - Pi must contain within it the molecular forces and energetics of formation of micelles, which could be estimated from theory. These will be a function of the surfactant molecule and will determine the value of its cmc. 

The determination of the charge, and thereby the valency, of a boron atom in an organic compound is usually straightforward if its "B NMR chemical shift within the 300+ ppm spectral window is compared to that of a close standard with a firmly established solution stmcture. But, there is a need for caution The structure of many boron-containing compounds depends on the nature of the solvent, and so multisolvent (i.e., aprotic vs. protic) analyses are often essential for a definitive characterization. Sadly, aqueous solution "B NMR spectral analyses are seldom reported—even, surprisingly, for compounds clearly prepared for their potential biological value. 

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