Standard state chemical potential

For a free energy of fonnation, the preferred standard state of the element should be the thennodynamically stable (lowest chemical potential) fonn of it e.g. at room temperature, graphite for carbon, the orthorhombic crystal for sulfiir. 

Standard-state potentials are generally not tabulated for chemical reactions, but are calculated using the standard-state potentials for the oxidation, E°o, and reduction half-reactions, fi°red- By convention, standard-state potentials are only listed for reduction half-reactions, and E° for a reaction is calculated as... 

The values given in the following table for the heats and free energies of formation of inorganic compounds are derived from a) Bichowsky and Rossini, Thermochemistry of the Chemical Substances, Reinhold, New York, 1936 (h) Latimer, Oxidation States of the Elements and Their Potentials in Aqueous Solution, Prentice-Hall, New York, 1938 (c) the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards and (d) the tables of Selected Values of Chemical Thermodynamic Properties of the National Bureau of Standards. The reader is referred to the preceding books and tables for additional details as to methods of calculation, standard states, and so on. 

However, the chemical potential is given by Eq. (4-341) for gas-phase reactions and standard states as the pure ideal gases at T°, this equation becomes... 

The term 7 7 ln p/p° is clearly the chemical potential of a surface of radius r with respect to a flat surface of the same material as standard state. It follows that the difference in chemical potential between two surfaces, where... 

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. 

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... 

Notes. In the case of a single oxide (or hydroxide) existing in different allotropic states, indicated by the letters a, b, c, d, etc. the oxides are arranged in descending order of stability, i.e. in ascending order of standard chemical potentials (expressed for an identical chemical formula). 

Activity can be thought of as the quantity that corrects the chemical potential at some pressure and/or composition condition" to a standard or reference state. The concept of a standard state is an important one in thermodynamics. The choice of the pressure and composition conditions for the standard state are completely arbitrary, and unusual choices are sometimes made. The common choices are those of convenience. In the next section, we will describe and summarize the usual choices of standard states. But, first, we want to describe the effect of pressure and temperature on a,. 

The isopiestic method is based upon the equality of the solvent chemical potentials and fugacities when solutions of different solutes, but the same solvent, are allowed to come to equilibrium together. A method in which a solute is allowed to establish an equilibrium distribution between two solvents has also been developed to determine activities of the solute, usually based on the Henry s law standard state. In this case, one brings together two immiscible solvents, A and B, adds a solute, and shakes the mixture to obtain two phases that are in equilibrium, a solution of the solute in A with composition. vA, and a solution of the solute in B with composition, a . 

This is done by starting with equation (6.84), which relates the chemical potential of a solute in solution with activity to the standard state chemical potential... 

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. 

In Chapter 6, fugacity and activity are defined and described and related to the chemical potential. The concept of the standard state is introduced and thoroughly explored. In our view, a more aesthetically satisfying concept does not occur in all of science than that of the standard state. Unfortunately, the concept is often poorly understood by non-thermodynamicists and treated by them with suspicion and mistrust. One of the firm goals in writing this book has been to lay a foundation and describe the application of the standard state in such a way that all can understand it and appreciate its significance and usefulness. 

Differentiation of Eq. (22) with respect to ri2 yields for the chemical potential of the polymeric solute relative to the pure liquid polymer as standard state... 

The temperature at which this condition is satisfied may be referred to as the melting point Tm, which will depend, of course, on the composition of the liquid phase. If a diluent is present in the liquid phase, Tm may be regarded alternatively as the temperature at which the specified composition is that of a saturated solution. If the liquid polymer is pure, /Xn —mS where mS represents the chemical potential in the standard state, which, in accordance with custom in the treatment of solutions, we take to be the pure liquid at the same temperature and pressure. At the melting point T of the pure polymer, therefore, /x2 = /xt- To the extent that the polymer contains impurities (e.g., solvents, or copolymerized units), ixu will be less than juJ. Hence fXu after the addition of a diluent to the polymer at the temperature T will be less than and in order to re-establish the condition of equilibrium = a lower temperature Tm is required. 

In words, the difference between the chemical potential of the crystalline repeating unit and the unit in the standard state, i.e., the pure... 

In a general case of a mixture, no component takes preference and the standard state is that of the pure component. In solutions, however, one component, termed the solvent, is treated differently from the others, called solutes. Dilute solutions occupy a special position, as the solvent is present in a large excess. The quantities pertaining to the solvent are denoted by the subscript 0 and those of the solute by the subscript 1. For >0 and x0-+ 1, Po = Po and P — kxxx. Equation (1.1.5) is again valid for the chemical potentials of both components. The standard chemical potential of the solvent is defined in the same way as the standard chemical potential of the component of an ideal mixture, the standard state being that of the pure solvent. The standard chemical potential of the dissolved component jU is the chemical potential of that pure component in the physically unattainable state corresponding to linear extrapolation of the behaviour of this component according to Henry s law up to point xx = 1 at the temperature of the mixture T and at pressure p = kx, which is the proportionality constant of Henry s law. 

For a solution of a non-volatile substance (e.g. a solid) in a liquid the vapour pressure of the solute can be neglected. The reference state for such a substance is usually its very dilute solution—in the limiting case an infinitely dilute solution—which has identical properties with an ideal solution and is thus useful, especially for introducing activity coefficients (see Sections 1.1.4 and 1.3). The standard chemical potential of such a solute is defined as... 

Standard States for Chemical Potential Calculations (for Use in Studies of Chemical Reaction Equilibria)... 

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