Standard chemical potential definition

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. 

In this equation, the standard chemical potential MAgjS 6e used because the deviation of 6 from stoichiometry is much less than 1. According to the definition of the standard potential, = 0, is the standard Gibbs energy of the element in the standard state AG . Then... 

There are four undetermined quantities Apfx, (Apf ), pf, and (pf) and two equations. We must, therefore, define two of the four quantities, which in turn determines the other two quantities and the relationship between them. We can define the reference states for the component and the species. The difference between the standard chemical potential of the component and that of the species is then expressed in terms of the mole fractions in the reference state. The problem is the determination of this difference. The different species may be known from our knowledge of the chemical system, or they may be assumed. However, a definite decision must be made concerning the species, and all calculations must be carried out based upon this decision. Several examples concerning reference and standard states are discussed here and in the following sections. 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by... 

Then, with the definition of the standard chemical potentials given in Equation (8.185),... 

The symbol or ° is used to indicate standard. They are equally acceptable. Definitions of standard states are discussed below (p.53). Whenever a standard chemical potential i or a standard equilibrium constant K or other standard quantity is used, the standard state must be specified. 

Sometimes (amount) concentration c is used as a variable in place of molality m both of the above equations then have c in place of m throughout. Occasionally mole fraction x is used in place of m both of the above equations then have x in place of m throughout, and x = 1. Although the standard state of a solute is always referenced to ideal dilute behaviour, the definition of the standard state and the value of the standard chemical potential g are different depending on whether molality m, concentration c, or mole fraction x is used as a variable. 

Equilibrium constants cannot be set up in a unique manner. This is evident by studying the fundamental definition that relates these quantities to the reference chemical potentials /r (r, P). We could equally well, or perhaps preferentially, relate the equilibrium constants to the standard chemical potentials, based on the relation /x/(r, P) = 1) - - RT Inx,. It is easy to verify that this leads to the... 

Standard state for chemical potential, definition of activity... 

From the definition (Edward, 1964 Boyd, 1969 Yates and McClelland, 1974) of activity coefficients and of their standard states (infinite dilution in water), the log values of eqns (12)-(15) are proportional to the difference in standard chemical potentials in two media, water and the acid solution of interest. Log is, therefore,... 

A large number of concentration units are used in the definition of the chemical potential. In the following paragraphs, we discuss the activity coefficients and standard chemical potentials for some commonly used units. The chemical potential of component i can be written in terms of /w,-, the gross molality or formality of /, that is, the number of moles of / per thousand grams of solvent [Eq. (2-3)] in the form... 

Comparing this expression with Eq. (10), which determines the difference between the standard chemical potentials of surfactants in the aqueous and oil phases (i.e., by the definition of the free energy of the surfactant transfer from the oil phase into the aqueous phase) ... 

This standard chemical potential is a characteristic of the reaction A - B it corresponds to the standard molar free enthalpy of reaction and its definition is the value taken by the chemical potential when equality between substance amounts is realized... 

In fact, the above relation is the only proper definition of the standard chemical potential within the realm of thermodynamics. 

The quantity at is sometimes called the relative activity of i, because it depends on the chemical potential relative to a standard chemical potential. An important application of the activity concept is the definition of equilibrium constants (Sec. 11.8.1). 

Values having been specified where necessary for and m , the standard chemical potential / of a substance B, and hence any other standard thermodynamic function of the substance B, depends only on the thermodynamic temperature T. The definition of the standard chemical potential Pb of ia substance B is given for a component of a gas mixture in Section 4, for a component of a liquid or solid (one-phase) mixture in Section 5, and for a solute in a solution and for the solvent (which may be a mixed one) in Section 6.t... 

The standard thermodynamic functions of a substance are often described as relating to the substance in its standard state. Any difficulties associated with a verbal description of such a standard state disappear when an algebraic definition of the standard chemical potential is given. 

Relation (2.1) involves the standard chemical potential p.° of a species. Definitively, it cannot be determined experimentally, nor is its chemical potential p.,-. However, we noticed when we were on the subject of mass law that a judicious linear combination of standard chemical potentials is experimentally accessible. In truth, it is impossible to know the absolute value of a chemical potential because it is a free enthalpy and because the absolute value of any free enthalpy itself cannot be known. However, the fact that an absolute value of a quantity cannot be determined is not rare. An example that is more common than those of enthalpies, free enthalpies, and free entropies is provided by an altitude point. The difference in altitude between two points is measurable. It is not the case for their absolute altitude. Numerous other quantities also follow suit. 

By definition, the definition of an activity requires choosing a standard state. For example, for a solute i, the standard state can be chosen as being the state in which its concentration is C° (or its molality J°, or its mole fraction is x°,), the temperature is r, and the solution is ideal (recall that pressure exerts a very weak influence on the behavior of condensed phases). At concentration C°, (which is that in the standard state), the solute chemical potential is its standard chemical potential A°,. Hence, when the solution is ideal, the solute chemical potential (A, at concentration C, or at molality m, is given by the expressions... 

The standard chemical potential, p° here Is the Gibbs free energy of one mole of the pure gas at one atmosphere pressure. This follows from substituting P = 1 into equation (1.5) combined with the definitions of pa and pg. 

The activity (a) of a substance provides a measure of the ability or potential of a substance to change the Gibbs energy (G) of a system. By definition, it is related to the chemical potential (/r) and the standard chemical potential (/r°) of a substance through the equation /X = + RT In fl. In practical... 

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. 

Electrochemical cells can be constructed using an almost limitless combination of electrodes and solutions, and each combination generates a specific potential. Keeping track of the electrical potentials of all cells under all possible situations would be extremely tedious without a set of standard reference conditions. By definition, the standard electrical potential is the potential developed by a cell In which all chemical species are present under standard thermodynamic conditions. Recall that standard conditions for thermodynamic properties include concentrations of 1 M for solutes in solution and pressures of 1 bar for gases. Chemists use the same standard conditions for electrochemical properties. As in thermodynamics, standard conditions are designated with a superscript °. A standard electrical potential is designated E °. 

The activity of a perfect gas, as for any substance, is unitary, by definition, at standard state. Moreover, for a perfect gas, activity is (numerically) equivalent to pressure, at all pressures. Let us consider the relationship existing, with T held constant, between the chemical potential of component i in gaseous phase g at 1 bar (/a, 17 ) and at pressure P... 

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