Standard state defined

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

Enthalpy of Formation The ideal gas standard enthalpy (heat) of formation (AHJoqs) of chemical compound is the increment of enthalpy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard states, defined as the existing phase at a temperature of 298.15 K and one atmosphere (101.3 kPa). Sources for data are Refs. 15, 23, 24, 104, 115, and 116. The most accurate, but again complicated, estimation method is that of Benson et al. " A compromise between complexity and accuracy is based on the additive atomic group-contribution scheme of Joback his original units of kcal/mol have been converted to kj/mol by the conversion 1 kcal/mol = 4.1868 kJ/moL... 

As shown in Fig. 21, in this case, the entire system is composed of an open vessel with a flat bottom, containing a thin layer of liquid. Steady heat conduction from the flat bottom to the upper hquid/air interface is maintained by heating the bottom constantly. Then as the temperature of the heat plate is increased, after the critical temperature is passed, the liquid suddenly starts to move to form steady convection cells. Therefore in this case, the critical temperature is assumed to be a bifurcation point. The important point is the existence of the standard state defined by the nonzero heat flux without any fluctuations. Below the critical temperature, even though some disturbances cause the liquid to fluctuate, the fluctuations receive only small energy from the heat flux, so that they cannot develop, and continuously decay to zero. Above the critical temperature, on the other hand, the energy received by the fluctuations increases steeply, so that they grow with time this is the origin of the convection cell. From this example, it can be said that the pattern formation requires both a certain nonzero flux and complementary fluctuations of physical quantities. 

Equations (16)-(18) contain two terms the first one is a function of the concentrations of the species involved in Eqs. (3"), (4"), and (11), while the second is a function of the activity coefficients of these species. The measurement of the standard free energy changes for these processes involves the determination of both concentration and activity terms. Whenever both terms can be accurately determined, the corresponding pKs are referred to as thermodynamic, that is, based on the standard state defined in Section III,F. 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows ... 

The standard state defined in terms of the ideal gas presents no difficulty. In order to go from the ideal gas to the real gas at the same temperature,... 

The thermodynamic functions have been defined in terms of the energy and the entropy. These, in turn, have been defined in terms of differential quantities. The absolute values of these functions for systems in given states are not known.1 However, differences in the values of the thermodynamic functions between two states of a system can be determined. We therefore may choose a certain state of a system as a standard state and consider the differences of the thermodynamic functions between any state of a system and the chosen standard state of the system. The choice of the standard state is arbitrary, and any state, physically realizable or not, may be chosen. The nature of the thermodynamic problem, experience, and convention dictate the choice. For gases the choice of standard state, defined in Chapter 7, is simple because equations of state are available and because, for mixtures, gases are generally miscible with each other. The question is more difficult for liquids and solids because, in addition to the lack of a common equation of state, limited ranges of solubility exist in many systems. The independent variables to which values must be assigned to fix the values of all of the... 

In Equation (8.22) fi°[T,P0] is the molar Gibbs energy of the substance in its standard state defined at the temperature T and the arbitrary pressure P0. The change of the Gibbs energy with temperature cannot be determined, because the absolute value of the entropy is not known, as stated before. 

AG° can also, of course, be defined in terms of Ka, the equilibrium constant written in terms of activities, a. [Note This symbol should not be confused with that for the acid ionisation constant, also Ka], In this present case the standard state defined for A G° is that associated with unit activities (a = 1) rather than with unit pressure ( P° = 1 bar), or in the case where gases are involved, with unit fugacities (/ = 1). We can then write that ... 

Here the pH is the value for acidity referred to the standard state defined from the limiting reference behavior for the hydrogen ions in the solvent in question, and PH is the pH value of the aqueous reference buffer corrected for liquid junction and transfer activity coefficient as follows ... 

In the previous section it was shown that the term heat of adsorption may represent different functions, depending on the experimental conditions under which it is determined. The situation is analogous with the entropy of adsorption which can also be defined in several ways (/1). It is always necessary to specify whether the function considered is a true differential, a derivative, or an integral entropy, and also whether it refers to an equilibrium state (defined by p and T) or to a standard state (defined by p° and T). Moreover, various entropies of adsorption may be defined by choosing different standard states for the adsorptive (this state may be gaseous, but also liquid or solid). In this section, all the thermodynamic quantities of the adsorbate will be defined relative to a Gibbs surface for simplicity, but defining them in terms of an interfacial layer yields the same results. 

On the scale of standard enthalpies of formations, how are the elements in their standard states defined ... 

Values for protonation-dissociation constants of generic surface sites can also be predicted using solvation and crystal chemical theory (Sverjensky and Sahai, 1996). Using tlie standard states defined above (Sverjensky, 2003), the values of log and log can be calculated from log 8 which are... 

Because of the inconvenient nature of the standard state defined above, the concentration units used to describe the concentration dependence of the chemical potential are usually different. More convenient choices for concentration are molality and molarity. When the solution is dilute the relationship between mole fraction and molality is quite simple (see equation (1.2.3)). In terms of molality, the expression for the concentration dependence of the chemical potential of component B becomes... 

The PV term is generally small and unless many atmospheres pressure are involved it is usually safe to ignore it (for instance when the vapour pressure of a liquid is not 1 atm). To simplify the notation for the standard states when applied to solutions we shall continue to use the standard states defined at 1 atm. We shall assume that the approximate equation... 

First critical comment Because activity has been carefully defined as a dimensionless ratio, K must also be dimensionless. For gases, with the standard state defined as unit fugacity, a=f/f p/p°=p bar/1 bar. 

Entropy of Formation The ideal gas standard entropy of formation (ASyass) of a chemical compound is the increment of entropy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard state defined as the existing phase at a temperature of 298.15 K and one atmosphere (101.325 kPa). Thus ... 

We emphasize that in writing (5.4.10) we have specified the temperature and pressure of the standard state, but we still have not made a unique choice for the standard state because we have not yet specified its phase. One common choice is the Lewis-Randall standard state, defined in (5.1.5), in which each standard-state fugacity is taken to be that for the pure component in the same phase and at the same temperature T and pressure P as the mixture. 

The A1 + AI2O3 standard state defines a very stable reference state for O, and as a result, a measured Oo greater than unity is common [100,101]. An interesting problem encountered with this procedure is the large discrepancy with the published data for the reactions (Equation 48.54a,d). Clearly more accurate measurements of the vapor species in the Al-O system are needed [38,39,95,100-102]. 

In older texts you might come across a standard state defined for 1 atm (101.325 kPa) in place of 1 bar. That is the old convention. In most cases, data for 1 atm differ only a little from data for 1 bar. You might also come across standard states defined as referring fo 298.15 K. Thai is incorrect temperature is not a part of the definition of standard state, and standard states may refer to any temperature (but it should be specified). Thus, it is possible to speak of the standard state of water vapor at 100 K, 273.15 K, or any other temperature. It is conventional, however, for data to be reported at the so-called conventional temperature of298.15 K (25.00°C), and from now on, unless specified otherwise, all data will be for that temperature. For simplicity, we shall often refer to 298.15 K as 25°C . Finally, a standard state need not be a stable state cuid need not be realizable in practice. Thus, the standard state of water vapor at 25 C is the vapor at 1 bar, but water vapor at that temperature and pressure would immediately condense to Hquid water. 

Slate or phase of system and/or species under consideration Standard state defined by pressure, temperature or composition... 

Thermodynamics information of the adsorption process at infinite dilution can be obtained from the retention volume. At infinite dilution, the standard free energy to transfer 1 mol of adsorbate from the gas phase to the surface at standard state, defined as the variation in the standard free energy of adsorption, (J/mol), can be expressed as ... 

The various indices do have the following meaning. The index reminds us that we talk about gases. The index indicates that the gas is a pure or one-component gas and not one component in a mixture of gases. The other index ° indicates a reference pressure. In thermodynamics the chemical potential is not an absolute quantity. We rather compute differences between chemical potentials—often there is some standard state, defined by specifying temperature and pressure values, with respect to which the difference is calculated. If our gas is ideal the above equation becomes... 

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