State reference

With the use of f and as in A the implication is that both the compound in question and its constituent elements arc in standard states and that the elements, moreover, are in their reference states for any given temperature the reference states of the elements will normally be those that are stable at the chosen standard-state pressure and at that temperature. A resulting feature of tabulations and 4 f G as functions of temperature for compounds is that discontinuous changes are sometimes to be seen these correspond to changes in the stable reference states of the elements, as phase-transition temperatures are passed. Thus, values of AfH (S02Cl2,g) would show discontinuous changes at three temperatures corresponding to the transitions S(cr,I)- S(cr,II), S(cr,II) S(/), and S(/) l/2 82(g), where I refers to rhombic and II to monoclinic crystal forms. 

A multiphase table contains the data for two or more phases of a pure substance. Each phase is limited to the temperature range in which it is more stable (i.e., has a lower A fG ) than the other phases in the table. There are discontin- 

Single-phase tables are more convenient than multiphase tables in certain computer applications. Interpolation and approximation (curve fitting) apply directly to the continuous properties in a single-phase table. Multiphase tables must first be divided into segments using the stored values of the transition temperatures then interpolation and approximation must be limited to the temperatures in the pertinent segment. 

Single-phase tables are essential in uses that involve unstable phases. This includes phases that persist in a metastable region or those that are unstable at all temperatures. The real world abounds in such cases. Single-phase tables are often applied to solid-solid or solid-liquid equilibrium in mixtures, where an unstable phase is stabilized in the presence of other components. Analysis of such equilibria often requires liquid or solid properties that are many hundreds of degrees into the metastable region of each pure phase. Single-phase tables are designed to supply these properties, but their preparation is not trivial. 

The glass transition is of practical concern when thermochemical tables are used near the glass temperature of any of the pure liquids. Although the ratio of the glass temperature to the melting temperature can vary from perhaps 0.35 to 0.8, it often is - 0.7. Temperatures this low are not uncommon when liquid tables are used in the analysis of binary or multicomponent phase diagrams. 

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CONSTANTS FOR 2ERO PRESSURE REFERENCE STATE FUGACITY EQUATION ... 

CONSTANTS FOR ZERO PRESSURE REFERENCE STATE FU6AC1TY EQUATION A... 

Here the composition is expressed as concentration c. and the reference state is for unit concentration 1 ... 

In analogy to the gas, the reference state is for the ideally dilute solution at c, although at the real solution may be far from ideal. (Teclmically, since this has now been extended to non-volatile solutes, it is defined at... 

The reference state for the solvent is nomially the pure solvent, so one may write... 

The value of the standard free energy AG depends on the choice of reference state, as does the equilibrium constant. Thus it would be safer to write the equilibrium constant K for a gaseous reaction as... 

Conventions about standard states (the reference states introduced earlier) are necessary because otherwise the meaning of the standard free energy of a reaction would be ambigrious. We sunnnarize the principal ones ... 

For analysing equilibrium solvent effects on reaction rates it is connnon to use the thennodynamic fomuilation of TST and to relate observed solvent-mduced changes in the rate coefficient to variations in Gibbs free-energy differences between solvated reactant and transition states with respect to some reference state. Starting from the simple one-dimensional expression for the TST rate coefficient of a unimolecular reaction a— r... 

At low solvent density, where isolated binary collisions prevail, the radial distribution fiinction g(r) is simply related to the pair potential u(r) via g ir) = exp[-n(r)//r7]. Correspondingly, at higher density one defines a fiinction w r) = -kT a[g r). It can be shown that the gradient of this fiinction is equivalent to the mean force between two particles obtamed by holding them at fixed distance r and averaging over the remaining N -2 particles of the system. Hence w r) is called the potential of mean force. Choosing the low-density system as a reference state one has the relation... 

Series expansion Smith and van Gunsteren [4] investigated the first approach expanding the free energy as a function of the coupling parameter A into a T ylor series around a given reference state, A = 0,... 

Liu, H., Mark, A. E., van Gunsteren, W. F. Estimating the relative free energy of different molecular states with respect to a single reference state. J. Phys. Chem. 100 (1996) 9485-9494... 

First, we would like to ehange the reference state from the isolated nuelei and eleetions to the elements in their standard states, C(graphite) and H2(g) at 298 K. This leads to the energy of formation at 0 K AfEo, whieh is identieal to the enthalpy of formation AfHo at 0 K. The energy and enthalpy are identieal only at 0 K. Next we would like to know the enthalpy ehange on heating propene from 0 to 298 K so as to obtain the enthalpy of formation from the isolated nuelei and eleetions elements This we will eonvert to from the elements in their standard... 

Cl results can vary a little bit from one software program to another for open-shell molecules. This is because of the HF reference state being used. Some programs, such as Gaussian, use a UHF reference state. Other programs, such as MOLPRO and MOLCAS, use a ROHF reference state. The difference in results is generally fairly small and becomes smaller with higher-order calculations. In the limit of a full Cl, there is no difference. 

It is possible to construct a Cl wave function starting with an MCSCF calculation rather than starting with a HF wave function. This starting wave function is called the reference state. These calculations are called multi-reference conhguration interaction (MRCI) calculations. There are more Cl determinants in this type of calculation than in a conventional Cl. This type of calculation can be very costly in terms of computing resources, but can give an optimal amount of correlation for some problems. 

The extended CIS method (XCIS) is a version of CIS for examining states that are doubly excited from the reference state. It does not include correlation and is thus similar in accuracy to CIS. 

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. 

As already mentioned, the choice of the supercooled liquid as reference state has been questioned by some workers who use the saturation vapour pressure of the solid, which is measured at the working temperature in the course of the isotherm determination. The effect of this alternative choice of p° on the value of a for argon adsorbed on a number of oxide samples, covering a wide range of surface areas, is clear from Table 2.11 the average value of is seen to be somewhat higher, i.e. 18 OA. ... 

The working temperature, 77 K, is well below the triple point of krypton, 116 K, but if the solid is taken as the reference state the isotherm shows an unusually sharp upward turn at the high-pressure end. The usual practice, following Beebe, is therefore to take p° as the saturation vapour pressure of the supereooled liquid (p° = 2-49 Torr at 77-35 K and 27-5 Torr at 90-2 K). 

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