As reference state

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. ... 

Here /g,hq and y ,ss are the activity coefficients of component B in the liquid and solid solutions at infinite dilution with pure solid and liquid taken as reference states. A fus A" is the standard molar entropy of fusion of component A at its fusion temperature Tfus A and AfusGg is the standard molar Gibbs energy of fusion of component B with the same crystal structure as component A at the melting temperature of component A. 

The states that have been agreed on as reference states in tabulating enthalpies of reaction are summarized in Table 4.1. Other standard states may be adopted in special problems. When no state is specified, it can be assumed to be that listed in Table 4.1. 

By this definition the enthalpy of formation of an element in its standard state is zero. In other words, elements in their standard states are taken as reference states in the tabulation of enthalpies of reaction, just as sea level is the reference point in measuring geographic heights. 

What are the advantages and disadvantages of choosing the pure liquid compound as reference state ... 

So far, we have used the pure liquid compound as reference state for describing the thermodynamics of transfer processes between different media (Chapter 3). When treating reactions of several different chemical species in one medium (e.g., water) it is, however, much more convenient to use the infinite dilution state in that medium as the reference state for the solutes. Hence, for acid-base reactions in aqueous solutions, in analogy to Eq. 3-34, we may express the chemical potential of the solute i as ... 

Note that we use the prime superscript to denote the infinite dilution reference state (as opposed to the pure liquid state), and that we omit any subscript to indicate that we are dealing with aqueous solutions. Also note that because we have chosen the aqueous solution as reference state, y, will in many cases not be substantially different from 1. Exceptions are the charged species at high ionic strength as, for example, encountered in seawater (see below). 

For a reasonable choice of parameters, this is the lowest LC in energy so that we choose as reference state... 

Configuration interaction calculations including single and double excitations (CISD) were carried out on the QC using as reference state (reference Slater determinant) the one obtained by the previous B3LYP/BS ground state evaluation and... 

The data for sulphur, bromine and iodine compounds in Table 20.1 are different from the data in the original paper. In Table 20.1 the elements in their stable form at 25 °C and 1 bar are taken as reference states, as is usual in thermodynamics in the original publication S2(g), Br2(g) and 12(g) were taken as reference state. 

The calculations — involving a thermodynamic cycle from the solid crystalline soap and the liquid acid as references states showed the 4 2 complex to be stable even in the gaseous state. 

An approximate thermodynamic evaluationbased on liquid water and crystalline sodium octanoate as reference states has recently evaluated the energy conditions in the premicellar aggregate. The calculations essentially were concerned with the free energy of a gaseous soap/water complex. No attempt was made to evaluate the chemical potential changes in any of the components when dissolved in the pentanol. 

Values of isosteric sorption enthalpy, -AH, standard sorption entropy, AS°, and standard Gibbs free sorption energy, AG°, are calculated as dependences on n, cf., [4-8]. To calculate AG°, the boiling-point temperature of N2O is chosen as reference state. This choice provides a check for thermodynamic consistency of experimental data since dG°... 

The potential of a unit mass of groundwater, as given by Equation 1.3 is thus determined by its place in the earth gravitational field and by the pressure and density of the groundwater. In groundwater practice, sea level and atmospheric pressure are taken as reference state, i.e. Zq = 0 and pQ = 1 atmosphere. If, in addition, the density of the groundwater is constant (p, is not a function of p, i.e. the water is incompressible), the hydraulic head becomes... 

Coupled cluster response calculaAons are usually based on the HF-SCF wave-function of the unperturbed system as reference state, i.e. they correspond to so-called orbital-unrelaxed derivatives. In the static limit this becomes equivalent to finite field calculations where Aie perturbation is added to the Hamiltonian after the HF-SCF step, while in the orbital-relaxed approach the perturbation is included already in the HF-SCF calculation. For frequency-dependent properties the orbital-relaxed approach leads to artificial poles in the correlated results whenever one of the involved frequencies becomes equal to an HF-SCF excitation energy. However, in Aie static limit both unrelaxed and relaxed coupled cluster calculations can be used and for boAi approaches the hierarchy CCS (HF-SCF), CC2, CCSD, CC3,... converges in the limit of a complete cluster expansion to the Full CI result. Thus, the question arises, whether for second hyperpolarizabilities one... 

Define the reference state, and identify Tq, Cq, (Atot)o d its species compositions, yjfs. Recall that, in most applications, the initial state is selected as reference state. 

To establish numerical values for /i, one has to pick arbitrarily a reference state and declare that for this state, = 0. Consider the compound HjO and the conditions 273 K and 1 bar if water is taken as the reference state so that Hvaiet = 0 kJ/kg-mole, then Hsuam — 500 kJ/kg-mole in these conditions. On the other hand, if the molecular gases H2 and O2 are taken as reference states, then on this basis Hsum = —230 000 kJ/kg-mole. In the first instance, h positive steam is less stable than the reference state and might spontaneously convert. In the second instance, h is negative steam is more stable than the reference state. 

Figure 6. Reduction potentials of the four reduction steps of 02. (a) pH dependence calculated form standard E° data with pQl = 1 atm as reference state and pK values of the intermediates. References Biclski et al. (1985), Sawyer and Valentine (1981), George (1965). Superoxide is a strong reducing agent. (b) Reaction path diagram for the reduction of Oa. The the formation of radicals in the first and third step is endergonic.

The excitation operators Gi being defined in terms of U(n) generators (cf. Eqs. 59-70 of (13)), these matrix elements may be evaluated as reference state mean values of multiple U(n) generator products using the same technique and codes that we developed when implementing the UGA CC method (13). 

So far it has not been possible to ascertain whether step (V.59) or step (V.60) makes the more important contribution. To reach a decision, one may determine the steady-state oxygen activity at the surface of the catalyst in a nonequilibrium SO2-SO3-O2 mixture, see the discussion for the reaction CO + Oa = CO2 on Ag or NiO as catalyst in Section V.D. In principle, the value of ao(st) may be obtained from measurements of the emf of cell (A) proposed in Sectio 11. Since nearly equilibrium for reaction (V.58) is supposed to be establislied, one has to expect ao(st) 2 po2 for oxygen at unit pressure as reference state. If the experimental value of ao(sf) is less than, reaction (V.59) prevails. Conversely, if ao(sf) is greater than, reaction (V.60) prevails. 

Nevertheless, there are thermochemical tables where S2(gas) is considered as reference state at all temperatures, beginning with T = 298.15 K. 

As discussed, for the solute 1 it is rational to take as reference state an ideal solution obeying the Henry law. Therefore, we may define a virtual activity coefficient y having as reference the infinite diluted solution, as expressed by the equation ... 

The melting temperature has naturally the physical dimension of a temperature. To find a relation wifh ofher quantities in a dimensionless form, we go through tables and discover that the coefficient of thermal expansion has the dimension of a reciprocal temperature. Now there could be some natural relation between these two quantities. We can fix a zero temperature as reference state or infinite temperature as reference state. It is more reasonable to fix zero temperature as reference state. Therefore, coming from low temperature, it is more likely to choose the coefficients of thermal expansion in the solid state than the coefficients of thermal expansion in the liquid state. 

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