Thermodynamics entropy standard state

More interesting for practical applications is the approach of Pompe et al. [22] where two GC thermodynamic parameters (standard-state changes of enthalpy, AH°, and of entropy, AS°) are estimated. Since these parameters can be used to describe the variation of retention with temperature (see Section 3.2.2), estimations of retention can be extended to other temperature conditions, including programmed temperature. 

The database contains thermochemical property data at standard state conditions for over 15 000 inorganic substances and small organic molecules having up to two carbon atoms. NISTTHERMO corresponds to the Tables of Chemical Thermodynamic Properties. Standard state properties at 298.15 K and 1 bar stored are enthalpy of formation, Gibbs energy of formation for the elements, enthalpy, heat capacity at constant pressure, and entropy. 

The thermodynamic ceiling temperature (26) T for a polymerization is computed by dividing the AfTp by the standard entropy of polymerization, The T is the temperature at which monomer and polymer are in equHibrium in their standard states at 25°C (298.15 K) and 101.3... 

Ideal gas absolute entropies of many compounds may be found in Daubert et al.,"" Daubert and Danner," JANAF Thermochemical Tables,TRC Thermodynamic Tables,and Stull et al. ° Otherwise, the estimation method of Benson et al. " is reasonably accurate, with average errors of 1-2 J/mol K. Elemental standard-state absolute entropies may be found in Cox et al." Values from this source for some common elements are listed in Table 2-389. ASjoqs may also be calculated from Eq. (2-52) if values for AHjoqs and AGJoqs are known. 

Just as the intrinsic energy of a body is defined only up to an arbitrary constant, so also the entropy of the body cannot, from the considerations of pure thermodynamics, be specified in absolute amount. We therefore select any convenient arbitrary standard state a, in which the entropy is taken as zero, and estimate the entropy in another state /3 as follows The change of entropy being the same along all reversible paths linking the states a and /3, and equal to the difference of the entropies of the two states, we may imagine the process conducted in the following two steps ... 

The activation parameters from transition state theory are thermodynamic functions of state. To emphasize that, they are sometimes designated A H (or AH%) and A. 3 4 These values are the standard changes in enthalpy or entropy accompanying the transformation of one mole of the reactants, each at a concentration of 1 M, to one mole of the transition state, also at 1 M. A reference state of 1 mole per liter pertains because the rate constants are expressed with concentrations on the molar scale. Were some other unit of concentration used, say the millimolar scale, values of AS would be different for other than a first-order rate constant. 

Table 5 lists equilibrium data for a new hypothetical gas-phase cyclisation series, for which the required thermodynamic quantities are available from either direct calorimetric measurements or statistical mechanical calculations. Compounds whose tabulated data were obtained by means of methods involving group contributions were not considered. Calculations were carried out by using S%g8 values based on a 1 M standard state. These were obtained by subtracting 6.35 e.u. from tabulated S g-values, which are based on a 1 Atm standard state. Equilibrium constants and thermodynamic parameters for these hypothetical reactions are not meaningful as such. More significant are the EM-values, and the corresponding contributions from the enthalpy and entropy terms. 

References (20, 22, 23, 24, 29, and 74) comprise the series of Technical Notes 270 from the Chemical Thermodynamics Data Center at the National Bureau of Standards. These give selected values of enthalpies and Gibbs energies of formation and of entropies and heat capacities of pure compounds and of aqueous species in their standard states at 25 °C. They include all inorganic compounds of one and two carbon atoms per molecule. 

Whether obtained from an actual experimentally feasible process or from a thought process, As i Gg, which is obtained from Eq. (2.9) by re-arrangement, pertains to the solvation of the solute and expresses the totality of the solute-solvent interactions. It is a thermodynamic function of state, and so are its derivatives with respect to the temperature (the standard molar entropy of solvation) or pressure. This means that it is immaterial how the process is carried out, and only the initial state (the ideal gaseous solute B and the pure liquid solvent) and the final state (the dilute solution of B in the liquid) must be specified. 

Table 5.36 Thermodynamic properties of pure pyroxene components in their various structural forms according to Saxena (1989) (1), Berman (1988) (2), and Holland and Powell (1990) (3) database. = standard state entropy of pure component at 7) = 298.15 K and Py = bar (J/mole) Hjp p = enthalpy of formation from elements at same standard state conditions. Isobaric heat capacity function Cp is... 

If the heat capacity functions of the various terms in the reaction are known and their molar enthalpy, molar entropy, and molar volume at the 2) and i). of reference (and their isobaric thermal expansion and isothermal compressibility) are also all known, it is possible to calculate AG%x at the various T and P conditions of interest, applying to each term in the reaction the procedures outlined in section 2.10, and thus defining the equilibrium constant (and hence the activity product of terms in reactions cf eq. 5.272 and 5.273) or the locus of the P-T points of univariant equilibrium (eq. 5.274). If the thermodynamic data are fragmentary or incomplete—as, for instance, when thermal expansion and compressibility data are missing (which is often the case)—we may assume, as a first approximation, that the molar volume of the reaction is independent of the P and T intensive variables. Adopting as standard state for all terms the state of pure component at the P and T of interest and applying... 

Entropy is a thermodynamic quantity that is a measure of disorder or randomness in a system. When a crystalline structure breaks down and a less ordered liquid structure results, entropy increases. For example, the entropy (disorder) increases when ice melts to water. The total entropy of a system and its surroundings always increases for a spontaneous process. The standard entropies, S° are entropy values for the standard states of substances. 

Interestingly, the standard entropies (and in turn heat capacities) of both phases were found to be rather similar [69,70]. Considering the difference in standard entropy between F2(gas) and the mixture 02(gas) + H2(gas) taken in their standard states (which can be extracted from general thermodynamic tables), the difference between the entropy terms of the Gibbs function relative to HA and FA, around room temperature, is about 6.5 times lower than the difference between enthalpy terms (close to 125 kJ/mol as estimated from Tacker and Stormer [69]). This indicates that FA higher stability is mostly due to the lower enthalpy of formation of FA (more exothermic than for HA), and that it is not greatly affected by entropic factors. Jemal et al. [71] have studied some of the thermodynamic properties of FA and HA with varying cationic substitutions, and these authors linked the lower enthalpy of formation of FA compared to HA to the decrease in lattice volume in FA. 

The conventional thermodynamic standard state values of the Gibbs energy of formation and standard enthalpy of formation of elements in their standard states are A(G — 0 and ArH = 0. Conventional values of the standard molar Gibbs energy of formation and standard molar enthalpy of formation of the hydrated proton are ArC (H +, aq) = 0 and Ar// (H +, aq) = 0. In addition, the standard molar entropy of the hydrated proton is taken as zero 5 (H+, aq) = 0. This convention produces negative standard entropies for some ions. 

Following this, the thermodynamic arguments needed for determining CMC are discussed (Section 8.5). Here, we describe two approaches, namely, the mass action model (based on treating micellization as a chemical reaction ) and the phase equilibrium model (which treats micellization as a phase separation phenomenon). The entropy change due to micellization and the concept of hydrophobic effect are also described, along with the definition of thermodynamic standard states. 

The two thermodynamic quantities AS° and A H° are the net difference in standard-state entropy and enthalpy of the energized molecule C and the stabilized reactant molecule C. 

The thermodynamic ceiling temperature (26) T for a polymerization is computed by dividing the Afi°polym by the standard entropy of polymerization, A+°polym. The T is the temperature at which monomer and polymer are in equilibrium in their standard states at 25°C (298.15 K) and 101.3 kPa (1 atm). (In the case of p-xylylene, such a state is, of course, purely hypothetical.) The T quantifies the binding forces between monomer units in a polymer and measures the tendency of the polymer to revert back to monomer. In other systems, the T indicates a temperature above which the polymer is unstable with respect to its monomer, but in the case of parylene it serves rather as a means of comparing the relative stability of the polymer with... 

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 summary, a reference state or standard state must be defined for each component in the system. The definition may be quite arbitrary and may be defined for convenience for any thermodynamic system, but the two states cannot be defined independently. When the reference state is defined, the standard state is determined conversely, when the standard state is defined, the reference state is determined. There are certain conventions that have been developed through experience but, for any particular problem, it is not necessary to hold to these conventions. These conventions are discussed in the following sections. The general practice is to define the reference state. This state is then a physically realizable state and is the one to which experimental measurements are referred. The standard state may or may not be physically realizable, and in some cases it is convenient to speak of the standard state for the chemical potential, for the enthalpy, for the entropy,... 

We find from this discussion that, when the reference state of a component in a multicomponent system is taken to be the pure component at all temperatures and pressures of interest, the properties of the standard state of the component are also those of the pure component. When the reference state of a component in a multicomponent system is taken at some fixed concentration of the system at all temperatures and pressures of interest, the system or systems that represent the standard state of the component are different for the chemical potential, the partial molar entropy, and for the partial molar enthalpy, volume, and heat capacity. There is no real state of the system whose properties are those of the standard state of a component. In such cases it may be better to speak of the standard state of a component for each of the thermodynamic quantities. 

P, T, and also composition are the state variables most often used to characterize the state of the system, as they can be easily measured and controlled. As we show in Part II, Equations 2.5 and 2.14 are important to perform the thermodynamic analysis of a process ATS-m, which expresses the change in entropy of a reaction at 298 K and at standard pressure. The reaction is defined to take place between compounds in their standard state, that is, in the... 

The Third Law of Thermodynamics postulates that the entropy of a perfect crystal is zero at 0 K. Given the heat capacity and the enthalpies of phase changes, Eq. (12-3) allows the calculation of the standard absolute entropy of a substance, S° = AS for the increase in temperature from 0 K to 298 K. Some absolute entropies for substances in thermodynamic standard states are listed in Table 12-1. 

It appears that there are two temperatures of a universal nature that describe the thermodynamic properties for the dissolution of liquid hydrocarbons into water. The first of these, 7h is the temperature at which the heat of solution is zero and has a value of approximately 20°C for a variety of liquids. The second universal temperature is Ts, where the standard-state entropy change is zero and, as noted, Ts is about 140°C. The standard-state free energy change can be expressed in terms of these two temperatures, requiring knowledge only of the heat capacity change for an individual substance... 

Figure 3.6 shows schematically the molar entropy of a pure substance as a function of temperature. If a structural transformation occurs in the solid state, an additional increase in the molar entropy comes from the heat of the transformations. As shown in the figure, the molar entropy of a pure substance increases with increasing temperature. In chemical handbooks we see the tabulated numerical values of the molar entropy calculated for a number of pure substances in the standard state at temperature 298 K and pressure 101.3 kPa. A few of them will be listed as the standard molar entropy, s , in Table 5.1. Note that the molar entropy thus calculated based on the third law of thermodynamics is occasionally called absolute entropy. 

Here, AH(A-B) is the partial molar net adsorption enthalpy associated with the transformation of 1 mol of the pure metal A in its standard state into the state of zero coverage on the surface of the electrode material B, ASVjbr is the difference in the vibrational entropies in the above states, n is the number of electrons involved in the electrode process, F the Faraday constant, and Am the surface of 1 mol of A as a mono layer on the electrode metal B [70]. For the calculation of the thermodynamic functions in (12), a number of models were used in [70] and calculations were performed for Ni-, Cu-, Pd-, Ag-, Pt-, and Au-electrodes and the micro components Hg, Tl, Pb, Bi, and Po, confirming the decisive influence of the choice of the electrode material on the deposition potential. For Pd and Pt, particularly large, positive values of E5o% were calculated, larger than the standard electrode potentials tabulated for these elements. This makes these electrode materials the prime choice for practical applications. An application of the same model to the superheavy elements still needs to be done, but one can anticipate that the preference for Pd and Pt will persist. The latter are metals in which, due to the formation of the metallic bond, almost or completely filled d orbitals are broken up, such that these metals tend in an extreme way towards the formation of intermetallic compounds with sp-metals. The perspective is to make use of the Pd or Pt in form of a tape on which the tracer activities are electrodeposited and the deposition zone is subsequently stepped between pairs of Si detectors for a-spectroscopy and SF measurements. 

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