Entropy standard state values

The polynomial expansion in equation 5.28 allows the calculation of the high-T enthalpy and entropy of the compound of interest, from standard state values, through the equations... 

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. 

In these equations, the real-gas properties are expressed relative to the standard state values, H°, S°, and G°, which are, respectively, the molar enthalpy, the molar entropy, and the molar Gibbs energy values which the gas would have at a standard pressure p° (1.013 25 bar) if it were ideal. 

Using the relations among the Gibbs energy, the entropy, the enthalpy, and so on, each thermodynamic function can be expressed relative to its standard state value. 

Neglecting the small heat of dilution effects, and thus assuming as a first approximation that our AH data are standard state values, one readly estimates for the above mentioned process an entropy change of 124 e.u. 

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states. 

The values of S° represent the virtual or thermal entropy of the substance in the standard state at 298.15 K (25°C), omitting contributions from nuclear spins. Isotope mixing effects are also excluded except in the case of the H—system. 

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. 

The integral does not furnish the absolute value of, the entropy, because the lower limit is undetermined. If this is regarded as fixed, the integral with various upper limits gives the values of the entropies referred to this arbitrary standard state, and the differences between these values and any one of them referred to this arbitrary standard state will be the values of the entropies referred to the new standard state (cf. 42). 

If k is expressed in liters per mole per second, the standard state for the free energy and entropy of activation is 1 mole/liter. If the units of k are cubic centimeters per molecule per second, the corresponding standard state concentration is 1 molecule/cm3. The magnitudes of AG and AS reflect changes in the standard state, so it is not useful to say that a particular reaction is characterized by specific numerical values of these parameters unless the standard states associated with them are clearly identified. These standard states are automatically determined by the units chosen to describe the reactant concentrations in the phenomenological rate expressions. 

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. 

Thermochemical data from the compilation of Stull et at., 1969. Entropy values are based on a 1 M standard state. The asterisk denotes symmetry-corrected quantities. Symmetry numbers were chosen as follows 18 for the n-alkanes, cis-3-hexene, dibuthyl sulphide, diethyl ether, and diethyl amine 2n for the cycloalkanes and 2 for all of the remaining ring compounds 3 for the alkanols, alkanethiols and alkyl amines 9 for the methyl alkyl sulphides... 

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. 

For a Gas. The procedure for the calculation of the entropy of a gas in its standard state is substantially the same as the that for a solid or liquid except for two factors. If the heat capacity data have been obtained at a pressure of 1 atm (101.325 kPa), the resultant value of Sjj, is appropriate for that pressure and must be corrected to the standard state pressure of 1 bar (0.1 MPa). This correction is given by... 

We have seen in chapter 2 that the heat capacity at constant P is of fundamental importance in the calculation of the Gibbs free energy, performed by starting from the standard state enthalpy and entropy values... 

Standard state entropy values and Maier-Kelley coefficients of heat capacity at constant P, with respective T limits of validity, are listed for the same components in table 5.13. The adopted polynomial expansion is the Haas-Fisher form ... 

These parameters (AG, A//, and A5 ) differ slightly from normal standard parameters in that the contribution of motion along the reaction coordinate toward the transition state is not included. The values are the difference in free energy, enthalpy, and entropy between 1 mole of activated complex and 1 mole of each reactant, all substances being at their standard-state concentrations (usually 1 M). 

Chemists have found it possible to assign a numerical quantity for the entropy of each substance. When measured at 25° C and 1 atm, these are called standard entropies. Table l4-4 lists 12 such values, symbolized by S° where the superscript denotes the standard state. 

The entropy change in a process is given by eqn. (14) and it follows that entropies can be assigned to individual substances. As entropy is a state function, its value will depend on the state of the substance and, with the aid of eqn. (14), the entropy difference between any two states can be calculated. The third law enables a zero to be fixed for the entropy scale and there are tables [5—9] which give the entropies of many substances in their standard states at the reference temperature of 298 K. As long as there is no change of phase, the entropy at any other temperature can be calculated using... 

Barrer (3) makes similar calculations for the entropies of occlusion of substances by zeolites and reaches the conclusion that the adsorbed material is devoid of translational freedom. However, he uses a volume, area or length of unity when considering the partition function for translation of the adsorbed molecules in the cases where they are assumed to be capable of translation in three, two or one dimensions. His entropies are given for the standard state of 6 = 0.5, and the volume, area or length associated with the space available to the adsorbed molecules should be of molecular dimensions, v = 125 X 10-24 cc., a = 25 X 10-16 cm.2 and l = 5 X 10-8 cm. When these values are introduced into his calculations the entropies in column four of Table II of his paper come much closer together, as is shown in Table I. The experimental values for different substances range from zero to —7 cals./deg. mole or entropy units, and so further examination is required in each case to decide... 

The experimental entropies of adsorption were calculated after obtaining the free energies of adsorption at 0 = /% from the gas pressure in equilibrium with half the amount of adsorbate required to form the monolayer. The same principles were used to obtain the figure for the entropy of adsorption of O2 on unreduced steel. The values for carbon tetrachloride were taken directly from Foster s paper (4). The results for adsorption in chabazite were obtained from the work of Barrer and Ibbitson (15) with the slight modification needed to allow for the different standard states in the two phases used by them. The figures in the last column... 

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. 

The translational partition function is a function of both temperature and volume. However, none of the other partition functions have a volume dependence. It is thus convenient to eliminate the volume dependence of 5trans by agreeing to report values that use exclusively some volume that has been agreed upon by convention. The choices of the numerical value of V and its associated units define a standard state (or, more accurately, they contribute to an overall definition that may be considerably more detailed, as described further below). The most typical standard state used in theoretical calculations of entropies of translation is the volume occupied by one mole of ideal gas at 298 K and 1 atm pressure, namely, y° = 24.5 L. 

AS0 is the change in entropy (entropy of products minus entropy of reactants) when all species are in their standard states. The positive value of AS° indicates that a mole of K +(aq) plus a mole of Cl (aq) is more disordered than a mole of KCI(.v). For Reaction 6-3, AS° = —130.4 J/(K-mol) at 25°C. The aqueous ions are less disordered than gaseous HC1. 

If the elements are liquid in the standard state specified by the formation reaction, the Neumann-Kopp rule (115) suggests that ACp = 0. For the standard formation reaction in which Kn = 0 at the compound melting temperature, the standard entropy of formation can be obtained from the temperature derivative of AGf°[ij] or, often more accurately, from a combination of values of AGf°[ij, Tmij] and AHf°[ij, Tmij]. When Kn = 1 at TmiJ , the value of the natural standard entropy of formation, A Sf°[ij, Tmij], must be corrected as follows ... 

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