Third law method

Kinetic studies of chemical equilibrium (Reaction 4) have provided very accurate thermodynamic information about the series Me3 SiH +i (with n having values from 0 to 3). ° In particular, the rate constants 4 and k, obtained by time-resolved experiments, allow the determination of the reaction enthalpy (AHr) either by second or third law method. In Table 2 the DHfRsSi-H) values obtained by Equation (5) are reported. 

The need for entropy values is bypassed when the van t Hoff equation (d In K/dT) =AH/RT2 is used. This can be integrated, either assuming AH is temperature-independent, or by incorporating a specific heat-temperature variation. This is the so-called second law method which contrasts with the third law method. In the latter method, the standard enthalpy is obtained from each equilibrium constant using free-energy functions of all the species present, for example... 

Equilibrium constants involving each compound were evaluated using the partial pressures by the third law method. Accepting the heats of formation of WF5 and WF obtained from bomb calorimetry, the values for WF (n = 1 to 4) could be extracted by iterative fitting to partial pressure data. The W/02/F2 and W/S/F2 systems were also examined to give heats of formation of tungsten oxo- and thiofluorides. This experimentally simple technique yields thermodynamic data on high-temperature species inaccessible to conventional calorimetry. 

Statistical mechanics affords an accurate method to evaluate ArSP, provided that the necessary structural and spectroscopic parameters (moments of inertia, vibrational frequencies, electronic levels, and degeneracies) are known [1], As this computation implicitly assumes that the entropy of a perfect crystal is zero at the absolute zero, and this is one of the statements of the third law of thermodynamics, the procedure is called the third law method. 

It is generally agreed that the third law method yields more accurate values than the second law method because it does not require any assumption regarding the temperature variation of the reaction enthalpy and entropy. The usual procedure to obtain third law data is to calculate the reaction enthalpy and entropy for each experimental value of Kp and take the average of all the values derived for a given temperature. 

A general discussion of the second and third law methods, including their advantages and limitations relative to first law techniques, was presented in sections 2.9 and 2.10. Now, after a summary of that introduction, we examine some examples that apply the second law method to the thermochemical study of reactions in solution. Recall that the third law method is only practical for reactions in the gas phase. 

Both the second and third law methods rely on the experimental determination of equilibrium constants. As shown in section 2.9, the equilibrium constant (K) of a reaction is defined in terms of the activities (ar) of reactants and products ... 

Since this review was completed a paper by Coomber and Whittle4111 has appeared in which they measured the equilibrium constant for C2F6 plus Br2 with CF3Br between 621 and 722°C. From a third law method they deduced the enthalpy of reaction. When combined with other thermochemical data, this result led to D CF3—CF3 = 96.5+1.0 kcal/mole or = —321.7 kcal/mole. 

The vaporization enthalpy values were combined with the published values for the enthalpy of formation of EuC12(s) (33), enthalpy of sublimation of europium (34) and dissociation energy for chlorine (35) to give D9 EuCl2(g) = 209.g +2.7 kcal/gfw (D298 = 210.8 2.7) and 212.0 2.8 kcal/gfw (D298 = 213.0 + 2.8) by the second-and third-law methods, respectively. 

Another application of intermediate coupling calculations has been to use the calculated results to reevaluate dissociation energies derived using the third-law method and mass- spectral data. Balasubramanian and Pitzer have shown how this can be accomplished in their calculations on Sn2 and Pb2 (90). This method requires the molecular partition function, which can be written... 

A eiei is the number of atoms of element i in the crystalline substance and (j m (298.I5 is the standard molar entropy of element i in its thermodynamic reference state. This equation makes it possible to calculate Af5 ° for a species when Sm ° has been determined by the third law method. Then Af G° for the species in dilute aqueous solution can be calculated using equation 15.3-2. Measurements of pATs, pA gS, and enthalpies of dissociation make it possible to calculate Af G° and Af//° for the other species of a reactant that are significant in the pH range of interest (usually pH 5 to 9). When this can be done, the species properties of solutes in aqueous solution are obtained with respect to the elements in their reference states, just like other species in the NBS Tables (3). 

Use of the third law is not the only way to get large molecules of biochemical reactants into tables of species properties. If apparent equilibrium constants and heats of reaction can be determined for a pathway of reactions from smaller molecules (for which Af G° and Af H° are known with respect to the elements) to form the large molecule, then the properties of the species of the large molecule can be determined relative to the elements in their reference states. This method has its problems in that it is very difficult to determine apparent equilibrium constants greater than about 10 to 10 and the number of reactions in the path may be large and some of the reactants may not be readily available in pure form. Thus it is fortunate that the third law method is available. 

The enthalpies of the transitions involving vaporization and sublimation are evaluated from equilibrum data by the second- and third-law methods. When reliable calorimetric measurements are available, the adopted enthalpy of transition is usually based on them. 

The effects of such corrections may be of significance. It should be noted that the second law cannot be applied to a single observation, but the third-law method, which is described below, can be so used. The second-law method also can be applied when only relative values of the equilibrium constant are available, for example, from mass-spectroscop-ic intensity measurements. 

The third-law method is based on a knowledge of the absolute entropy of the reactants and products. It allows the calculation of a reaction enthalpy from each data point when the change in the Gibbs energy function for the reaction is known. The Gibbs energy function used here is defined as... 

The experimental data presented by Rawling and Toguri in the temperature range of 800 to 900 K have been analysed by the third-law method using the selected heat capacity functions for H2Se(g), H2(g) and Se(cr, I). The derived enthalpy of formation for H2Se(g) from this analysis is Af//°(H2Se, g, 298.15 K) = (29.5 1.5) kJ-mol. ... 

Enthalpy changes can additionally be evaluated according to the third-law method... 

Table 10. Wu [282] identified the molecules Li O and LijO for the first time and determined their enthalpies of atomization (see Table 10) according to the third-law method.

Farber et al. [304] determined the enthalpy of formation at 298 K of KBOjfg) according to the second- and third-law methods as — 672.8 + 10kJmol and — 672.4 + lOkJmol, respectively, thereby improving the value given in the JANAF tables [90]. 

Odoj and Hilpert [58] showed the incongruent vaporization of BaZr03(s) to BaO(g). They determined the enthalpy of formation of BaZr03(s) from the component oxides as AfH° = — 106 21 kJmol by evaluating the enthalpies of vaporization according to the second- and third-law methods. 

There is no basis for a revision of these values as follows from a critical assessment of the literature data (cf. Ref. 364). Plies [367] showed the existence of the molecules GeWO and GeW207 and determined enthalpies of dissociation by the second-law method (Table 16). The dissociation energies of(PbO) (g) (n = 2, 3, 4. .. 6) were determined for the first time by Drowart et al. [395]. They were redetermined by Semenikhin et al. [369] (Table 14) by the use of the second- and third-law methods. The data obtained by the two groups agree... 

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