Spectroscopic entropy

Conventional Partial Molal Entropy of (H30)+ and (OH)-. Let us now consider the partial molal entropy for the (1I30)+ ion and the (OH)- ion. If we wish to add an (HsO)+ ion to water, this may be done in two steps we first add an H2O molecule to the liquid, and then add a proton to this molecule. The entropy of liquid water at 25°C is 16.75 cal/deg/mole. This value may be obtained (1) from the low temperature calorimetric data of Giauque and Stout,1 combined with the zero point entropy predicted by Pauling, or (2) from the spectroscopic entropy of steam loss the entropy of vaporization. 2 Values obtained by the two methods agree within 0.01 cal/deg. 

The entropy, S , of carbonyl difluoride gas at the normal boiling temperature was found from experimental data to be 238.9 0.6 J moP [1580]. The spectroscopic entropy of 239.5 J moP K was calculated by statistical methods from the moments of inertia and the fundamental vibrational frequency assignments [1580], The spectroscopic entropy at 188.58 K is made up of the following contributions [1580] ... 

The agreement between the calorimetric and spectroscopic entropy signifies the absence of any residual entropy of randomness in the solid. 

It is known that the calorimetrically measured entropy is less than the entropy obtained from the spectroscopic data by 0.81 e.u. This is due to the residual entropy. The calculated entropy of liquid is compared with the spectroscopic entropy which may be evaluated from the difference between the spectroscopic entropy of gas and the entropy of vaporization. 

Using the coordinates of special geometries, minima, and saddle points, together with the nearby values of potential energy, you can calculate spectroscopic properties and macroscopic therm ody-riatriic and kinetic parameters, sncfi as enthalpies, entropies, and thermal rate constants. HyperChem can provide the geometries and energy values for many of these ealeulatiori s. 

The entropy value of gaseous HCl is a sum of contributions from the various transitions summarized in Table 4. Independent calculations based on the spectroscopic data of H Cl and H Cl separately, show the entropy of HCl at 298 K to be 186.686 and 187.372 J/(mol K) (44.619 and 44.783 cal/(mol K), respectively. The low temperature (rhombic) phase is ferroelectric (6). SoHd hydrogen chloride consists of hydrogen-bonded molecular crystals consisting of zigzag chains having an angle of 93.5° (6). Proton nmr studies at low temperatures have also shown the existence of a dimer (HC1)2 (7). 

Thermodynamic parameters have been obtained from kinetic HNMR spectroscopic studies of the thermal decomposition of ethyl 2,7-di-to7-butyl-5-methylthiepin-4-carboxylaten and two 1-benzothiepin compounds.12 The activation parameters for sulfur extrusion are AH = 93.7 kJ mol - 1 and AS = — 112.6 J Kmol-1 (in [2H18]Decalin) for the thiepin derivative,11 and AH = 75.3 and 87.9 kJ mol1 and AS = —100.4 and —104.6J Kmol-1 (in [2Hs]toluene) for the benzothiepin compounds.12 The large negative activation entropy values are consistent with a high degree of order in the anticipated thianorcaradiene transition state of the sulfur extrusion reaction. 

Initial protonation of iron in protodesilylation of trimethylsilylferrocene was not, however, favoured as a mechanism by Marr and Webster689, who measured rates by the spectroscopic method using hydrochloric acid in 20 vol. % aqueous methanol (Table 235) and found that the rate of desilylation of the ferrocene compound was little more than that for the 4-methoxyphenyl and 2,4-dimethyl compounds. The similarity of the spread of rates in the different media and the similar activation energies and entropies were considered as evidence that the transition states for reaction of all three compounds were similar. The lower activation energy obtained for the 4-methoxyphenyl relative to the ferrocene compound may arise from the different media involved the difference in entropy seems, however, to be rather larger than one might have expected even allowing for the solvent differences. 

The contribution of this lack of regularity to the entropy of ice is thus R In 3/2 = 0.805 E. U. The observed entropy discrepancy of ice at low temperatures is 0.87 E. U., obtained by subtracting the entropy difference of ice at very low temperatures and water vapor at standard conditions, for which the value 44.23 E. U. has been calculated from thermal data by Giauque and Ashley,7 from the spectroscopic value 45.101 E. U. for the entropy of water vapor given by Gordon.8 The agreement in the experimental and theoretical entropy values provides strong support of the postulated structure of ice.9... 

Quite similar equations can be formulated for AG and AH by use of the partition function f of the activated complex. It follows from equations (6) and (7) that AEp can only be evaluated if the partition functions and AEz are available from spectroscopic data or heat capacity measurements. However, if AG = AH, the entropy change AS equals zero, and if AEz also equal to zero, either AG or AH can then be identified with the potential energy change. If... 

The entropy difference A5tot between the HS and the LS states of an iron(II) SCO complex is the driving force for thermally induced spin transition [97], About one quarter of AStot is due to the multiplicity of the HS state, whereas the remaining three quarters are due to a shift of vibrational frequencies upon SCO. The part that arises from the spin multiplicity can easily be calculated. However, the vibrational contribution AS ib is less readily accessible, either experimentally or theoretically, because the vibrational spectrum of a SCO complex, such as [Fe(phen)2(NCS)2] (with 147 normal modes for the free molecule) is rather complex. Therefore, a reasonably complete assignment of modes can be achieved only by a combination of complementary spectroscopic techniques in conjunction with appropriate calculations. 

The interaction between 4-(4-hydroxybut-2-ynyloxy)-3-(phenylsulfonyl)-l,2,5-oxadiazole-2-oxide 16 and bovine serum albumin (BSA) was studied by spectroscopic methods including fluorescence and UV-Vis absorption spectroscopy. The results indicate that molecules 16 bind with BSA forming 1 1 complex. Thermodynamic parameters, such as AH, AG, and A.Y, were calculated. The results indicate that the binding reaction is mainly entropy driven and hydrophobic forces play a major role in this reaction <2006CHJ1050>. 

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. 

Conventional absorptiometric and fluorimetric pH indicators show a shift of band positions in absorption and emission spectra between the protonated and deprotonated forms. This feature allows the spectroscopic measurement of the acid dissociation constant in the ground state, Ka, and also the evaluation of the dissociation constant in the excited state, Ka (Eq. (5.5)), from the Forster cycle under the assumption of equivalent entropies of reaction in the two states.<109 112)... 

A satisfactory explanation for this discrepancy was not available until the development of statistical thermodynamics with its methods of calculating entropies from spectroscopic data and the discovery of the existence of ortho- and parahydrogen. It then was found that the major portion of the deviation observed between Equations (11.24) and (11.25) is from the failure to obtain a tme equilibrium between these two forms of H2 molecules (which differ in their nuclear spins) during thermal measurements at very low temperatures (Fig. 11.4). If true equilibrium were established at all times, more parahydrogen would be formed as the temperature is lowered, and at 0 K, all the hydrogen molecules would be in the... 

With the development of statistical thermodynamics and the calculations of the entropies of many substances from spectroscopic data, several other substances in addition to hydrogen have been found to have values of molar entropies that disagree with those calculated from thermal data alone [13] (Table 11.1). The discrepancies can be accounted for on the assumption that even near absolute zero not all molecules are in the same state and that tme equilibrium has not been attained. For CO, COCI2, N2O, NO, and CIO3F, the close similarity in the sizes of the atoms makes different... 

A few typical values of molar entropies have been assembled in Tables 11.2 through 11.5, with a separate table for each database. Data obtained from spectroscopic studies have been included even though the methods used in their calculations... 

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