Enthalpy prediction using equations

Phase equilibria calculations from both an Orye-type BWR and the Soave Redlich-Kwong equation of state were compared with data from an LNG plant. Both correlations showed good comparisons with the plant data and experimental data measured by P-V-T, Inc. The enthalpies predicted using the Soave Redlich-Kwong equation of state were poorer than those predicted using the Lee-Kesler correlation. 

A similar exercise can be made with other anions and cations, producing a list of relative values of standard enthalpies of formation, anchored on Af77°(H+, ao) = 0. This database is rather useful, because it allows the enthalpies of formation (equation 2.53) and the lattice enthalpies (equation 2.47) of many crystalline ionic salts to be predicted, since their solution enthalpies are usually easy to measure. 

The prediction of an enthalpy of vaporization by using equation 4 for both the liquid and gaseous phases of RX is discussed in Reference 37. 

In some cases experimental values of A,//°and AA are available, but in general these data are calculated using experimental or estimated values of the standard enthalpies of formation, AfH°, and entropies, S°, of all species involved in the reaction. It should also be pointed out that most organometallic reactions of interest occur in solution at temperatures not far from ambient, and that under these conditions the enthalpy term in Equation (6) is often dominant. Therefore, thermodynamic stability trends of organometallic compounds can frequently be analyzed solely in terms of A H°. When necessary, however, computational chemistry calculations or simple estimation schemes can normally be used to predict A, ° with an acceptable accuracy. " ... 

Sometimes the Born-Haber cycle is used in reverse to predict whether the enthalpy of formation of an unknown ionic compound is favorable or not For example, the theoretical enthalpy of formation of Nap2 can be predicted using the Born-Haber cycle as shown here. The fictional Nap2 molecule would dissociate into three ions one Na + and two F ions. The lattice energy of Nap2 was calculated using the Kapustinskii equation, where r(F ) = 133 pm and assuming that r(Na2+) r(Mg2+) = 72 pm. 

Figure 5.103 Experimental and predicted phase equilibrium data and excess enthalpies for alkanes with ketones predicted using modified UNIFAC respectively the group contribution equation of state VTPR modified UNIFAC, — group contribution equation of state VTPR.

When we know the equilibrium constant at one temperature and the enthalpy of the reaction, we can use Equation 5.50 to predict the equilibrium constant at another temperature. Or, by knowing the equilibrium constant at two temperatures, we can obtain the enthalpy of the reaction. 

The sign of AG can be used to predict the direction in which a reaction moves to reach its equilibrium position. A reaction is always thermodynamically favored when enthalpy decreases and entropy increases. Substituting the inequalities AH < 0 and AS > 0 into equation 6.2 shows that AG is negative when a reaction is thermodynamically favored. When AG is positive, the reaction is unfavorable as written (although the reverse reaction is favorable). Systems at equilibrium have a AG of zero. 

Theoretical studies of the relative stabilities of tautomers 14a and 14b were carried out mostly at the semiempirical level. AMI and PM3 calculations [98JST(T)249] of the relative stabilities carried out for a series of 4(5)-substituted imidazoles 14 (R = H, R = H, CH3, OH, F, NO2, Ph) are mostly in accord with the conclusion based on the Charton s equation. From the comparison of the electronic spectra of 4(5)-phenylimidazole 14 (R2 = Ph, R = R3 = H) and 2,4(5)-diphenylimidazole 14 (R = R = Ph, R = H) in ethanol with those calculated by using ir-electron PPP method for each of the tautomeric forms, it follows that calculations for type 14a tautomers match the experimentally observed spectra better (86ZC378). The AMI calculations [92JCS(P1)2779] of enthalpies of formation of 4(5)-aminoimidazole 14 (R = NH2, R = R = H) and 4(5)-nitroimidazole 14 (R = NO2, R = R = H) point to tautomers 14a and 14b respectively as being energetically preferred in the gas phase. Both predictions are in disagreement with expectations based on Charton s equation and the data related to basicity measurements (Table III). These inconsistencies may be... 

Lattice enthalpies of ionic solids can be predicted from several equations, which account for the coulombic interactions [45-47,49]. The estimates can then be used to derive the standard enthalpies of formation, by equation 2.47. However,... 

In Figure 10 are shown comparisons of the equation of state methods with the experimental data. The Lee-Kesler methods represent the data the best. Again, if the water acentric factor determined to best represent the pure steam enthalpy data is applied to the mixtures, further improvement is noted for the predictions by the Lee-Kesler method. Use of interaction constants within the Lee-Kesler, or other models, would undoubtedly provide even better representation of the data. 

The equation-of-state method, on the other hand, uses typically three parameters p, T andft/for each pure component and one binary interactioncparameter k,, which can often be taken as constant over a relatively wide temperature range. It represents the pure-component vapour pressure curve over a wider temperature range, includes the critical data p and T, and besides predicting the phase equilibrium also describes volume, enthalpy and entropy, thus enabling the heat of mixing, Joule-Thompson effect, adiabatic compressibility in the two-phase region etc. to be calculated. 

Equilibrium constants are also dependent on temperature and pressure. The temperature functionality can be predicted from a reaction s enthalpy and entropy changes. The effect of pressure can be significant when comparing speciation at the sea surface to that in the deep sea. Empirical equations are used to adapt equilibrium constants measured at 1 atm for high-pressure conditions. Equilibrium constants can be formulated from solute concentrations in units of molarity, molality, or even moles per kilogram of seawater. 

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