Equilibrium constant calculating values

Examination of the NMR spectrum of thiane 3,3,5,5-d4 oxide enabled the estimation of the axial/equatorial equilibrium constant . The value was found to be 1.62 (at — 90 °C), corresponding to a free-energy difference of 0.175 kcal mol , which is in good agreement with field force calculations. ... 

Free energy changes and equilibrium constants calculated from the enthalpy and entropy values estimated by the group-contribution method generally are reliable only to the order of magnitude. For example, Andersen et al. [1] have found that their estimated enthalpies and entropies usually differ from experimental values [7]... 

As mentioned in Section 1.4.2, the oxygen partial pressure is controlled by changing the ratio of mixed gases, and the value of the pressure can be calculated, in principle, by the known equilibrium constants. The value... 

The realistic figures are Jco = 0.97 and = 0.03, and the large difference between the two pairs of y values comes from non-differentiation by the equilibrium constant calculation between the actual two-phase HjO product and an ideal gas ... 

Thermodynamic calculations are used to evaluate vapor-liquid equilibrium constants, enthalpy values, dew points, bubble points, and flashes. Established techniques simulate the heat exchangers and distillation columns, and handle convergence and optimization. 

The agreement between theory and experiment holds good for other gas reactions, and is not merely accidental. Another example is the dissociation of carbon dioxide according to the equation 2002 = 200 + 02- In the following table iCexp. is the degree of dissociation (per cent.) of CO2 at a total pressure of 1 atmosphere,t and log / cxp. is the equilibrium constant calculated from iCexp. The heat of reaction at the ordinary temperature (300° abs.) is 13600 cal., and Ncp = 2x8 — 2x7-7= — 5. The constant J" is calculated from the value of ajexp. at 1443°, viz. a = 2 5 X10 2. Thus... 

Green and Sugden (5), based on the studies of the positive ions in flames by mass spectrometry, prefer the value derived from the proton affinity of water obtained by Tal rose and Frankevitch, rather than the electron impact data. From the approximate equilibrium constant calculations for the reaction HCO (g) + H 0(g) = H 0 (g) + CO(g), Clifton (6) has also found that the heat of... 

For equilibrium constant calculations, this is reasonably good agreement with the value obtained from part (a), especially if one considers that will not be perfectly constant over so large a temperature range. 

The agreement between the values of kinetic parameters and the thermodynamics of the process. On the one hand, the activation energy for an elementary endothermic reaction cannot be less than the heat of reaction. On the other hand, if the data about rate constants for both direct and reverse reactions are available, their ratio should be equal to the equilibrium constant calculated independently from thermodynamic data for species participating in the reaction. 

Most tables of equilibrium constants list values for Kj, as obtained by extrapolation towards / — 0, but the spreadsheet calculation requires the uncorrected Ka s. Below we will indicate how to make the activity correction. 

From the known values of the acid-base constants for vanadium oxocompounds one can establish the relationship between different acid-base forms in the studied chloride melt over a wide range of pO. The corresponding dependence is presented in Fig. 1.2.9b. It is seen that in the case of Vv oxo-compounds more than two acid-base forms can coexist in a relatively wide pO range, which gives rise to additional errors in the equilibrium constant calculations. Nevertheless, in the given case this does not lead to an appreciable directed shift of the calculated values of the equilibrium constants, or to an increase of the confidence ranges for reactions (1.2.86) and (1.2.87). 

Since the experimental results hardly correspond to the stoichiometry of reaction (1.2.4) (they are characterized by a considerable shift of the value of the equilibrium constant calculated according to the equation mentioned). Besides the calculations according to the generally accepted equilibrium (1.2.4), the thermodynamic parameters were calculated for equilibrium (2.5.68), in which dimerized hydroxide ions take part. The results of the investigations in the molten KCl-LiCl eutectic at 400 and 500 °C are collectively displayed in Table 2.5.6. 

Equilibrium constant calculations are rather straightforward, but we must keep several things in mind. (1) The values in the equilibrium constant expression are the concentrations at equilibrium. (2) The equilibrium constant expression has no addition or subtraction within it. (3) All the substances involved in the equilibrium constant expression are in the same solution (or the same gas mixture), and so have the same volume. (4) Pure solids and liquids, and the solvents for dilute solutions, do not appear in the equilibrium constant expression. (5) The equilibrium constant expression is written for a specific equilibrium equation if we reverse the equation, the value of the new K is the reciprocal of the original one. 

The distribution of deuterium and hydrogen atoms among the three species of water is random, so that the equilibrium constant for this reaction has the value of 4.0. These assumptions are plausible, but are not subject to complete experimental confirmation because liquid HDO cannot be isolated, because it disproportionates into H2O and D2O. Values for the equilibrium constant calculated by statistical mechanics are around 3.8. 

The numerical values for the standard state heat of reaction A nW°(7 ) and the equilibrium constant calculated from these equations are plotted in Fig. 1. 

The values of the enthalpy obtained do not depend on the model chosen for the dimer, as shown by Lussan (19) in a comprehensive summary of the possible theoretical treatments of the NMR data. Lussan demonstrates the form of the equilibrium constant calculation in the case of (1) monomer-dimer (open or cyclic), (2) monomer-cyclic trimer, and (3) monomer-higher acyclic multimers in the two cases of (3a) all K s equal and (3b) ki for monomer-dimer equilibrium unique, k s for higher multimers all equal. He then takes the experimental curves for a number of alcohols in carbon tetrachloride and achieves a reasonable fit to the data up to 0.6 mole fraction by using one or the other of the theoretical relationships. In some cases two sets of theoretical points are plotted on the same graph as the experimental data both are a good fit in the low concentration region, up to 0.1 mole fraction. Above this concentration one or the other of the theoretical curves is much closer to the experimental curve. Lussan implies that hypothesis 3b may be a more accurate fit to the data in the more concentrated solutions. Methanol, ethanol, 2-methyl-2-propanol (tert-butyl alcohol) and 2,2,4-trimethyl-3-pentanol follow the curve for equilibrium 3a, while 2,2,4,4-tetramethyl-3-pentanol fits the monomer-dimer data. Lussan points out that the behavior of the latter alcohol fits in with that of two similar heavily substituted tertiary alcohols which have been found by infrared methods to form only dimers. 

Equilibrium constants calculated according to Equation 4i with values of Ra and Rn estimated as described in text... 

Apply Concepts Like all equilibrium constants, the value of varies with temperature. equals 2.92 X 10-15 at io°C, 1.00 X 10-14 t 25°C, and 2.92 x 10-14 at 4o°c. In light of this information, calculate and compare the pH values for pure water at these three temperatures. Based on your calculations, is it correct to say that the pH of pure water is always 7.0 Explain. 

The criterion of agreement to within 5 percent is arbitrary. However, in view of the variation in reported equilibrium constants (reported values for a single reaction usually vary by more than 5 percent) and because of the purpose for which the calculations are generally made, accuracy better than 5 percent is rarely needed or justified. 

The evaluation and checking of the objectivity of the results are to a certain extent facilitated by the fact that whereas the molar absorptivity values are dependent on the wavelength, the equilibrium constants naturally are not. Hence, comparison of the equilibrium constants calculated from the concentration dependence of the absorbances measured at the different wavelengths is of assistance in the calculation of the correct constants and correct molar absorptivities. When the real equilibrium data are known, the distribution curves describing the system can be calculated and from these one can read off directly how the concentrations of the various species in solution vary with the change of the analytical concentrations (cf., Figs 8.1 and 8.2). 

I o study the correlation between the composition of the solvent mixture and the equilibrium constants, the value of x was calculated in the following relation between the molar fraction of the dioxane (M) and the logarithms of the thermodynamic equilibrium constants (A) ... 

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