Equilibrium constant calculating values using

Limited analytical window. The analytical windows of the different techniques available are smaller than that required to cover all the complexing sites of a humic substance. Moreover, average equilibrium constants calculated by using different techniques will give noncomparable values. 

Acid-base equilibrium constants have been used to calculate the a-values of azoles as substituents on an aromatic ring or on an aliphatic chain. An example of this last case is the determination of ct, values of 1- (acetic acids 740,741, and 721 (Table 11-5) (82KGS264). 

This expression is plotted in Figure 11.18 as flux as a function of feed pressure for different values of the equilibrium constant, K. In this example, at an equilibrium constant K of 0.01 atm-1, very little of carrier R reacts with permeant A even at a feed pressure of 10 atm, so the flux is low. As the equilibrium constant increases, the fraction of carrier reacting with permeant at the feed side of the membrane increases, so the flux increases. This result would suggest that, to achieve the maximum flux, a carrier with the highest possible equilibrium constant should be used. For example, the calculations shown in Figure 11.18 indicate a carrier with an equilibrium constant of 10 atm-1 or more. 

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. 

In the accompanying tables there are given values of equilibrium constants or equivalent constants for the reactions of formation of some complexes. The values of equilibrium constants must be used with some caution in making calculations. Thus for the reaction... 

We have seen that the equilibrium constant for a given reaction can be calculated from known equilibrium concentrations. Once we know the value of the equilibrium constant, we can use Equation (14.2) to calculate unknown equilibrium concentrations— remembering, of course, that the equilibrium constant has a constant value only if the temperature does not change. In general, the equilibrium constant helps us to predict the direction in which a reaction mixture will proceed to achieve equilibrium and to calculate the concentrations of reactants and products once equilibrium has been reached. These uses of the equilibrium constant will be explored in this section. 

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. 

Equations (0 and (m) can be used to calculate the equilibrium constant thru the use of either N or N. For samples with near-monodisperse molecular weight distribution both Eqs. (f) and (m) yield the same value for the equilibrium constant. This situation does not hold though, for polymer systems having polydisperse molecular weight distributions. Thus, the equilibrium constant results presented by Van Beylen and co-workers for polydisperse polystyrenes having the barium... 

For calculating the equilibrium constant we will use standard potentials free enthalpy values from the reference book. According to those, values of AZ°9g are equal (in kcal mole ) CaS0 -2H20 - 429.36, Ca - 132.35,... 

That oxidation-reduction potentials are related to equilibrium constants may be used to underscore the fact that they apply to (theoretically) reversible reactions. The oxidized member of any couple will reduce some of the reduced member of any other couple, provided a reaction mechanism exists. The potentials of the two couples permit an estimation only of the possible extent of the reaction nothing can be predicted about the rate, or indeed, whether the reaction will occur at all. In determining the extent of any reaction, actual concentrations of all reagents must be considered, since the actual equilibrium is important, not the equilibrium of an ideal 1 M solution that might be calculated from AE or AFo values. 

From measured values of the equilibrium constants the values of may be calculated by use of equation (4 18). If the temperature to which this calculation refers is, say, 1000 K, the result is denoted A/GJodo called the standard free mcrgy of formation of the par-... 

Equations (9.3.9) and (9.3.10) provide us with a means of calculating the equilibrium constant K(T) using the tabulated values of AG° [k]. If the activities are expressed in terms of partitfl pressures, we have Kp. Some examples are shown in Box 9.5. 

Guides to Writing the Equilibrium Constant Expression, Calculating the Value, Using the Equilibrium Constant, Calculating and Calculating Molar Solubility from Ksp have been updated and rewritten. 

Equilibrium constants are systematically used in general analytical chemistry. They are of huge importance. Their values permit us to calculate the concentrations of the reaction species, once the equilibria have been attained. Some equilibrium constants bear a particular name according to the kind of chemical reaction they quantify. For example,... 

Calculate the equilibrium constant for the reaction CO + 7O2 CO2 under standard state condihons at T = lOOOK using data in Table 6.1. Compare with the equilibrium constant calculated for the same temperature assuming that the heat capacities of the three substances vary linearly with temperature and using these values ... 

Calculating equilibrium constants The value of is a constant for a given reaction at a given temperature. A value greater than 1 indicates that products are favored at equilibrium. If is less than 1, reactants are favored. The equilibrium concentrations of the reactants and products may be used to calculate as shown in this example problem. 

Ihe allure of methods for calculating free energies and their associated thermod)mai values such as equilibrium constants has resulted in considerable interest in free ene calculations. A number of decisions must be made about the way that the calculatior performed. One obvious choice concerns the simulation method. In principle, eit Monte Carlo or molecular dynamics can be used in practice, molecular dynamics almost always used for systems where there is a significant degree of conformatio flexibility, whereas Monte Carlo can give very good results for small molecules which either rigid or have limited conformational freedom. 

The product is equal to the equilibrium constant X for the reaction shown in equation 30. It is generally considered that a salt is soluble if > 1. Thus sequestration or solubilization of moderate amounts of metal ion usually becomes practical as X. approaches or exceeds one. For smaller values of X the cost of the requited amount of chelating agent may be prohibitive. However, the dilution effect may allow economical sequestration, or solubilization of small amounts of deposits, at X values considerably less than one. In practical appHcations, calculations based on concentration equihbrium constants can be used as a guide for experimental studies that are usually necessary to determine the actual behavior of particular systems. 

The comparison of the experimental mean values with the theoretically calculated ones for individual tautomers (Section 4.04.1.5.1) (76AHC(S1)1) or conformers (Section 4.04.1.4.3) has been used in the literature to determine equilibrium constants. Thus, the experimental value for l,l -thiocarbonylbis(pyrazole) (40) is 3.19 D and the vector sums of the simple group moments after addition of the extra mesomeric moments are shown in Figure 8. From these values Carlsson and Sandstrom (6SACS1655) concluded that conformation (40b) exerts the largest influence. 

Usually rounded off from JANAF Thermochemical Tables, NSRDS-NBS-37, 1971 (1141 ppj- Equilibrium constants can he calculated hy combining AhJ values from Table 2-221, h-r— ho is from Table 2-222, and 5 values from the above, using the formula In kp = —AG/(RT), where AG = AhJ + hj — /i29s) T . 

These data can be used to obtain the value of the equilibrium constant at any temperature and this in turn can be used to calculate the degree of dissociation through the equation for the conceiiuation dependence of the constant on the two species for a single element, die monomer and the dimer, which coexist. Considering one mole of the diatomic species which dissociates to produce 2x moles of the monatomic gas, leaving (1 — jc) moles of the diatomic gas and producing a resultant total number of moles of (1 +jc) at a total pressure of P atmos, the equation for the equilibrium constant in terms of these conceiiU ations is... 

Using the average value for the equilibrium constant, the distribution concentration of the different components of a methanol water mixture were calculated for initial methanol concentrations ranging from zero to 100%v/v. The curves they obtained are shown in Figure 28. The molar refractivities of 11.88 is also in accordance with that expected since the molar refractivity s of water and methanol are 3.72 and 8.28 respectively. The refractive index of the associate of 1.3502 is, as would be expected, higher than that of either water or methanol. 

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