Equilibrium constants experimental determination

Association reactions can be characterized by equilibrium constants. Experimental determination of equilibrium constants for each step in an association reaction provides vital information about the properties of the associating system. In particular, the mode of association (e.g., monomer-dimer, monomer-tetramer, indefinite), and the strength of the association (that is, the degree to which various oligomers can exist at various total concentrations) can be obtained. The evaluation of equilibrium constants over a range of solution conditions (such as salt concentration and temperature) can be used to obtain information on the enthalpy and entropy of the various steps in the association and the types of bonds involved in the assembly process. Note that this information can be obtained in the complete absence of structural information, although, of course, any available structural information can be used to aid in the interpretation of the thermodynamic data. 

The mass balance equations can only be solved if the relation between Yi and X are known. We assumed a linear relation for the equilibrium curve. This relation is given by the equation Y, = Ke X, were Ke is a equilibrium constant experimentally determined. 

Hiickel theory [or the Giintelberg or Davies equation (Table 3.3)] may be used to convert the solubility equilibrium constant given at infinite dilution or at a specified / to an operational constant, valid for the ionic strength of interest. In seawater solubility equilibrium constants, experimentally determined in seawater, may be used. For example, the CaC03 calcite solubility in seawater of specified salinity may be defined by = [Ca " ] [CO f ], where [Caj ] and [C03f ] are the total concentrations of calcium and carbonate ions, for example,... 

The vapor-solid equilibrium constant is determined experimentally and is defined as the ratio of the mol fraction of the hydrocarbon component in gas on a water-free basis to the mol fraction of the hydrocarbon component in the solid on a water-free basis. That is ... 

This permits provisional calculation of the compositional dependence of the equilibrium constant and determination of provisional values of the solid phase activity coefficients (discussed below). The equilibrium constant and activity coefficients are termed provisional because it is not possible to determine if stoichiometric saturation has been established without independent knowledge of the compositional dependence of the equilibrium constant, such as would be provided from independent thermodynamic measurements. Using the provisional activity coefficient data we may compare the observed solid solution-aqueous solution compositions with those calculated at equilibrium. Agreement between the calculated and observed values confirms, within the experimental data uncertainties, the establishment of equilibrium. The true solid solution thermodynamic properties are then defined to be equal to the provisional values. 

In monoethanolamine solutions the unknown interaction parameters and equilibrium constants were determined by fitting the model to data for the three component systems CC +MEA+ O and H2S+MEA+H2O. The agreement of the fitted model with Che data was found to be good. The parameters obtained in this way were then used to predict the partial pressures of mixtures of HoS and CO2 over aqueous MEA solutions. The predictions were in good agreement with experimental data, except at the higher partial pressures. 

Each reaction has its own characteristic equilibrium constant, with a value that can be changed only by varying the temperature (Table 9.1). Whatever the initial composition of the reaction mixture, the composition adjusts so that at equilibrium it corresponds to the value of K for the reaction, because that composition guarantees that the reaction free energy is 0 and therefore that there is no further tendency to undergo change. It follows that, to determine the value of an equilibrium constant experimentally, we can take any convenient initial mixture of reagents for the reaction, allow the reaction to reach equilibrium at the temperature of interest, measure the concentrations of the reactants and products, and substitute them into the expression for K (Fig. 9.5). 

The question we now consider is how to tell whether a reaction mixture with an arbitrary concentration will have a tendency to form more products or to decompose into reactants. To answer this question, we first determine the equilibrium constant experimentally or calculate it from standard free energy data. Then we calculate the reaction quotient, Q, from the actual composition of the reaction mixture, as described in Section 9.2. To predict whether a particular mixture of reactants and products will tend to produce more products or more reactants, we compare Q with K ... 

The righthand side of Equation 5.16 is the same as that given in Equation 5.7 above for the Langmuir adsorption model, with Ka = kjkd. The experimental significance of Equation 5.16 is that measuring any two factors (adsorption rate, desorption rate, or equilibrium constant) uniquely determines the third. 

It is evident, therefore, from equations (17) and (18), that the equilibrium constant depends on the difference of the standard potentials of the interacting systems if the equilibrium constant were determined experimentally it would be possible to calculate the difference of standard potentials, exactly as in the case of the replacement of one metal by another (cf. p. 254). Alternatively, if the difference in standard potentials is known, the equilibrium constant can be evaluated. 

Adsorption and desorption equilibrium constants are determined in different soils. The route and rate of degradation in water, sediments, and soil is studied under aerobic, anaerobic, and photolysis conditions and at different temperatures in the laboratory under standardized conditions. If the experimental results show that there is a risk for leaching, semi-field and field studies become necessary. Lysimeter is the name of a set-up, in which intact soil cores (e.g., 1-m diameter and... 

This is one of the most important equations in chemical thermodynamics it shows that the equilibrium constant is determined entirely by the standard free energy change. At the same time it provides another experimental method of determining standard free energies. 

The determination of more comprehensive coking mechanisms and rate equations requires simultaneous treatment of all experimental data to enable all the relevant parameters related to coking to be considered. After analysing the experimental data, numerical values of the rate and adsorption equilibrium constants were determined by statistical tests, and models were rejected if a negative constant was estimated at more than one temperature. It was found that the hyperbolic type of decay, as described in Equation (1), gives the best fit from the 9 models tested because it gives the least error from the sum of squares analysis [8],... 

These equilibrium constants were determined by a least-squares method and the uncertainty estimate is given at the 3a level. All experimental details are given in the publication and these values have been selected by the present review. In a previous pubhcation Maggio et al. [1967MAG/ROM] have determined the equihbiium constant for the protonation of N3 under the same conditions as in [1974MAG/ROM] and report login (X.6) = 4.78 for the reaction ... 

To conclude the derived values of log,o K° and their associated uncertainties are based only on the aqueous phase model and the experimental data, and not on the selected values or uncertainties of the AfG° IRT values of Th" or other auxiliary species used in the modelhng. This holds trae for all the other cases where values of equilibrium constants are determined directly from the experimental data. NONLIN-SIT is a comprehensive program that uses ion interaction parameters and chemical potentials of all of the species expected in a given system, but it may be regarded as a method to optimise equilibrium constants, even if it operates v/o AfG°/Rr values. 

Based on the electronic and NMR spectra, the equilibrium constants were determined for reactions (13.30)-( 13.32). The constants K[ and K l were determined experimentally ... 

The first moments of the two components of propranolol hydrochloride were plotted against the inverse superficial velocity of mobile phase in Figure 4. Straight lines were fitted to the experimental points. According to Equation 4, the equilibrium constants were determined from the slopes of the hnes, which were found to be 4.36 and 6.31 for (S)-propranolol hydrochloride and f/ j-propranolol hydrochloride, respectively. 

In determining the values of Ka use is made of the pronounced shift of the UV-vis absorption spectrum of 2.4 upon coordination to the catalytically active ions as is illustrated in Figure 2.4 ". The occurrence of an isosbestic point can be regarded as an indication that there are only two species in solution that contribute to the absorption spectrum free and coordinated dienophile. The exact method of determination of the equilibrium constants is described extensively in reference 75 and is summarised in the experimental section. Since equilibrium constants and rate constants depend on the ionic strength, from this point onward, all measurements have been performed at constant ionic strength of 2.00 M usir potassium nitrate as background electrolyte . 

The following experiments involve the experimental determination of equilibrium constants and, in some cases, demonstrate the importance of activity effects. 

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. 

As the titration begins, mostly HAc is present, plus some H and Ac in amounts that can be calculated (see the Example on page 45). Addition of a solution of NaOH allows hydroxide ions to neutralize any H present. Note that reaction (2) as written is strongly favored its apparent equilibrium constant is greater than lO As H is neutralized, more HAc dissociates to H and Ac. As further NaOH is added, the pH gradually increases as Ac accumulates at the expense of diminishing HAc and the neutralization of H. At the point where half of the HAc has been neutralized, that is, where 0.5 equivalent of OH has been added, the concentrations of HAc and Ac are equal and pH = pV, for HAc. Thus, we have an experimental method for determining the pV, values of weak electrolytes. These p V, values lie at the midpoint of their respective titration curves. After all of the acid has been neutralized (that is, when one equivalent of base has been added), the pH rises exponentially. 

Enthalpy changes for biochemical processes can be determined experimentally by measuring the heat absorbed (or given off) by the process in a calorimeter (Figure 3.2). Alternatively, for any process B at equilibrium, the standard-state enthalpy change for the process can be determined from the temperature dependence of the equilibrium constant ... 

One interesting problem frequently recurring in heterocyclic chemistry, particularly with respect to nitrogen heterocycles, is tautomeric equilibria. Too many methods are available for the elucidation of equilibrium positions and tautomeric equilibrium constants (Kj) to adequately review the whole question here. However, the Hammett equation provides one independent method this method has the advantage that it can be used to predict the equilibrium position and to estimate the equilibrium constant, even in cases where the equilibrium position is so far to one side or the other that experimental determination of the concentration of the minor component is impossible. The entire method will be illustrated using nicotinic acid as an example but is, of course, completely general. 

The formation of these structures is represented with the help of chemical equilibria. The equilibrium constants can be determined consistently with the help of experimental methods. 

The complexation of Pu(IV) with carbonate ions is investigated by solubility measurements of 238Pu02 in neutral to alkaline solutions containing sodium carbonate and bicarbonate. The total concentration of carbonate ions and pH are varied at the constant ionic strength (I = 1.0), in which the initial pH values are adjusted by altering the ratio of carbonate to bicarbonate ions. The oxidation state of dissolved species in equilibrium solutions are determined by absorption spectrophotometry and differential pulse polarography. The most stable oxidation state of Pu in carbonate solutions is found to be Pu(IV), which is present as hydroxocarbonate or carbonate species. The formation constants of these complexes are calculated on the basis of solubility data which are determined to be a function of two variable parameters the carbonate concentration and pH. The hydrolysis reactions of Pu(IV) in the present experimental system assessed by using the literature data are taken into account for calculation of the carbonate complexation. 

Values of the equilibrium constant K = [BrCl]2/([Br2][Cl2]) in the gaseous phase have been determined experimentally values were typically in the range 6.57-9, with 40-46 % dissociation at room temperature (ref. 2). The weak temperature dependence of the equilibrium constant indicates low heat of reaction indeed, it has been calculated from equilibrium data to be - 0.406 kcal/mole BrCl (ref. 2). 

Equation (7.28) may not provide a good fit for the equilibrium data if the equilibrium mixture is nonideal. Suppose that the proper form for Kkmetic is determined through extensive experimentation or by using thermodynamic correlations. It could be a version of Equation (7.28) with exponents different from the stoichiometric coefficients, or it may be a different functional form. Whatever the form, it is possible to force the reverse rate to be consistent with the equilibrium constant, and this is recommended whenever the reaction shows appreciable reversibility. 

Examples 7.12 and 7.13 treated the case where the kinetic equilibrium constant had been determined experimentally. The next two examples illustrate the case where the thermodynamic equilibrium constant is estimated from tabulated data. 

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