Equilibrium constant derivation

However, for most reactions in solution, a less rigorously defined practical equilibrium constant, derived from Equation 3.9 and expressed in terms of molar concentrations of species at equilibrium, may be sufficient, and we note that, defined in Equation 3.10, Kc is not dimensionless, but has units (unless [vx + Vy + ] = [va + + ]) ... 

CuOH+ + CuCl+ + CuGS+, and the overall equilibrium constant derived as shown ... 

Thus, the equilibrium constant derived from any of these reactions may be used to complete the definition of the system. Any of the three reactions of... 

The equilibrium constants derived from the 31P NMR spectra at temperatures below coalescence show that there is a considerable predominance of the axial conformer of 2-diphenylphosphinoyltetrahydrothiopyran (Table 26) which contrasts with the equatorial preference in the corresponding cyclohexane derivative. This result indicates a strong anomeric effect, estimated at 2.40 kcal mol-1. The corresponding data for the anancomeric cis and trans 4-/-butyl derivative at chemical equilibration are presented in Table 26. The large difference in AG° at 173 and 323 K is compatible with a significant entropy effect, calculated AS° = +4.8 0.7 cal K.mol-1, with... 

The second equilibrium constant derived from equation (7-3) is... 

The equilibrium constants derived from the two different experimental techniques are reasonably consistent considering the uncertainties inherent in the problems. Combination of these two sets of data leads to reliable 2nd law heat and entropy since the temperature ranges are different by 400 K. 

Therefore, readers attempting to use values of equilibrium constants derived from measurements of first moments should pay careful attention to the exact model and definitions used by authors. Not only are their units different (Kce is in dimension of and l[Pg.63]

Figure 3.31 Distribution of the equilibrium constants of adsorption calculated by means of the biToth model for 1-indanol on cellulose tribenzoate. The arrows indicate the equilibrium constants derived from the competitive bi-Langmuir isotherm. Reproduced with permission from A. Felinger, D. Zhou, G. Guiochon,. Chromatogr. A, 1005 (2003) 35.

These new equilibrium constants are independent of the properties of the solid and the amount of solid. Without this dependency, equilibrium constants derived from adsorption data on different samples of the same solid, and from adsorption data on different types of solids, can be compared directly. 

The surface complex equilibrium constants derived above can be used in calculating surface potentials. Figure 3 illustrates the surface potential from the SCF/DLM model (solid line) and C-potential evaluated from the mobility measurements using the treatment of Wiersema et. al. (26). The modeled potential values in tlie neighborhood of zero agree well with the ones derived experimentally. 

The n-pentyl radical is the largest alkyl radical for which Arrhenius parameters have been determined for a gas-phase metathetical reaction. Problems with volatility of reactants and dimer products are considerable in studies involving radicals larger than C4. The few results available for n-pentyl are given in Table 21. but in fact for only the first of the four reactions listed was there an experimental determination the other three results were obtained from data for the reverse reactions and the equilibrium constants derived from thermodynamic data. The selection of the rate coefficient for the n-pentyl dimerization reaction, upon which to base the absolute data for the reaction... 

In an intrinsic semiconductor, the number of holes win equal the number of electrons. However, the equilibrium equation also applies to doped semiconductors, and the equilibrium constant derived for a pure intrinsic semiconductor is valid for a doped sample of the same semiconductor. This is an extremely useful finding because it means that as the concentration of electrons in a semiconductor is increased by doping the concentration of holes decreases, and vice versa. Thus an n-type semiconductor can be changed to a p-type semiconductor simply by increasing the number of holes present, by appropriate doping, and vice versa. This possibility underlies the fabrication of semiconductor devices. This information is used in Sections 13.2.2 and 13.2.4. 

Values of as functions of temperature and composition can be analysed to give the equilibrium constant and enthalpy of formation of the assumed 1-1 complexing reaction. This procedure was first used most successfully by Andersen et al. in 1962 when applied to mixtures of 1-hydro-n-perfluoro-heptane with acetone. An intercomponent H-bond is formed in this system and, by combining experimental H s with equilibrium constants derived from n.m.r. measurements, it was found that the derived values of JTf were in close agreement with the experimental enthalpy of the reference system n-QFi + acetone in which only physical interactions were assumed to be present. 

You may wonder why equilibrium constants are reported without units. The equilibrium constant is related to the kinetics of a reaction as well as to the thermodynamics. (We explore this latter connection in Chapter 19.) Equilibrium constants derived from thermodynamic measurements are defined in terms of activities rather than concentrations or partial pressures. 

In real systems, activities are also ratios that have no units. Even though these activities may not be exactly numerically equal to concentrations, we will ignore the differences. All we need to know at this point is that activities have no units. As a result, the thermodynamic equilibrium constants derived from them also have no units. It is therefore common practice to write all types of equilibrium constants without units, a practice that we adhere to in this text. In more advanced chemistry courses, you may make more rigorous distinctions between concentrations and activities. 

The reaction equilibrium constant derived from thermodynamics as function of temperature is given by (Smith et al., 2010) ... 

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