Equilibrium constant, K, equation

Reversibility falls in line with the fact that the ratio of the expressions of the two rate constants matches the expression of the equilibrium constant, K (equation 6),... 

Tt is possible tn define another equilibrium constant. K. (Equation 3.19), which does not include the artivity rnpffinVnts and hence will not he a frnp rnn-... 

The fifth form is the only one that is defined unambiguously in experimental terms. The relationship between the adsorption equilibrium constant K. [equation (31)] and the Henry s law constant Kh was derived earlier [equation (32)] ... 

Later on, the velocity of the reaction will tend towards zero as A i [P] and ki [S] approach the same value. At that moment, equilibrium is reached and the equilibrium constant K (equation 13) can be defined by applying these conditions to equation (11). 

Equilibrium constants,, for all possible dimerization reactions are calculated from the metastable, bound, and chemical contributions to the second virial coefficients, B , as given by Equations (6) and (7). The equilibrium constants, K calculated using Equation (3-15). 

The logarithm of the equilibrium constant, K,. for the chemical equation shown in Figure 3-8a for a substituted benzoic acid can be related to the logarithm of the... 

One of the fundamental equations of thermo dynamics concerns systems at equilibrium and relates the equilibrium constant K to the dif ference in standard free energy (A6°) between the products and the reactants... 

The equilibrium constant for equation 6.13 is K. Since equation 6.13 is obtained by adding together reactions 6.11 and 6.12, may also be expressed as the product of Ka for CH3COOH and Kb for CH3COO-. Thus, for a weak acid, HA, and its conjugate weak base, A-,... 

Taking known values for the molar refractivities of water and methanol, and again assuming a range of values for the equilibrium constant (k) and the refractive index (ni) of the methanol/water associate, the actual values that fit the equation for these... 

The following equation is used to calculate tlie chemical reaction equilibrium constant K at a temperature T. 

Many equilibrium calculations are accomplished using tlie plrase equilibrium constant K,. Tliis constant has been referred to in industry as a coiiiponential split factor, since it provides the ratio of the mole fractions of a component in two equilibrium pluises. The defining equation is... 

As pointed out earlier, the equilibrium constant of a system changes with temperature. The form of the equation relating K to T is a familiar one, similar to the Clausius-Clapeyron equation (Chapter 9) and the Arrhenius equation (Chapter 11). This one is called the van t Hoff equation, honoring Jacobus van t Hoff (1852-1911), who was the first to use the equilibrium constant, K. Coincidentally, van t Hoff was a good friend of Arrhenius. The equation is... 

The quantity Q that appears in this equation is the reaction quotient referred to in Chapter 12. It has the same mathematical form as the equilibrium constant, K the difference is that the terms that appear in Q are arbitrary, initial pressures or concentrations rather than equilibrium values. 

Thermodynamic quantities for a system may be determined from the van t Hoff equation Eq.(3), which defines the equilibrium constant, K, in terms of the reaction enthalpy, AH and the temperature, T. 

Since nitrobenzene is a much stronger base than alkyl halides, the concentration of RCI.AICI3 will be small and hence k i will be large and, therefore, much greater than k 2. Equation (180), therefore, reduces to a third-order expression which includes the equilibrium constant k jk i) of the first step and this accounts for the lower rates with 4-nitrobenzyl chloride since it is a poorer base than the 3,4-dichloro compound. 

Therefore, we must find a new equilibrium constant, K , that Is analogous to Ks. We have considered (21) several methods of evaluating the model parameters (the equation that gives Kjj, as a function of temperature) from the available data. 

The vaporization of a liquid can be treated as a special case of an equilibrium. How does the vapor pressure of a liquid vary with temperature Hint Devise a version of the van t Hoff equation that applies to vapor pressure by first writing the equilibrium constant K for vaporization. 

The equations which describe the variation with temperature of the equilibrium constant, K, for a chemical system and of the rate constant, ki, for a chemical reaction are well known. They are... 

The Brpnsted equations relate a rate eonstant k to an equilibrium constant K. In Chapter 6, we saw that the Marcus equation also relates a rate term (in that case AG ) to an equilibrium term AG°. When the Marcus treatment is applied to proton... 

Suppose that A is in equilibrium with an isomer B, which possesses the following energy levels with respect to the ground state of isomer A AE/2, 3A /4 and A . Derive an expression for the equilibrium constant K = [B]/[A] and calculate the limiting values of K at low and high temperature. Discuss the meaning of the obtained values. Hints use the following equations ... 

To understand the chemisorptive property of lr/ln/H-ZSM-5 in a comparison with that of ln/H-ZSM-5, the chemisorption data were analyzed in detail. The data shown in Fig. 3 are relatively well fitted to the Langmuir isotherm, as shown in Fig. 5. From these relations, the equilibrium constant (K) and the amount of NO2 adsorbed at saturation (Vo) were determined according to the following equations ... 

These equations show that whereas the kinetic coefficients of an individual reaction can assume any value, the coefficients of its forward and reverse process are always interrelated. The relation between the standard equilibrium potential EP and the rate constants and is analogous to the well-known physicochemical relation between equilibrium constant K and the rate constants of the forward and reverse process. 

As explained by Franks (1972), this again shows that the component balance equations, for the different components of the mixture, will thus have different time constants, which depend on the relative magnitudes of the equilibrium constants K and which again can lead to possible problems of numerical stiffness. 

Equation (22) indicates that the production formation rate is proportional to the hydrogen gas pressure. When the hydrogen gas pressure doubles, the product formation rate should be doubled. The product formation rate is inversely proportional to the equilibrium constant K. When the K value decreases, the product formation rate increases. 

Brown, see Cajander et al. (1960), developed a method which relates the equilibrium constant K to four parameters component, pressure, temperature, and the convergence pressure. The convergence pressure is the pressure at which all K values tend to 1. The Brown Kw equation is limited to low pressure and its use is generally restricted to vacuum... 

Most chemical reactions do not progress completely from reactants to products. Instead, the net reaction stops in the forward direction when equilibrium is established. Analysis of the contents of the reaction vessel would show a constant concentration of monomers and polymer once equilibrium is reached. This situation is actually a dynamic equilibrium, where the monomers are forming polymers at the same rate as the polymers depolymerize to monomer. Therefore, at equilibrium, the net concentrations of any one species remains constant. The amount of monomer converted into polymer will be defined by the equilibrium constant, K. This constant is the ratio of the concentration of the products to the reactants, with each concentration raised to the stoichiometric coefficients in the balanced equation. For Eq. 3.5 ... 

When the concentration of chloride ion was below 3 M, further aquation reactions from Tc(H20)ClJ to Tc(H20)2C14, etc. were observed. Similarly, aquation of hexabromotechnetate(IV) was studied (molar absorption coefficient, s445 nm = 5720 M "1 cm "1). The equilibrium constants K for Eq. (9) at different temperatures are summarized in Table 2. Analysis of the aquation rate gave the following equation ... 

Each differential equation contains a flow term identified by Q/V (flow rate/reactor volume) and also a reaction term which can be identified by a rate of reaction or equilibrium constant (k, K, k ). These reaction and equilibrium constants are functions of temperature which, in this study, was fixed. The viscosity dependence of the equilibrium constant (relating reactive species to total polymer) shown in Equations 6 and 7 was observed experimentally and is known as the Trommsdorf effect (6). Table I lists values and units of all parameters in Equations 1-7. 

In the analysis of kinetic data from reactions believed to be first-order in both directions, the equation that is most suitable for use depends on the pertinent equilibrium data available. Equations 5.1.17 and 5.1.11 are perhaps the most useful, but others may be more appropriate for use in some cases. The integrated forms permit one to determine the sum (kx + k x), while equilibrium data permit one to determine the equilibrium constant K = kl/k v Such information is sufficient to determine kx and /c x. 

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