Equilibrium Constants of Reactions

We use a different measure of concentration when writing expressions for the equilibrium constants of reactions that involve species other than gases. Thus, for a species J that forms an ideal solution in a liquid solvent, the partial pressure in the expression for K is replaced by the molarity fjl relative to the standard molarity c° = 1 mol-L 1. Although K should be written in terms of the dimensionless ratio UJ/c°, it is common practice to write K in terms of [J] alone and to interpret each [JJ as the molarity with the units struck out. It has been found empirically, and is justified by thermodynamics, that pure liquids or solids should not appear in K. So, even though CaC03(s) and CaO(s) occur in the equilibrium... 

The symbols kf and kd are the rate constants for the formation and dissociation of the complex. The equilibrium constant of reaction (5.6.17) is given by the relationship... 

KP Equilibrium constant of reaction based on partial pressure in the vapor phase (-)... 

Worked Example 4.15 The isomerization of 1-butene (X) to form frans-2-butene (XI). The equilibrium constants of reaction are given below. Determine the enthalpy of reaction AH using a suitable graphical method. 

The [RPm+] can be most easily ascertained if the initiation efficiency is unity (no side-reactions) and if the [RPm+] is constant (termination rate Vt = 0) and equal to the nominal, analytical, concentration [Int]0 of the initiator this means (a) that the equilibrium constant of reactions such as (iii) should be effectively zero,... 

Equation 14.28 would be the correct one to evaluate the equilibrium constant of reaction 14.21 at each temperature. However, instead of using this equation, Oldani and Bor calculated the equilibrium constant at each temperature from... 

Activity ceofficients, surface and absorption effects, equilibrium constants of reactions... 

Isotopes of hydrogen. Three isotopes of hydrogen are known H, 2H (deuterium or D), 3H (tritium or T). Isotope effects are greater for hydrogen than for any other elements (and this may by a justification for the different names), but practically the chemical properties of H, D and T are nearly identical except in matters such as rates and equilibrium constants of reactions (see Tables 5.1a and 5.1b). Molecular H2 and D2 have two forms, ortho and para forms in which the nuclear spins are aligned or opposed, respectively. This results in very slight differences in bulk physical properties the two forms can be separated by gas chromatography. 

Polymer chemistry shows that the larger the various polymers become, the more their reactivity becomes independent of the length of the polymer chains. This fact, known as the principle of equal reactivity of cocondensing functional groups, has been verified in fused polyphosphate systems (which, for several properties, may be considered as analogous to silicate melts cf Fraser, 1977) with polymeric chains longer than 3 units (Meadowcroft and Richardson, 1965 Cripps-Clark et ah, 1974). Assuming this principle to be valid, the equilibrium constant of reaction 6.4 ... 

We can calculate the equilibrium constant of reaction 8.230 under any given P-T condition by computing the standard molal Gibbs free energy values of the various components at the P-T of interest—i.e.,... 

Equilibrium constants. The estimation of aromaticity may be made on the basis of equilibrium constants of reactions in which one of the interconverting forms contains a cyclic system of conjugated bonds. 

Figure 2-8 The equilibrium constant of Reaction 2-79 as a function of temperature in InK versus lOOO/T plot. The rough straight line means that the standard state enthalpy change of Reaction 2-79 is constant. Solid circles are 1-atm data from Zhang et al. (1997a) and open circles are 500-MPa data from Zhang (unpublished data).

Fig. 4. Equilibrium constant of reaction (1) for mechanism B in the carbon-carbon dioxide reaction as a function of temperature. [After S. Ergun, J. Phys. Chem. 60, 480 (1956).]...

In these relations, Ki denotes the equilibrium constant of reaction step i. For the numerical evaluation of the model, it is assumed that the backward reaction of step lb has the same transition state as the transition state for the re-desorption of A2 in Model 1, and that the entropy of the molecular precursor on the surface is negligible. The results are shown in Figure 4.37. It is observed that the model predicts that catalysts of much larger reactivity (more negative AEt) will be optimal for reactions where the diatomic molecule is strongly bound to the surface before the dissociation. 

The thermodynamic equilibrium constant of reaction A + B C + D is defined as follows ... 

Since the equilibrium constant of reaction 15.19 is 0.93, purple solid iodine is significantly more soluble in aqueous iodide solutions than in pure water. For dilute solutions, however, this can be ignored, as can a similar reaction involving chlorine and chloride in connection with reaction 15.7. Finally, we should remind ourselves that we have assumed that all the activity coefficients are unity (although here again the discrepancy so introduced can be ignored for simplicity). 

The equilibrium constant of reaction (16) depends on the electronic character of the ligand as shown in Fig. 1. More electronegative ligands [as indicated by increasing vc0 from Ni(CO)3L] give smaller values of log K. 

Denoting, as before, equilibrium constant of reaction (272) as K, we have,... 

Rate constants, k+ and k, are related to the equilibrium constant of reaction (356) by... 

Three approaches were used to estimate the equilibrium constant of reaction (1), Ki, at elevated temperatures (1) an equation derived by Helgeson (15) valid to 200°C (2) free energy of formation data to 200°C for As(IH)-As(V) species in Naumov et al. (16) and (3) the Criss and Cobble (17-18) correspondence principle approach, applicable to 250°C. The effect of increasing temperature on the stability fields of As(IH)-As(V) species is illustrated in an Eh-pH diagram in Figure 2. The pressure dependence of Ki was not determined, but is assumed to be within the uncertainty of the elevated temperature Ki estimates. 

Accordingly, the equilibrium constant of reaction (4) is given by a quotient of symmetry numbers (a). 

An equilibrium problem related to the kinetic Scheme (143) is presented by the basicity constants of anions (i.e. equilibrium constants of reactions of the type of (152))... 

---