Equilibrium constant dependence

We can see from Table 9.2 that the equilibrium constant depends on the temperature. For an exothermic reaction, the formation of products is found experimentally to be favored by lowering the temperature. Conversely, for an endothermic reaction, the products are favored by an increase in temperature. 

A catalyst speeds up both the forward and the reverse reactions by the same amount. Therefore, the dynamic equilibrium is unaffected. The thermodynamic justification of this observation is based on the fact that the equilibrium constant depends only on the temperature and the value of AGr°. A standard Gibbs free energy of reaction depends only on the identities of the reactants and products and is independent of the rate of the reaction or the presence of any substances that do not appear in the overall chemical equation for the reaction. 

Given any two of the four quantities EC, Aik, pH, Pco,/ the other two can always be calculated provided appropriate equilibrium constants are available (the equilibrium constants depend on temperature, salinity and pressure). Hydrogen ion concentration, for example, be calculated from Aik and EC with the equation... 

In addition to defined standard conditions and a reference potential, tabulated half-reactions have a defined reference direction. As the double arrow in the previous equation indicates, E ° values for half-reactions refer to electrode equilibria. Just as the value of an equilibrium constant depends on the direction in which the equilibrium reaction is written, the values of S ° depend on whether electrons are reactants or products. For half-reactions, the conventional reference direction is reduction, with electrons always appearing as reactants. Thus, each tabulated E ° value for a half-reaction is a standard reduction potential. 

The ionization of water is so important in the study of aqueous equilibria that the equilibrium constant is given the special symbol, Kw. It can be seen that, Kw, like all equilibrium constants, depends on temperature. Since Kw is larger (the forward reaction is encouraged) at higher temperatures, the forward reaction must consume heat, so the ionization of water must be endothermic. 

Condensation reactions are conveniently written as carbanion reactions, and yet it is clear that the metallic cation is important too. For example, sodium and lithium give quite different results in the condensation of acetophenone and tert-butyl acetate.422 The various rate and equilibrium constants depend on the nature of the associated metal. Lithium, zinc, and magnesium, which give the aldol condens-... 

Primary steric effects are due to repulsions between electrons in valence orbitals on atoms which are not bonded to each other. They are believed to result from the interpenetration of occupied orbitals on one atom by electrons on the other resulting in a violation of the Pauli exclusion principle. All steric interactions raise the energy of the system in which they occur. In terms of their effect on chemical reactivity, they may either decrease or increase a rate or equilibrium constant depending on whether steric interactions are greater in the reactant or in the product (equilibria) or transition state (rate). 

The reactions involved are unimolecular, and the cyclohexenyl derivative 3 undergoes solely the spontaneous heterolysis while both spontaneous heterolysis and ligand coupling occur with the iodane 14. The relative contributions of the two reactions of 14 depend on the solvent polarity. The results summarized in Table I show that the iodonium ion and the counteranion are in equilibrium with the hypervalent adduct, X3-iodane. The equilibrium constants depend on the identity of the anion and the solvent employed, and the iodane is less reactive than the free iodonium ion as the k /k2 raios demonstrate. Spontaneous heterolysis of 3 occurs more than 100 times as fast as th t of the adduct 14 as observed in methanol the leaving ability of the iodonid group is lowered by association by more than 100 times. 

No general discussion of the multitude of behaviour patterns, especially as regards dependence on concentration of catalyst, or of components of a syncatalyst, can be profitable at this stage. As for the termination reactions - our special concern here - this kinetic pattern implies that Vt is of first order, Vt of zero order, with respect to monomer. This means that k3 or k4 contain a term k iplky, they may also contain one or more equilibrium constants - depending on the nature of the catalytic system. 

These equations show that the equilibrium constants depend on r. All three cases correspond to the situation expressed in Eqs. (26)-(29) of our study on particle distribution in microporous materials [16], This means that the r dependence of the equilibrium constants 10°, and can be described by the same formula ... 

Please realize that the effect of temperature on the equilibrium constant depends on which of the two opposing reactions is exothermic and on which is endothermic. You must have information on the heat of a reaction before you can apply Le Chateliers principle to judge how temperature alters the equilibrium. 

The equilibrium constant depends on the temperature at which a reaction takes place, but at any given temperature, it is independent of pressure. If the standard enthalpies of the reactants and products of a reaction are known, the equilibrium constant for the reaction at a temperature other than that of the standard state may be calculated using the van t Hoff equation, i.e. 

The point of discussing free energy is to relate the equilibrium constant to the energetics (AH° and AS°) of a reaction. The equilibrium constant depends on AG° in the following manner ... 

The form of the equilibrium constant expression and the numerical value of the equilibrium constant depend on the form of the balanced chemical equation. 

In general, the temperature dependence of the equilibrium constant depends on the sign of A H° for the reaction. 

The equation Kc = kf/kr also helps explain why equilibrium constants depend on temperature. Recall from Section 12.10 that rate constants increase as the temperature increases, in accord with the Arrhenius equation k = Ae E RT. In general, the forward and reverse reactions have different values of the activation energy, so kf and kT increase by different amounts as the temperature increases. The ratio kf/kT = Kc is therefore temperature-dependent. For an exothermic reaction, which has AE = Ea(forward) — Ea(reverse) < 0, Ea(reverse) is greater than Ea(forward). Consequently, kT increases by more than kf increases as the temperature increases, and so Kc = kt/kr for an exothermic reaction decreases as the temperature increases. Conversely, Kc for an endothermic reaction increases as the temperature increases. 

The copolymerization equation is valid if all propagation steps are irreversible. If reversibility occurs, a more complex equation can be derived. If the equilibrium constants depend on the length of the monomer sequence (penultimate effect), further changes must be introduced into the equations. Where the polymerization is subjected to an equilibrium, a-methylstyrene was chosen as monomer. The polymerization was carried out by radical initiation. With methyl methacrylate as comonomer the equilibrium constants are found to be independent of the sequence length. Between 100° and 150°C the reversibilities of the homopolymerization step of methyl methacrylate and of the alternating steps are taken into account. With acrylonitrile as comonomer the dependence of equilibrium constants on the length of sequence must be considered. 

The equilibrium constant depends on the value of the standard free energy change of a reaction ... 

The two forms may be distinguished from each other by the fact that aci-form absorbs bromine and gives characteristic colour reaction with ferric chloride. The equilibrium constant depends on the solvent used, and mainly on its basicity. Thus p- nitrophenylnitromethane contains 0.18% of aci-form in ethyl alcohol, 0.79% and 16% in aqueous methyl alcohol and pyridine respectively [59],... 

Standard enthalpies and entropies for the ketone to enol equilibrium have been determined from data obtained by the kinetic halogenation method (see Section 3) at 5, 15, 25 and 35°C. Since the keto-enol equilibrium constants depend on the absolute rate constant arbitrarily chosen for the diffusion-controlled halogen addition to the enol, only the differences in from one ketone to another must be considered... 

Ke = equilibrium constant, dependent only on temperature (Gaskell, 1981), bar PSo2, Pq2, PSo3 = equilibrium partial pressures of S02, 02 and S03, bar. 

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