Equilibrium constant direction

In this scheme, M <1 and K equilibrium constants. Direct binding experiments have confirmed the generality of this scheme for nicotinic receptors. Thus, distinct conformational states govern the different temporal responses that ensue upon addition of a ligand to the nicotinic receptor. No direct energy input or covalent modification of the receptor channel is required. 

There are alternative methods for estimating the temperature dependence of the equilibrium constant. One can use Pitzer s theoretical approach to estimate activity coefficients, which will be discussed in the following section, for the constituents of a reaction (Eqs. 2.13 and 2.16) coupled with experimental measurements of the molalities to estimate activities and the equilibrium constant directly at various temperatures. Alternatively, one can estimate the temperature dependence with the theoretical equation... 

Experimental determinations made in terms of concentrations give concentration quotients which are non-ideal constants. Corrections for non-ideality are made in terms of the calculated ionic strength and the various Debye-Huckel expressions. However, emf experiments, including pH measurements, can sometimes furnish equilibrium constants directly in terms of activities, and as such these will be ideal equilibrium constants. 

The equilibrium constant at constant temperature is directly related to the maximum energy, called the free energy AG. which is obtainable from a reaction, the relationship being... 

The best-known equation of the type mentioned is, of course, Hammett s equation. It correlates, with considerable precision, rate and equilibrium constants for a large number of reactions occurring in the side chains of m- and p-substituted aromatic compounds, but fails badly for electrophilic substitution into the aromatic ring (except at wi-positions) and for certain reactions in side chains in which there is considerable mesomeric interaction between the side chain and the ring during the course of reaction. This failure arises because Hammett s original model reaction (the ionization of substituted benzoic acids) does not take account of the direct resonance interactions between a substituent and the site of reaction. This sort of interaction in the electrophilic substitutions of anisole is depicted in the following resonance structures, which show the transition state to be stabilized by direct resonance with the substituent ... 

We will use two useful relationships when working with equilibrium constants. First, if we reverse a reaction s direction, the equilibrium constant for the new reaction is simply the inverse of that for the original reaction. For example, the equilibrium constant for the reaction... 

Although not commonly used, thermometric titrations have one distinct advantage over methods based on the direct or indirect monitoring of plT. As discussed earlier, visual indicators and potentiometric titration curves are limited by the magnitude of the relevant equilibrium constants. For example, the titration of boric acid, ITaBOa, for which is 5.8 X 10 °, yields a poorly defined equivalence point (Figure 9.15a). The enthalpy of neutralization for boric acid with NaOlT, however, is only 23% less than that for a strong acid (-42.7 kj/mol... 

In general, esters having equilibrium constants below unity are not prepared by direct interaction of alcohol and acid in these cases, the acid anhydrides or acid chlorides are used, since the equiUbrium favors the ester product. 

Complex Clieinical-Reaction Equilibria When the composition of an equilibrium mixture is determined by a number of simultaneous reactions, calculations based on equilibrium constants become complex and tedious. A more direct procedure (and one suitable for general computer solution) is based on minimization of the total Gibbs energy G in accord with Eq. (4-271). The treatment here is... 

In the case of tire direct oxidation, the oxygen partial pressure must be greater than that at the Pb/PbO equilibrium, while in the process involving sodium-based salts, the oxygen pressure is less than this. The two equilibrium constants for the refining reactions... 

Kinetic data provide information only about the rate-determining step and steps preceding it. In the hypothetical reaction under consideration, the final step follows the rate-determining step, and because its rate will not affect the rate of the overall reaction, will not appear in the overall rate expression. The rate of the overall reaction is governed by the second step, which is the bottleneck in the process. The rate of this step is equal to A2 multiplied by the molar concentration of intermediate C, which may not be directly measurable. It is therefore necessary to express the rate in terms of the concentrations of reactants. In the case under consideration, this can be done by recognizing that [C] is related to [A] and [B] by an equilibrium constant ... 

The overall rate being measured is that of step 2, but there may be no means of directly measuring [ROH2+]. The concentration of the protonated intermediate ROH2+ can be expressed in terms of the concentration of the starting material by taking into consideration the equilibrium constant, which relates [ROH], [Br ], and [H+] ... 

The acidity of a lydrocarbon can be determined in an analogous way. If the electronic spectra of the neutral and anionic forms are sufficiently different, the concentrations of each can be determined directly, and the equilibrium constant for... 

In this mechanism, a complexation of the electrophile with the 7t-electron system of the aromatic ring is the first step. This species, called the 7t-complex, m or ms not be involved directly in the substitution mechanism. 7t-Complex formation is, in general, rapidly reversible, and in many cases the equilibrium constant is small. The 7t-complex is a donor-acceptor type complex, with the n electrons of the aromatic ring donating electron density to the electrophile. No position selectivity is associated with the 7t-complex. 

Table 4-1 lists some rate constants for acid-base reactions. A very simple yet powerful generalization can be made For normal acids, proton transfer in the thermodynamically favored direction is diffusion controlled. Normal acids are predominantly oxygen and nitrogen acids carbon acids do not fit this pattern. The thermodynamicEilly favored direction is that in which the conventionally written equilibrium constant is greater than unity this is readily established from the pK of the conjugate acid. Approximate values of rate constants in both directions can thus be estimated by assuming a typical diffusion-limited value in the favored direction (most reasonably by inspection of experimental results for closely related... 

The overall direction of the reaction will be determined by the relative concentrations of ATP, ADP, Cr, and CrP and the equilibrium constant for the reaction. The enzyme can be considered to have two sites for substrate (or product) binding an adenine nucleotide site, where ATP or ADP binds, and a creatine site, where Cr or CrP is bound. In such a mechanism, ATP and ADP compete for binding at their unique site, while Cr and CrP compete at the specific Cr-, CrP-binding site. Note that no modified enzyme form (E ), such as an E-PO4 intermediate, appears here. The reaction is characterized by rapid and reversible binary ES complex formation, followed by addition of the remaining substrate, and the rate-determining reaction taking place within the ternary complex. 

Every chemical reaction can go in either forward or reverse direction. Reactants can go forward to products, and products can revert to reactants. As you may remember from your general chemistry course, the position of the resulting chemical equilibrium is expressed by an equation in which /Cec], the equilibrium constant, is equal to the product concentrations multiplied together, divided by the reactant concentrations multiplied together, with each concentration raised to the power of its coefficient in the balanced equation. Eor the generalized reaction... 

The value of the equilibrium constant tells which side of the reaction arrow is energetically favored. If Keq is much larger than 1, then the product concentration term [C 4 [Dlrf is much larger than the reactant concentration term A " B, and the reaction proceeds as written from left to right. If Keq is near 1, appreciable amounts of both reactant and product are present at equilibrium. And if Koq is much smaller than l, the reaction does not take place as written but instead goes in the reverse direction, from right to left. 

Numerical values of equilibrium constants can be calculated if the partial pressures of products and reactants at equilibrium are known. Sometimes you will be given equilibrium partial pressures directly (Example 12.3). At other times you will be given the original partial pressures and the equilibrium partial pressure of one species (Example 12.4). In that case, the calculation of K is a bit more difficult, because you have to calculate the equilibrium partial pressures of all the species. 

The direction of the reaction may change, but the expression for the equilibrium constant does not... 

The form of the expression for Q, known as the reaction quotient, is the same as that for the equilibrium constant, K. The difference is that the partial pressures that appear in Q are those that apply at a particular moment, not necessarily when the system is at equilibrium. By comparing the numerical value of Q with that of K, it is possible to decide in which direction the system will move to achieve equilibrium. 

These reactions have very large equilibrium constants, as we will see in Section 14.3, and so go virtually to completion. As a result, the added H+ or OH- ions are consumed and do not directly affect the pH. This is the principle of buffer action, which explains why a buffered solution is much more resistant to a change in pH than one that is unbuffered (Figure 14.1, p. 384). 

Although these potential barriers are only of the order of a few thousand calories in most circumstances, there are a number of properties which are markedly influenced by them. Thus the heat capacity, entropy, and equilibrium constants contain an appreciable contribution from the hindered rotation. Since statistical mechanics combined with molecular structural data has provided such a highly successful method of calculating heat capacities and entropies for simpler molecules, it is natural to try to extend the method to molecules containing the possibility of hindered rotation. Much effort has been expended in this direction, with the result that a wide class of molecules can be dealt with, provided that the height of the potential barrier is known from empirical sources. A great many molecules of considerable industrial importance are included in this category, notably the simpler hydrocarbons. 

The value of T and the propagation/depropagation equilibrium constant (A e[ ) can be measured directly by studying the equilibrium between monomer and polymer or they can be calculated at various temperatures given values of AHp and ASP using cq. 11 and 12 respectively. 

Equations (9.7) and (9.8) define K, the equilibrium constant for the reaction.b It is sometimes referred to as the thermodynamic equilibrium constant. As we shall see, this ratio of activities can be related to ratios of pressure or concentration which, themselves, are sometimes called equilibrium constants. But K, as defined in equations (9.7) and (9.8), is the fundamental form that is directly related to the free energy change of the reaction. 

The Effect of Pressure With the addition of one restricting condition, we like the simple and direct statement of Rossini1 in describing the effect of pressure on the equilibrium constant ... 

It is important to note that, for any given temperature, the [thermodynamic] equilibrium constant is directly related to the standard change in free energy. Since, at any given temperature, the free energy in the standard state for each reactant and product, G°, is independent of the pressure, it follows that the standard change in free energy for the reaction, AfG°, is independent of the pressure.g Therefore, at constant temperature, the equilibrium constant K. .. is also independent of the pressure. That is,... 

In any given system, the value of the equilibrium constant may be available from a direct study of the equilibrium. If so, one compares that value of K with the value of k /k-. Another method reduces the two rate constants sought to one by introducing K into the calculation. This gives... 

We have noted previously that the forward and reverse rates are equal at equilibrium. It seems, then, that one could use this equality to deduce the form of the rate law for the reverse reactions (by which is meant the concentration dependences), seeing that the form of the equilibrium constant is defined by the condition for thermodynamic equilibrium. By and large, this method works, but it is not rigorously correct, since the coefficients in the equilibrium condition are only relative, whereas those in the rate law are absolute.19 Thus, if we have this net reaction and rate law for the forward direction,... 

---