Altering equilibrium constants

The third step in changing the basis is to set the equilibrium constants for the revised reactions. The new equilibrium constant K j for a species reaction can be found from its value Kj before the basis swap according to 

and K are the equilibrium constants for the reactions by which we swap species, minerals, and gases into the basis. 

The equilibrium constants for mineral and gas reactions are calculated from their revised reaction coefficients in similar fashion as, 

Basis entries that do not change over the swap have no effect in these equations, since they are represented by null swap reactions (e.g., H2O = H2O) with equilibrium constants of unity. 

What is the equilibrium constant for CO3- in the example from the previous section The value at 25°C for the reaction written in terms of the original basis is IO1034, and the equilibrium constants of the swap reactions for calcite and CO2(g) are 101 71 and KT7 82. The new value according to the equation above is 

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In a single-phase liquid system, pressure can influence an equilibrium only by altering equilibrium constant K. This requires very high pressures (>>1000 atm). The pressures applied in gas-liquid systems are much lower. They range from 1 atm to a few hundred atm. Higher pressures are usually not necessary, since they would not change the concentration of the gas in the liquid phase by very much. 

The system is initially at equilibrium with concentrations Ca and c. Now we rapidly perturb the system so as to alter the magnitude of the equilibrium constant. Let the new equilibrium concentrations, toward which the actual concentrations will relax, be Ca and c. (Clearly one of these will be greater than and one will be less than the initial concentrations.) The concentrations at any time t are Ca and c. ... 

The sensitivity of the equilibrium constant to temperature, therefore, depends upon the enthalpy change AH . This is usually not a serious limitation, because most reaction enthalpies are sufficiently large and because we commonly require that the perturbation be a small one so that the linearization condition is valid. If AH is so small that the T-jump is ineffective, it may be possible to make use of an auxiliary reaction in the following way Suppose the reaction under study is an acid-base reaction with a small AH . We can add a buffer system having a large AH and apply the T-jump to the combined system. The T-jump will alter the Ka of the buffer reaction, resulting in a pH jump. The pH jump then acts as the forcing function on the reaction of interest. 

This is because the concentrations of solid copper and solid silver are incorporated into the equilibrium constant. The concentration of solid copper is fixed by the density of the metal—it cannot be altered either by the chemist or by the progress of the reaction. The same is true of the concentration of solid silver. Since neither of these concentrations varies, no matter how much solid is added, there is no need to write them each time an equilibrium calculation is made. Equation (21) will suffice. 

This ease with which we can control and vary the concentrations of H+(aq) and OH (aq) would be only a curiosity but for one fact. The ions H+(aq) and OH (aq) take part in many important reactions that occur in aqueous solution. Thus, if H+(aq) is a reactant or a product in a reaction, the variation of the concentration of hydrogen ion by a factor of 1012 can have an enormous effect. At equilibrium such a change causes reaction to occur, altering the concentrations of all of the other reactants and products until the equilibrium law relation again equals the equilibrium constant. Furthermore, there are many reactions for which either the hydrogen ion or the hydroxide ion is a catalyst. An example was discussed in Chapter 8, the catalysis of the decomposition of formic acid by sulfuric acid. Formic acid is reasonably stable until the hydrogen ion concentration is raised, then the rate of the decomposition reaction becomes very rapid. 

Chemical relaxation techniques were conceived and implemented by M. Eigen, who received the 1967 Nobel Prize in Chemistry for his work. In a relaxation measurement, one perturbs a previously established chemical equilibrium by a sudden change in a physical variable, such as temperature, pressure, or electric field strength. The experiment is carried out so that the time for the change to be applied is much shorter than that for the chemical reaction to shift to its new equilibrium position. That is to say, the alteration in the physical variable changes the equilibrium constant of the reaction. The concentrations then adjust to their values under the new condition of temperature, pressure, or electric field strength. 

It is of interest that, as a consequence of the peculiar state of reactants in such systems, reactions rates and equilibrium constants are very often altered by several orders of magnitude as compared with those in homogeneous solution [114,115],... 

In order that the value of the equilibrium constant does not change, K should equal fCp for this to happen pBj must decrease and/orpAB must increase, i.e., more of B2 and A2 will react to yield AB. A similar consequence would follow on the addition of the component B2 at equilibrium. Another factor can be the addition of an inert gas. This can be done at constant volume. In this case, since there is no change in the total volume, the concentrations of A2, B2 and AB will have the same individual values as before the addition of the inert gas and as such there will be no change in the reaction or in the value of the equilibrium constant. An alternative way of adding the inert gas is to do so at constant pressure. In this case, the addition will cause an increase in the number of moles in the gas mixture and this will merely lead to an increase in the total volume at constant temperature, without altering the initial quantities of A2 or B2. Since the mass law equation for this type of reac-... 

This expression for the equilibrium constant is found to contain the term V in the denominator. Since K must remain constant, an increase in V would cause % also to increase. Stated in an another form, the dissociation of AB is favoured by a reduction in the pressure. A pressure increase would bring down V, and to maintain the constant value of K, x must decrease. Thus, a pressure increase would tend to inhibit the dissociation of AB. As in the previous case, it will be of interest in this case also to examine the effects of some other factors on the equilibrium. It is left to the readers as an exercise to establish for this case the following results (i) the effect of the addition of either A or B is to suppress the degree of dissociation of AB (ii) the addition of an inert gas at constant volume does not alter the degree of dissociation of AB and (iii) the addition of an inert gas at constant pressure increases the degree of dissociation of AB. 

For pure water, [H+] = [OH ] and pH = 7. Any solution with pH = 7 is by definition a neutral solution. No matter what other solutes occur in a given solution, the product of hydrogen and hydroxide ion activities will always be 1CT14 at 25 °C. This may be noted that the value of this equilibrium constants alter with temperature, as do all equilibrium constants. For this reason at 230 °C, K = 10 11/1 and a neutral solution would have a pH of 5.7. This brief diversion specifically focusing attention on the ionic compositional aspects of water is quite relevant with regard to its role played as a leaching agent. 

We now consider what would happen if the binding of the first molecule of agonist altered the affinity of the second identical site. The dissociation equilibrium constants for the first and second bindings will be denoted by KA(U and KM2), respectively, and E is defined as before. 

In principle, these features can be built into models of receptor activation, although the large number of disposable parameters makes testing difficult. Some of the rate and equilibrium constants must be known beforehand. One experimental tactic is to alter the relative proportions of receptors and G-protein and then determine whether the efficacy of agonists changes in the way expected from the model. The discovery that some receptors are constitutively active has provided another new approach as well as additional information about receptor function, as we shall now see. 

The final rate expressions, which were used in the present work, were given by Hou and Hughes (2001). In these rate expressions all reaction rate and equilibrium constants were defined to be temperature-dependent through the Arrhenius and van t Hoff equations. The particular values for the activation energies, heats of adsorption, and pre-exponential constants are available in the original reference and were used in our work without alteration. 

Notice how the equilibrium constant K in Equation (6.49) is also an acidity constant, hence the subscripted a . The value of K remains constant provided the temperature is not altered. 

By preparing planar lipid monolayers or bilayers on hydrophobically derivatized or native hydrophilic glass, respectively, the adsorption equilibrium constants of a blood coagulation cascade protein, prothrombin, have been examined by TIRF on a surface that more closely models actual cell surfaces and is amenable to alterations of surface charge. It was found that membranes of phosphatidylcholine (PC) that contain some phosphatidyl-serine (PS) bind prothrombin more strongly than pure PC membranes/83... 

A substance that accelerates a chemical reaction but does not become consumed, generated, or permanently changed by such reaction. Thus, a catalyst does not alter the overall stoichiometric expression for the reaction or the overall equilibrium constant. The enhanced reactivity produced by a catalyst is referred to as catalysis. 

At very high concentrations, the enzyme can alter the equilibrium constant. If is calculated by determining the equilibrium concentrations of all free products and reactants, and if the products and reactants have different affinities for the free enzyme, then high [Etot] favors formation of significant amounts of EA and EP, and this may cause an apparent shift in In such instances, the enzyme is now a stoichiometric participant in the reaction, and the true equilibrium constant has to take this into account. 

Catalysts are very effective at stabilizing the transition state, and enzymatic reactions often proceed at rates that are 10 -10 times faster than their uncatalyzed counterparts. Because a catalyst returns to the same chemical form after each catalytic round, the catalyst cannot alter the equilibrium constant of a reaction. Thus, an enzyme must accelerate the S P interconversion by the equivalent factor representing the acceleration of P S. 

The equilibrium constant of an enzyme-catalyzed reaction can depend greatly on reaction conditions. Because most substrates, products, and effectors are ionic species, the concentration and activity of each species is usually pH-dependent. This is particularly true for nucleotide-dependent enzymes which utilize substrates having pi a values near the pH value of the reaction. For example, both ATP" and HATP may be the nucleotide substrate for a phosphotransferase, albeit with different values. Thus, the equilibrium constant with ATP may be significantly different than that of HATP . In addition, most phosphotransferases do not utilize free nucleotides as the substrate but use the metal ion complexes. Both ATP" and HATP have different stability constants for Mg +. If the buffer (or any other constituent of the reaction mixture) also binds the metal ion, the buffer (or that other constituent) can also alter the observed equilibrium constant . ... 

Figure 3. Free energy diagram for ligand binding interactions to an MWC dimer. Note that the relative stability of the To to Rq alters the ligand saturation curve as shown in each graph. The energy changes between each R-state are equivalent because each ligand binding interaction has the same equilibrium constant.

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. 

Isotopic labels (and especially enriched materials) have proven crucial in the investigation of the mechanisms of homogeneously catalyzed reactions [130]. Further, isotope effects on the rate or the equilibrium constant of a reaction can be diagnostic, and structural information can be provided by isotope-induced changes in the chemical shifts of neighbouring nuclei, and/or alterations in the coupling pattern of the detected spectra. The isotope- and position-specific information inherent to NMR techniques are ideally suited for the analysis of isotope effects in catalysis [131]. 

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