Concentrations equilibrium constants proportional

The solution is illustrated in Fig. 8.15, which shows the equilibrium concentration of methanol for different initial gas mixtures. Note that the maximum methanol concentration occurs for the pure CO + H2 mixture. Hence, in principle, a mixture of just CO and H2 could be used, with minor amounts of CO2, to produce the maximum amount of methanol. However, it is not only the equilibrium constant that matters but also the rate of methanol formation, and one must remember that methanol forms from CO2 not CO. Hence, the rate is proportional to the CO2 pressure and this is why the methanol synthesis is not performed with the simple stoichiometric 3 1 mixture of H2 and CO2 that Eq. (19) suggests. 

The kinetic factor is proportional to the energetic state of the system and (for heterogeneous catalytic systems) the number of active sites per unit volume (mass) of catalyst. The driving-force group includes the influence of concentration and distance from chemical equilibrium on the reaction rate, and the hindering group describes the hindering effect of components of the reaction mixture on the reaction rate. The kinetic factor is expressed as the rate constant, possibly multiplied by an equilibrium constant(s) as will be shown later. 

These results show that if the relationship between the concentration of an agonist and the proportion of receptors that it occupies is measured directly (e.g., using a radioligand binding method), the outcome should be a simple hyperbolic curve. Although the curve is describable by the Hill-Langmuir equation, the dissociation equilibrium constant for the binding will be not KA but Ke, which is determined by both E and KA. 

Ketones play an important role in the decomposition of peroxides to form radicals in alcohols undergoing oxidation. The formed hydroxyhydroperoxide decomposes to form radicals more rapidly than hydrogen peroxide. With an increase in the ketone concentration, there is an increase in the proportion of peroxide in the form of hydroxyhydroperoxide, with the corresponding increase in the rate of formation of radicals. This was proved by the acceptor radical method in the cyclohexanol-cyclohexanone-hydrogen peroxide system [59], The equilibrium constant was found to be K — 0.10 L mol 1 (373 K), 0.11 L mol 1 (383 K), and 0.12 L mol 1 (393 K). The rate constant of free radical generation results in the formation of cyclohexylhydroxy hydroperoxide decomposition and was found to be ki = 2.2 x 104 exp(—67.8/7 7) s 1 [59]. 

In an immunosensor the core-cover interface of an optical waveguide structure is coated with a chemo-optical transducer receptor layer, which can selectively bind to specific analyte molecules present in the cover medium. The receptor-analyte reaction obeys the law of mass action, which states that the rate of a reaction is proportional to the concentration of the reactants. At equilibrium, the rate of formation of the receptor-analyte complex is equal to the rate of breaking, and the equilibrium constant, K. can be written as... 

Eutectic point (Tc) A single point on a temperature concentration phase (or state) diagram for a binary solution (e.g., water and sugars or salts) where the solution can exist in equilibrium with both crystalline solute and crystalline solvent. Under equilibrium conditions, cooling at Te results in simultaneous crystallization of solvent and solute in constant proportion and at constant temperature until maximum solidification has occurred (based on Fennema, 1996). 

Although molalities are simple experimental quantities (recall that the molality of a solute is given by the amount of substance dissolved in 1 kg of solvent) and have the additional advantage of being temperature-independent, most second law thermochemical data reported in the literature rely on equilibrium concentrations. This often stems from the fact that many analytical methods use laws that relate the measured physical parameters with concentrations, rather than molalities, as for example the Lambert-Beer law (see following discussion). As explained in section 2.9, the equilibrium constant defined in terms of concentrations (Kc) is related to Km by equation 14.3, which assumes that the solutes are present in very small amounts, so their concentrations (q) are proportional to their molalities nr, = q/p (p is the density of the solution). 

Further experiments by Brown and particularly Henri were made with invertase. At that time the pH of the reactions was not controlled, mutarotation did not proceed to completion, and it is no longer possible to identify how much enzyme was used (Segal, 1959). Nevertheless, in a critical review of kinetic studies with invertase, Henri concluded (1903) that the rate of reaction was proportional to the amount of enzyme. He also stated that the equilibrium of the enzyme-catalyzed reaction was unaffected by the presence of the catalyst, whose concentration remained unchanged even after 10 hours of activity. When the concentration of the substrate [S] was sufficiently high the velocity became independent of [S]. Henri derived an equation relating the observed initial velocity of the reaction, Vq, to the initial concentration of the substrate, [S0], the equilibrium constant for the formation of an enzyme-substrate complex, Ks, and the rate of formation of the products, ky... 

The now classical example is lactate dehydrogenase. Sil-verstein and Boyer were the first to determine the rates of exchange between cognate pairs of reactants ie., lactate and pyruvate as well as NAD and NADH). Convenient [NADH]/[NAD ] and [pyruvate]/[lactate] ratios were chosen such that when combined they satisfied the apparent equilibrium constant for the LDH reaction. These investigators first established that each exchange rate was directly proportional to the duration of exchange and likewise directly proportional to enzyme concentration. As an additional control, they also demonstrated the equality of the pyruvate lactate exchange... 

As can be seen from the interconversion reaction between two hydrous species H20m and OH (Reaction 3-79), the coefficient for OH is 2. This seemingly trivial point turns out to be the key in understanding H2O diffusion. Because of this factor of 2, the equilibrium constant K involves the square of OH concentration but only the first power of H20 i concentration (Equation 3-80b). That is, the species concentrations of OH and H20 i are not proportional to each other, and neither concentration is proportional to total H2O concentration (H20t) in the entire concentration range. Solving Equations 3-80a,b for the two unknowns of H20m and OH yields... 

The effect (upon the overall rate of conversion of dichromate to chromate) of changing the chromate ion concentration was studied. The rate was inversely proportional to the square of the chromate concentration, as well as proportional to the dichromate concentration. Since oxygen and nitrogen dioxide had no effect on the rate, the nitryl ion, N(>2+ was postulated as intermediate. However, the equilibrium constant for the reaction could not be determined because too little N02+ was formed. 

On the other hand, an attempt to accelerate the step of coordination of the substrate to the Cu catalyst was successful because it used the hydrophobic domain of the polymer ligand156 That was the oxidation catalyzed by polymer-Cu complexes in a dilute aqueous solution of phenol, which occurred slowly. The substrate was concentrated in the domain of the polymer catalyst and was effectively catalyzed by Cu in the domain. A relationship was found to exist between the equilibrium constant (Ka) for the adsorption of phenol on the polymer ligand and the catalytic activity (V) of the polymer-ligand-Cu complex for various polymer ligands K a = 0.21 1/mol and V = 1(T6 mol/1 min for QPVP, K a = 26 and V = 1(T4 for PVP, K a = 52 and V = 10-4 for the copolymer of styrene and 4-vinylpyridine (PSP) (styrene content 20%), and K a = 109 and V = 10-3 for PSP (styrene content 40%). The V value was proportional to the Ka value, and both Ka and V increased with the hydrophobicity of the polymer ligand. The oxidation rate catalyzed by the polymer-Cu complex in aqueous solutions depended on the adsorption capacity of the polymer domain. 

The second expression, for bss, is independent of the equilibrium constant and has exactly the same form as that derived for the irreversible system (eqn (2.9)). For the intermediate A, the stationary-state concentration is increased by the reversibility of the steps the first term in eqn (2.30) is that corresponding to the irreversible solution (eqn (2.10)), the second is proportional to the inverse of the equilibrium constant. Thus, as Ke - oo, ass tends smoothly to our previous result. 

Absorbance is proportional to concentration (not activity), so concentrations must be converted into activities to get true equilibrium constants. 

Isosbestic (crossing) points are observed when a solution contains variable proportions of two components with a constant total concentration. A Scatchard plot is used to measure an equilibrium constant, and the method of continuous variation allows us to determine the stoichiometry of a complex. In flow injection analysis,... 

The constant Ke, which was not present in Equation 15-15, is a new constant (the ratio of the forward and reverse rate constants) called the equilibrium constant. Each of the quantities in brackets is the equilibrium concentration of the substance shown. At any given temperature, the value ofKe remains constant no matter whether you start with A, B, and C or with M and N, and regardless of the proportions in which they are mixed. Ke varies with temperature because k, and kT vary with temperature, but not by exactly the same... 

The equilibrium constant for the reaction is given by Kc = [B]/ [A], where the concentrations are equilibrium concentrations in units of mol/L. Since the equilibrium constant expression has the same number of concentration terms in the numerator and denominator, the volume cancels and Kc = (moles of B)/(moles of A). Because the number of moles is directly proportional to the number of molecules, Kc = (molecules of B)/(molecules of A) in the equilibrium mixture (1). To determine whether the other mixtures are at equilibrium, count the number of molecules and compare the B/A ratio in mixtures (2)—(4) with the B/A ratio in the equilibrium mixture. 

Diethyl ether is the principal by-product of the reaction of ethyl alcohol with diethyl sulfate. Various methods have been proposed to diminish its formation (70—72), including separation of diethyl sulfate from the reaction product. Diethyl sulfate not only causes an increase in ether formation but is also more difficult to hydrolyze to alcohol than is ethyl hydrogen sulfate. The equilibrium constant for the hydrolysis of ethyl hydrogen sulfate is independent of temperature, and the reaction rate is proportional to the hydrogen ion concentration (73—75). 

There is reason to believe that an equilibrium of this type exists between the sodium ions and the electrion to form an ion pair as a result of coulombic interactions. If the conductance data for sodium are used to determine the equilibrium constant of sodium in liquid ammonia for computing the constant of the ion pair equilibrium, the experimental data do not conform to values required for such an equilibrium. This is because electrons in dilute solutions exhibit magnetic properties, from which we may conclude that, at very low concentrations, the electron has a spin of l/2 Bohr unit. It is, therefore, necessary to take into account the effect of the decreasing proportion of electrons that may be spin-coupled and interacting with the positive ions of the solvent. One of us (Evers) made the simplest possible assumption, following a model proposed by Becker, Lindquist, and Alder (BLA), namely that when two ion pairs, consisting of a sodium ion and an electron, come together the spins of the two electrons couple to form disodium spinide, and that this coulombic compound is not dissociated into ions at low concentrations. 

For HNO3, Raman spectroscopy was used to determine concentrations, and hence equilibrium constants, in HN03(aq) solutions. But this technique is often not possible in other systems because vibrational or electronic transitions that can be used to differentiate between the ion and the molecule are not present, and other techniques must be used. As we do so, we must keep in mind that the different techniques are based upon assumptions that lead to the measurement of the equilibrium concentration. For example, a lightscattering technique such as Raman spectroscopy usually relies on the assumption that the concentration of the species in solution is proportional to the intensity of the observed band. 

For convenience we often express equilibrium constants as the negative logarithm, or pK value. Thus the relative proportion of the neutral and charged species, will be a function of the pKa and solution pH. When the pH is equal to pKa, equal concentrations of the neutral and ionized forms will be present. When pH is less than the pKa, the neutral species will be predominant when pH is greater than pKa, the ionized species will be in excess. The exact equilibrium distribution can be calculated from the equilibrium expression above and the law of mass conservation. 

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