E and the Equilibrium Constant

A galvanic cell produces electricity because the cell reaction is not at equilibrium. If the cell runs long enough, reactants are consumed and products are created until the reaction comes to equilibrium and the cell voltage, E, reaches 0. This is what happens to a battery when it runs down.  

If El is the standard reduction potential for the right half-cell and El is the standard reduction potential for the left half-cell, for the net cell reaction is 

Subtract the left half-reaction from the right half-reaction to get a net reaction Net reaction  

Equation 14-21 is true at any time. In the special case when the cell is at equilibrium, E = 0 and Q = K, the equilibrium constant. At equilbrium, 

Equation 14-23 gives the equilibrium constant for a net cell reaction from E°. 

Now let s relate E for a whole cell to the reaction quotient, Q, for the net cell reaction. For the two half-reactions 

The cell voltage cannot depend on how we write the reaction  

Don t invent species not shown in the cell. Use what is shown in the line diagram to select the half-reactions. 

Problem 14-20 gives an example of the use of the Nernst equation to find E 

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E. (a) Write half-reactions for Figure 14-3. Calculate E° and the equilibrium constant for the net cell reaction. 

Hammen equation A correlation between the structure and reactivity in the side chain derivatives of aromatic compounds. Its derivation follows from many comparisons between rate constants for various reactions and the equilibrium constants for other reactions, or other functions of molecules which can be measured (e g. the i.r. carbonyl group stretching frequency). For example the dissociation constants of a series of para substituted (O2N —, MeO —, Cl —, etc.) benzoic acids correlate with the rate constant k for the alkaline hydrolysis of para substituted benzyl chlorides. If log Kq is plotted against log k, the data fall on a straight line. Similar results are obtained for meta substituted derivatives but not for orthosubstituted derivatives. 

Federica Bertoncin is gratefully acknowledged for the synthesis and purification of 2.4b-e and some equilibrium constant measurements with these compounds. 

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. 

Suppose that the two sites are identical (an oversimplification) and that the binding of the first molecule of agonist does not affect the affinity of the site that remains vacant. The dissociation equilibrium constant for each site is denoted by KA and the equilibrium constant for the isomerization between A2R and A2R by E, so that [A2R ] = [A2R],... 

Figures 3 and 4 illustrate how G( r) changes with Keq in the fast reaction regime (tc -C to). For both figures, k and the equilibrium constant A e( = l

A word is needed about the assignment of rate constants to specific carbene spin states. Where a measured rate constant can be attributed with some confidence to a particular spin multiplicity, that multiplicity is indicated (i.e. XA and 3BA). Where the multiplicity is uncertain, the experimentally determined rate constant is reported and no spin state is indicated (i.e. FL). In the latter cases, the reported rate constant can often be viewed as the product of the actual bimolecular rate constant and the equilibrium constant (Table 8) connecting the carbene spin states 6 Griller el al., 1984c. This conclusion is reached solely from the analysis of products in C6H12... 

As seen in equations (32)-(34), the forward adsorptive flux depends upon the concentration of free cell surface carriers. Unfortunately, there is only limited information in the literature on determinations of carrier concentrations for the uptake of trace metals. In principle, graphical and numerical methods can be used to determine carrier numbers and the equilibrium constant, As, corresponding to the formation of M — Rcen following measurement of [M] and (M —Rceii. For example, a (Scatchard) plot of (M — RCeii /[M] versus (M — RCeii should yield a straight line with a slope equal to the reciprocal of the dissociation constant and abscissa-intercept equal to the total carrier numbers (e.g. [186]). 

TLM Activity Coefficients. In the version of the TLM as discussed by Davis et al. (11), mass action equations representing surface complexation reactions were written to include "chemical" and "coulombic" contributions to the overall free energy of reaction, e.g., the equilibrium constant for the deprotonation reaction represented by Equation 2 has been given as... 

Both notations are correct and the equilibrium constants, such as, can always be expressed as functions of the formation constants e.g. 

So far, only gaseous reactants have been considered. If solids are involved, the terms arising from the activities of the solids are usually omitted and the equilibrium constant includes only the fugacities of the gaseous reactants, e.g. for the reaction... 

To date, there are no direct tropospheric measurements of N2Os at the levels predicted to be in natural or polluted air masses. However, concentrations of n2o5 as high as 10-15 ppb have been calculated for the Los Angeles area using simultaneous measurements of ambient N03 and N02 and the equilibrium constant for reaction (24) (e.g., see Atkinson et al., 1986). 

Here q is the Bjerrum-distance ( -efe /2DkT), the Boltzmann Constance, to the mechanical mobility of an ion Kd(E=0) the equilibrium constant in the absence of electric field and D and dielectric constant of the medium. From these expressions we see that the shift in dissociation constant upon the application of an electric field is given by ... 

The melting point of ammonium hydrosulphide in a closed vessel was found by E. Briner to be 120° and, in the presence of an excess of hydrogen sulphide, the m.p. is a triple point NHiSHv HgS+NHg, and the equilibrium constant is K=0 04 at 22°. The heat of vaporization of the solid hydrosulphide, in consequence of dissociation, will be equal to the heat of formation of the solid from the component gases, viz., 22 4 Cals., as found by J. Thomsen. According to F. Isambert, the heat of vaporization between 77° and 132° is 23 Cals., and, according to J. H. van t Hoff, calculated between 9 5° and 25 1° at constant press., 22 7 Cals. J. Walker and J. S. Lumsden find that the value of this constant increases with a rise of temp., being 19 7 Cals, between 4 2° and 18°, and 22 0° between 30 9° and 44 4°. 

From HemleyJs work on the potassium system (11) one may infer that kaolinite, quartz, and K-mica ( illite) may be stable together, and the equilibrium constant [K+]/[H+] may be extrapolated, (from 200°C.) to 106 at 25°C.—e.g., Hollands (15) value of 10,50 O5. Hem-ley s work on the sodium system (12) in the same way indicates that quartz, Na-montmorillonite, and kaolinite can form a stable assemblage, and a somewhat risky extrapolation of the equilibrium ratio [Na+]/[H+] from 300° to 25°C. gives 107° (15). These ratios are not far from the corresponding ratios in sea water. One could not expect them to be exactly the same since the hydromica and montmorillonite phases in sea water are solid solutions, containing more components than the phases in Hemley s experiments. His experiments surely do not contradict the idea that the previously mentioned phases could exist together at equilibrium. 

To examine the potential importance of molecular disproportionation, a means for estimating ki3 must be found. Estimates of ki3 will be obtained from estimates of both the rate constant for the reverse reaction (radical disproportionation, reaction -13), and the equilibrium constant, Ki3 i.e., ki3 = Ki3 k x3. 

This is the same as Bronsted s theory which was designed particularly for solutions. The concentration of the activated complex can be expressed in terms of the reactants and the equilibrium constant K. Also the heat of the reaction, AH, to give the activated complex, can be calculated approximately from the quantum theory or from the Arrhenius theory. Since AF= —RT In K and AF = AII — TAS, and since K can, in some cases, be calculated from known, fundamental constants, the entropy term remains the only unknown. Rodebush has long pointed out that the unknown quantity 5 in the formula k = se E/RT is related to an entropy term. As a first approximation it has been related to a collision frequency in bimolecular reactions and to a vibration frequency in unimolecu-lar reactions. Combining the two thermodynamic equations23... 

Spectra shown in Figure 3 may be obtained at various glyme concentrations. Their examination permits us to determine the stoichiometry and the equilibrium constant of the reaction ordinary Na+,N " (i.e.,... 

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