Cells equilibrium constants

Cis (NH3)2PtCl2 and other Pt(II) complexes react only slowly with the nucleic bases. The slowness may be essential to their efficacy as tumor Inhibitors, for It provides Integrity and neutrality during circulation and passage Into cells. Equilibrium constants for association of els (NH3)2Pt(II) complexes with nucleic bases remain unknown. It has been argued that published constants fall to reflect systems at equilibrium (. The aqueous chemistry of Pt(II) relevant to biological molecules has received review (2),... 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

The change in the concentration of H3O+ is monitored with a pH ion-selective electrode, for which the cell potential is given by equation 11.9. The relationship between the concentration of H3O+ and CO2 is given by rearranging the equilibrium constant expression for reaction 11.10 thus... 

Through all these calculations of the effect of pH and metal ions on the ATP hydrolysis equilibrium, we have assumed standard conditions with respect to concentrations of all species except for protons. The levels of ATP, ADP, and other high-energy metabolites never even begin to approach the standard state of 1 M. In most cells, the concentrations of these species are more typically 1 to 5 mM or even less. Earlier, we described the effect of concentration on equilibrium constants and free energies in the form of Equation (3.12). For the present case, we can rewrite this as... 

Several additional points should be made. First, although oxygen esters usually have lower group-transfer potentials than thiol esters, the O—acyl bonds in acylcarnitines have high group-transfer potentials, and the transesterification reactions mediated by the acyl transferases have equilibrium constants close to 1. Second, note that eukaryotic cells maintain separate pools of CoA in the mitochondria and in the cytosol. The cytosolic pool is utilized principally in fatty acid biosynthesis (Chapter 25), and the mitochondrial pool is important in the oxidation of fatty acids and pyruvate, as well as some amino acids. 

One of the most important characteristics of a cell is its voltage, which is a measure of reaction spontaneity. Cell voltages depend on the nature of the half-reactions occurring at the electrodes (Section 18.2) and on the concentrations of species involved (Section 18.4). From the voltage measured at standard concentrations, it is possible to calculate the standard free energy change and the equilibrium constant (Section 18.3) of the reaction involved. 

As pointed out previously, the value of the standard cell voltage, E°, is a measure of the spontaneity of a cell reaction. In Chapter 17, we showed that the standard free energy change, AG°, is a general criterion for reaction spontaneity. As you might suppose, these two quantities have a simple relation to one another and to the equilibrium constant, K, for the cell reaction. 

Electrochemical Method.—In this the value of the equilibrium constant K is calculated from the maximum work measured by means of the electromotive force of a voltaic cell (cf. Chap. XVI.). 

Other measurements of AfG involve measuring AG for equilibrium processes, such as the measurement of equilibrium constants, reversible voltages of electrochemical cells, and phase equilibrium measurements. These methods especially come into play in the measurement of Afand AfG for ions in solution, which are processes that we will now consider. 

Measurement of Equilibrium Constants Electrochemical cells can be used to measure equilibrium constants for chemical reactions. For example, consider the cell... 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Where the parenthesis refer to the chemical activities of the reactants and K is the equilibrium constant for the previous equation. Similar considerations apply to the oxidation of less electropositive impurities from the anode when a current is passed through the cell. Thus, for the case of iron impurity in the anode, the reaction... 

We saw in Section 9.3 that the standard reaction Gibbs free energy, AGr°, is related to the equilibrium constant of the reaction by AGr° = —RT In K. In this chapter, we have seen that the standard reaction Gibbs free energy is related to the standard emf of a galvanic cell by AGr° = —nFE°, with n a pure number. When we combine the two equations, we get... 

This expression can be rearranged to allow us to calculate the equilibrium constant from the cell emf ... 

The equilibrium constant of a reaction is an exponential function of the standard emf of the corresponding cell. We can expect a cell reaction with a large positive emf to have a strong tendency to take place, and therefore to produce a high proportion of products at equilibrium. Therefore, we expect K > 1 when ° > 0 (and often K 1). The opposite is true for a cell reaction with a negative standard emf. 

The equilibrium constant of a reaction can be calculated from standard potentials by combining the equations for the balf-reactions to give the cell reaction of interest and determining the standard potential of the corresponding cell. 

Calculate the equilibrium constant for a reaction from the standard cell emf (Toolbox 12.3 and Example 12.8). 

Electrochemistry is one of the main methods used to determine equilibrium constants that are either very large or very small. To measure the equilibrium constant for the reaction of Fe(CN) 4 with Na2Cr207, the following cell was built ... 

Write the cell reaction and determine its equilibrium constant. 

Relation between the equilibrium constant for a cell reaction and the emf of a cell ... 

To illustrate this, we shall start with 2500 A ingredients and set the transition probabilities to Pi (A B) = 0.01, Pi (B A) = 0.02, Pi (A C) = 0.001, and Pi (C A) = 0.0005. Note that these values yield a situation favoring rapid initial transition to species B, since the transition probability for A B is 10 times than that for A C. However, the formal equilibrium constant eq[C]/[A] is 2.0, whereas eq[B]/[A] = 0.5, so that eventually, after the establishment of equilibrium, product C should predominate over product B. This study illustrates the contrast between the short run (kinetic) and the long run (thermodynamic) aspects of a reaction. To see the results, plot the evolution of the numbers of A, B, and C cells against time for a 10,000 iteration run. Determine the average concentrations [A]avg, [B]avg, and [C]avg under equilibrium conditions, along with their standard deviations. Also, determine the iteration Bmax at which ingredient B reaches its maximum value. 

Report the concentrations of A and C cells and plot [A] and [C] versus iterations for the last 500 iterations. Determine the average equilibrium concentrations of A and C, along with their standard deviations. Also determine the equilibrium constant Kgq. 

Example 8.3 above showed that equilibrium was achieved when we started with reactants A and B, but what happens when we approach this from the opposite direction, i.e., starting from the product side We can test this by starting with [A]o = [B]o = 0 cells, and [C]o = [D]o = 500 cells. Run the simulation just as in Example 8.3, but with these changed initial values. Is equilibrium achieved from the product direction If so, what is the equilibrium constant Kgq (Include the uncertainty in Kgq.)... 

C19-0039. Write a paragraph explaining the linkages among cell potential, free energy, and the equilibrium constant. 

Direct measurements of solute activity are based on studies of the equilibria in which a given substance is involved. The parameters of these equilibria (the distribution coefficients, equilibrium constants, and EMF of galvanic cells) are determined at different concentrations. Then these data are extrapolated to very low concentrations, where the activity coincides with concentration and the activity coefficient becomes unity. 

The above important relationship now allows evaluation of the thermodynamic driving force of a redox reaction in terms of a measurable cell emf. Moreover, it is possible to utilize the relationship between the standard state potential and the standard state free energy to arrive at an expression for the equilibrium constant of a redox reaction in terms of the emf. Thus... 

Having introduced matters pertaining to the electrochemical series earlier, it is only relevant that an appraisal is given on some of its applications. The coverage hereunder describes different examples which include aspects of spontaneity of a galvanic cell reaction, feasibility of different species for reaction, criterion of choice of electrodes to form galvanic cells, sacrificial protection, cementation, concentration and tempera lure effects on emf of electrochemical cells, clues on chemical reaction, caution notes on the use of electrochemical series, and finally determination of equilibrium constants and solubility products. 

The data of Table 6.11 create a wealth of information on the free energies of inorganic reactions. Although reported as emfs, these data are readily transformed into free energies by the expression AG° = —n i it. Such free-energy data are of considerable utility in determining equilibrium properties and, in particular, the equilibrium constant for the overall cell reaction. The possibility of the reduction of ferric ion to ferrous ion by zinc as a reduct-ant is considered as an example. The reaction in which one would be interested might be executed in the cell... 

The result displays that basically all the iron will be reduced to the ferrous state by zinc. There are some illustrations of cells wherein the overall reaction corresponds to the solution of an insoluble salt. In such cases the equilibrium constant that can be demarcated is a solubility product. This can be shown by the cell ... 

The foregoing two examples have been taken to convey that the data of Table 6.11 can very well be used to determine the equilibrium constant for any reaction which is the overall reaction for a cell assembled with electrodes contained in the electrochemical series table. 

If the equilibrium constant of the cell reaction is denoted as K, then it... 

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