Nernst potential-dependent constant

Since the absolute and the conventional electrode potentials differ only by an additive constant, the absolute potential depends on the concentration of the reactants through the familiar Nernst s equation. This dependence is implicitly contained in Eq. (2.6) the real Gibbs energies of solvation contain an entropic term, which depends on the concentration of the species in the solution. 

The Nernst equation defining the potential of the silver-silver chloride electrode is Equation (14.9). Since the [CF] in such an electrode is a constant, the potential also must be a constant (the requirement of a reference electrode) because [CF] is the only variable on which the potential depends. 

As the stability constants of Ag(I) cyanide complexes are high, we have to deal with rather low concentrations of free Ag ions. In the extreme cases, the concentrations of some components can take on the enormously low values devoid of physical sense (this takes place in the Au Au(I), CN" system considered next). However, in the calculations of this is not important, because from a thermodynamic point of view, it does not matter which of the species is regarded as potential dependent. Therefore, any convenient form of the Nernst equation can be used (see Chapter 2). 

This discussion assumes a constant surface concentration of FeOHa. However, according to Reaction (l-59b), the equilibrium of this charge transfer process should be potential-dependent and will follow the Nernst equation. 

An example is described here for the measurement of fluoride ions in solution. The fluoride electrode uses a LaF3 single crystal membrane and an internal reference, bonded into an epoxy body. The crystal is an ionic conductor in which only fluoride ions are mobile. When the membrane is in contact with a fluoride solution, an electrode potential develops across the membrane. This potential, which depends on the level of free fluoride ions in solution, is measured against an external constant reference potential with a digital pH/mv meter or specific ion meter. The measured potential corresponding to the level of fluoride ions in solution is described by the Nernst equation ... 

Here, w = m, n, and S. V represents the membrane potential, n is the opening probability of the potassium channels, and S accounts for the presence of a slow dynamics in the system. Ic and Ik are the calcium and potassium currents, gca = 3.6 and gx = 10.0 are the associated conductances, and Vca = 25 mV and Vk = -75 mV are the respective Nernst (or reversal) potentials. The ratio r/r s defines the relation between the fast (V and n) and the slow (S) time scales. The time constant for the membrane potential is determined by the capacitance and typical conductance of the cell membrane. With r = 0.02 s and ts = 35 s, the ratio ks = r/r s is quite small, and the cell model is numerically stiff. The calcium current Ica is assumed to adjust immediately to variations in V. For fixed values of the membrane potential, the gating variables n and S relax exponentially towards the voltage-dependent steady-state values noo (V) and S00 (V). Together with the ratio ks of the fast to the slow time constant, Vs is used as the main bifurcation parameter. This parameter determines the membrane potential at which the steady-state value for the gating variable S attains one-half of its maximum value. The other parameters are assumed to take the following values gs = 4.0, Vm = -20 mV, Vn = -16 mV, 9m = 12 mV, 9n = 5.6 mV, 9s = 10 mV, and a = 0.85. These values are all adjusted to fit experimentally observed relationships. In accordance with the formulation used by Sherman et al. [53], there is no capacitance in Eq. (6), and all the conductances are dimensionless. To eliminate any dependence on the cell size, all conductances are scaled with the typical conductance. Hence, we may consider the model to represent a cluster of closely coupled / -cells that share the combined capacity and conductance of the entire membrane area. 

Nernst equation — A fundamental equation in -> electrochemistry derived by - Nernst at the end of the nineteenth century assuming an osmotic equilibrium between the metal and solution phases (- Nernst equilibrium). This equation describes the dependence of the equilibrium electrode - potential on the composition of the contacting phases. The Nernst equation can be derived from the - potential of the cell reaction (Ecen = AG/nF) where AG is the - Gibbs energy change of the - cell reaction, n is the charge number of the electrochemical cell reaction, and F is the - Faraday constant. 

Formal potential — Symbol Efr (SI Unit V), has been introduced in order to replace the standard potential of -> cell reaction when the values of - activity coefficients of the species involved in the cell reaction are unknown, and therefore concentrations used in the equation expressing the composition dependence of ceii instead of activities. It also involves the activity effect regarding the -+ standard hydrogen electrode, consequently in this way the formal electrode potential is also defined. Formal potentials are similar to conditional (apparent) equilibrium constants (-> equilibrium constant), in that, beside the effect of the activity coefficients, side reaction equilibria are also considered if those are not known or too complex to be taken into account. It follows that when the logarithmic term which contains the ratio of concentrations in the -> Nernst... 

Because the potential of an electrochemical cell depends on the concentrations of the participating ions, the observed potential can be used as a sensitive method for measuring ion concentrations in solution. We have already mentioned the ion-selective electrodes that work by this principle. Another application of the relationship between cell potential and concentration is the determination of equilibrium constants for reactions that are not redox reactions. For example, consider a modified version of the silver concentration cell shown in Fig. 11.11. If the 0.10 M AgN03 solution in the left-hand compartment is replaced by 1.0 M NaCl and an excess of solid AgCl is added to the cell, the observed cell potential can be used to determine the concentration of Ag+ in equilibrium with the AgCl(s). In other words, at 25°C we can write the Nernst equation as... 

The potential difference (PD) between the IRE and the internal membrane surface is constant, as fixed by its design (e.g. the nature of the reference electrode and the activity fli reference of the reference solution). Alternatively, the PD, which appears between the external surface of the membrane and the sample solution (An en b) depends upon the activity of the target ion (fli soiution)- The potential difference across the membrane is described by the Nernst equation ... 

An ISE consists of a membrane, an internal reference electrode, and an internal reference electrolyte of fixed activity. The ISE is immersed in a sample solution that contains the analyte of interest, along with a reference electrode. The membrane is chosen to have a specific affinity for a particular ion, and if activity of this ion in the sample differs from that in the reference electrolyte, a potential develops across the membrane that is dependent on the ratio of these activities. Since the potentials of the two reference electrodes (internal and external) are fixed, and the internal electrolyte is of constant activity, the measured potential, , is dependent on the membrane potential and is given by the Nernst equation ... 

Axial-ligand binding constants, for example to Fe and Fe porphyrins, can be measured in favorable cases by measuring the Ei/2 values for the Fe VFe and Fe VFe waves by cyclic voltammetry as a function of the concentration of axial ligand and then fitting the ligand concentration dependence of the reduction potential observed for each half-reaction to the full Nernst equation, ... 

To confirm that a redox component regulates the apparent quantum yield of PSI we studied the dependence of PS I-activity on the redox-potential of the medium. Thy-lakoids were kept in the dark for 5-10 min and it was taken care, that the redox-potential of the medium was constant prior to the measurement. The plots of two experiments shown in figure 4 were fitted by a Nernst-curve of a titration with an one-electron step (n=l). The calculated midpoint-potential was +140m / (pH 7,8) in both experiments. 

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