Cell potential difference, calculation

An aqueous solution of potassium permanganate (KMn04) appears deep purple. In aqueous acidic solution, the permanganate ion can be reduced to the pale-pink manganese(II) ion (Mn ). Under standard conditions, the reduction potential of an MnOijlMn half-cell is = 1.49 V. Suppose this half-cell is combined with a Zn Zn half-cell in a galvanic cell, with [Zn ] = [MnO ] = [Mn ] = [H3O ] = 1 M. (a) Write equations for the reactions at the anode and the cathode, (b) Write a balanced equation for the overall cell reaction, (c) Calculate the standard cell potential difference, A%°. 

Sometimes it is convenient to analyze interfacial thermodynamic data at constant electrode charge density Om rather than at constant cell potential difference E. Once the interfacial tension data at a given concentration have been differentiated with respect to to obtain one may calculate the function which is given by... 

Late Necturus Proximal Tubule Concentration Ratios, Electrical Potential Differences, Calculated Cl Equilibrium Potentials Across the Inner (Luminal) and Outer (Peritubular) Cell Boundaries. Mean Values Standard Error are Given. All Values Given are Derived from Purely Electrometric... 

The dependence of the cell potential difference on current density is called the cell polarization curve. The experimentally obtained open circnit potential (OCP) in a H2/O2 PEMFC is always below the theoretically calculated OCP, 1.229 V (at 25°C), due to (1) crossover of chemicals through the membrane and (2) a small internal electron current. This parasitic current density (jp) can reduce the OCP down to around... 

Multiple choice Conventionally, the cell potential difference for this electrochemical cell should be calculated in the following manner. 

The standard cell potential is calculated from the difference between the standard electrode potentials of two half-cells. 

The calculations were performed in the framework of a one-step model of photoe-mission derived from the one originally formulated by Pendry [1]. Nowadays the model includes relativistic effects [2-5], the possibility of having several atoms per unit cell [6], different types of layers and a realistic model for the surface potential [7]. It is further possible to consider ov erlayers on a surface. We will not review the theory here, which has been done already in several publications [2,4,6,8], but instead concentrate on the results. 

The potential difference at each electrode may be calculated by the formula given above, and the e.m.f. of the cell is the algebraic difference of the two potentials, the correct sign being applied to each. 

For the Daniell element in Fig. 3, a potential difference A is obtained by calculation from the values in Fig. 5 according to Eq. (11) under equilibrum conditions the potential difference corresponds to the terminal voltage of the cell. 

The water flux into a cell, and hence the volume increase, is driven by the effective water potential difference between the inside and the outside of the plasmalemma. In calculating an effective water potential difference it is necessary to take account of the reflection coefficient, a, a measure of the degree of semipermeability of the membrane. The volumetric increase in cell size with attendant water influx can be described by ... 

The calculation o E° for this cell illustrates an important feature of cell potentials. A standard cell potential is the difference between two standard reduction potentials. This difference does not change when one half-reaction is multiplied by 2 to cancel electrons in the overall redox reaction. 

A semi-permeable membrane, which is unequally permeable to different components and thus may show a potential difference across the membrane. In case (1), a diffusion potential occurs only if there is a difference in mobility between cation and anion. In case (2), we have to deal with the biologically important Donnan equilibrium e.g., a cell membrane may be permeable to small inorganic ions but impermeable to ions derived from high-molecular-weight proteins, so that across the membrane an osmotic pressure occurs in addition to a Donnan potential. The values concerned can be approximately calculated from the equations derived by Donnan35. In case (3), an intermediate situation, there is a combined effect of diffusion and the Donnan potential, so that its calculation becomes uncertain. 

So far, a cell containing a single electrolyte solution has been considered (a galvanic cell without transport). When the two electrodes of the cell are immersed into different electrolyte solutions in the same solvent, separated by a liquid junction (see Section 2.5.3), this system is termed a galvanic cell with transport. The relationship for the EMF of this type of a cell is based on a balance of the Galvani potential differences. This approach yields a result similar to that obtained in the calculation of the EMF of a cell without transport, plus the liquid junction potential value A0L. Thus Eq. (3.1.66) assumes the form... 

The scale of electrochemical work functions makes it possible to calculate the outer potential difference between a solution and any electrode provided the respective reaction is in equilibrium. A knowledge of this difference is often important in the design of electrochemical systems, for example, for electrochemical solar cells. However, in most situations one needs only relative energies and potentials, and the conventional hydrogen scale suffices. 

R is the ideal gas constant, T is the Kelvin temperature, n is the number of electrons transferred, F is Faraday s constant, and Q is the activity quotient. The second form, involving the log Q, is the more useful form. If you know the cell reaction, the concentrations of ions, and the E°ell, then you can calculate the actual cell potential. Another useful application of the Nernst equation is in the calculation of the concentration of one of the reactants from cell potential measurements. Knowing the actual cell potential and the E°ell, allows you to calculate Q, the activity quotient. Knowing Q and all but one of the concentrations, allows you to calculate the unknown concentration. Another application of the Nernst equation is concentration cells. A concentration cell is an electrochemical cell in which the same chemical species are used in both cell compartments, but differing in concentration. Because the half reactions are the same, the E°ell = 0.00 V. Then simply substituting the appropriate concentrations into the activity quotient allows calculation of the actual cell potential. 

The calculation of the cell potential may be done in different ways. Here is one method ... 

The movement of solute across a semipermeable membrane depends upon the chemical concentration gradient and the electrical gradient. Movement occurs down the concentration gradient until a significant opposing electrical potential has developed. This prevents further movement of ions and the Gibbs-Donnan equilibrium is reached. This is electrochemical equilibrium and the potential difference across the cell is the equilibrium potential. It can be calculated using the Nemst equation. 

In section 11.1, you learned that a cell potential is the difference between the potential energies at the anode and the cathode of a cell. In other words, a cell potential is the difference between the potentials of two half-cells. You cannot measure the potential of one half-cell, because a single half-reaction cannot occur alone. However, you can use measured cell potentials to construct tables of half-cell potentials. A table of standard half-cell potentials allows you to calculate cell potentials, rather than building the cells and measuring their potentials. Table 11.1 includes a few standard half-cell potentials. A larger table of standard half-cell potentials is given in Appendix E. 

In this section, you learned that you can calculate cell potentials by using tables of half-cell potentials. The half-cell potential for a reduction half-reaction is called a reduction potential. The half-cell potential for an oxidation half-reaction is called an oxidation potential. Standard half-cell potentials are written as reduction potentials. The values of standard reduction potentials for half-reactions are relative to the reduction potential of the standard hydrogen electrode. You used standard reduction potentials to calculate standard cell potentials for galvanic cells. You learned two methods of calculating standard cell potentials. One method is to subtract the standard reduction potential of the anode from the standard reduction potential of the cathode. The other method is to add the standard reduction potential of the cathode and the standard oxidation potential of the anode. In the next section, you will learn about a different type of cell, called an electrolytic cell. 

The voltage we measure is characteristic of the metals we use. As an additional example, unit activity solutions of CuCE and AgCl with copper and silver electrodes, respectively, give a potential difference of about 0.45 V. We could continue with this type of measurement for aU the different anode-cathode combinations, but the number of galvanic cells needed would be very large. Fortunately, the half-reactions for most metals have been calculated relative to a standard reference electrode, which is arbitrarily selected as the reduction of hydrogen ... 

With this background, consider the calculation of the equilibrium-potential difference Ve across the cell... 

Now assume that aCu2+/ Zu2+ = 1. Thai, = 1.10 V, which means that the copper electrode is positive with respect to the zinc electrode the sign of the potential difference across a cell corresponds to the polarity of the electrode on the right For ratios of ()thcr than unity, one can calculate Ve from Eq. (7.284). 

There is an important piece of information that emerges from the calculation of the equilibrium cell potential. For example, if unit activities of Zn2+and Curare taken, it has been found (Section 7.13.3) that the potential difference across the Daniel cell (Fig. 7.2) is... 

The correction for the increase of chloride ions due to the hydrolysis of the chlorine has largely eliminated the deviations between the observed and calculated values. 6. N. Lewis and F. F. Kupert find for the electrode potential of chlorine against the normal electrode to be —1 0795. F. Dolezalek measured the difference in the e.m.f. of two 5N- to 12A-hydrochloric acid cells of different strengths by the vap. press, method, and obtained satisfactory results. F. Boericke, G. N. Lewis and H. Storch found for the normal electrode potentials against hydrogen at 25°... 

Practically, AE is calculated by measuring the potential over two reference electrodes (e.g. Agl AgCl electrodes), each electrode being positioned at one side of the glass membrane (Fig. 3.4a). The potential of both reference electrodes is the same because they are identical, so if a difference in potential is measured over these electrodes, this difference should be related to the presence of the glass membrane. As explained above, the contribution of Ei is constant, so the potential difference measured over the entire cell system is related to E2, or to the hydrogen-ion activity of the solution of unknown pH. 

Here / is the current density with the subscript representing a specific electrode reaction, capacitive current density at an electrode, or current density for the power source or the load. The surface overpotential (defined as the difference between the solid and electrolyte phase potentials) drives the electrochemical reactions and determines the capacitive current. Therefore, the three Eqs. (34), (35), and (3) can be solved for the three unknowns the electrolyte phase potential in the H2/air cell (e,Power), electrolyte phase potential in the air/air cell (e,Load), and cathode solid phase potential (s,cath), with anode solid phase potential (Sjan) being set to be zero as a reference. The carbon corrosion current is then determined using the calculated phase potential difference across the cathode/membrane interface in the air/air cell. The model couples carbon corrosion with the oxygen evolution reaction, other normal electrode reactions (HOR and ORR), and the capacitive current in the fuel cell during start-stop. 

The free energies in (18) are illustrated in Fig. 10. It can be seen that GA is that part of AG ° available for driving the actual reaction. The importance of this relation is that it allows AGXX Y to be calculated from the properties of the X and Y systems. In thermodynamics, from a list of n standard electrode potentials for half cells, one can calculate j (m — 1) different equilibrium constants. Equation (18) allows one to do the same for the %n(n— 1) rate constants for the cross reactions, providing that the thermodynamics and the free energies of activation for the symmetrical reactions are known. Using the... 

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