Standard state cell voltage

Example 13.10 Estimate the standard state cell voltage for the production of aluminum (Eq. 13.BF) at 298.15 K. 

Now if we combine a Zn-Zn+2 half-cell in its standard state with a H2-2H+ half-cell in its standard state, the voltage (potential) we measure (0.76 volt) is the value assigned to the halfreaction ... 

The cell potential E (also called the cell voltage or electromotive force) is an electrical measure of the driving force of the cell reaction. Cell potentials depend on temperature, ion concentrations, and gas pressures. The standard cell potential E° is the cell potential when reactants and products are in their standard states. Cell potentials are related to free-energy changes by the equations AG = —nFE and AG° = —mFE°, where F = 96,500 C/mol e is the faraday, the charge on 1 mol of electrons. 

When conditions are other than in the standard state, the voltage of a cell is given by the Nernst equation,... 

The plot at the bottom of Fig. 2 gives an example also for the stochastic ageing of cells in a stack, as observed by the steady-state cell voltages. The scatter observed between cells at the EoL has considerably inaeased compared with that at the BoL. hi fact the standard deviation inaeased from 5mV per measured channel of two cells to 52mV. 

The back e.m.f. is a voltage that opposes the passage of a current through an electrolytic cell. There are three sources of the back e.m.f. The first is the reversible back e.m.f. due to the cell reaction. For example, in a Daniell cell with unit activities the reversible back e.m.f. is the equilibrium standard-state cell potential of 1.100 V. For activities other than unit activities, the reversible back e.m.f. can be calculated from the Nernst equation. For an infinitesimal electrolytic current, the reversible back e.m.f. is the only contribution to the back e.m.f. For a finite current, the IR drop in the voltage across the electrolyte solution due to its electrical resistance also contributes. In many cases, we will be able to neglect this contribution. The third source of back e.m.f. for a finite current is the overpotential, which is due to the polarization of the electrode. 

Since concentration variations have measurable effects on the cell voltage, a measured voltage cannot be interpreted unless the cell concentrations are specified. Because of this, chemists introduce the idea of standard-state. The standard state for gases is taken as a pressure of one atmosphere at 25°C the standard state for ions is taken as a concentration of 1 M and the standard state of pure substances is taken as the pure substances themselves as they exist at 25°C. The half-cell potential associated with a halfreaction taking place between substances in their standard states is called ° (the superscript zero means standard state). We can rewrite equation (37) to include the specifications of the standard states ... 

In the discussion of the Daniell cell, we indicated that this cell produces a voltage of 1.10 V. This voltage is really the difference in potential between the two half-cells. The cell potential (really the half-cell potentials) is dependent upon concentration and temperature, but initially we ll simply look at the half-cell potentials at the standard state of 298 K (25°C) and all components in their standard states (1M concentration of all solutions, 1 atm pressure for any gases and pure solid electrodes). Half-cell potentials appear in tables as the reduction potentials, that is, the potentials associated with the reduction reaction. We define the hydrogen half-reaction (2H+(aq) + 2e - H2(g)) as the standard and has been given a value of exactly 0.00 V. We measure all the other half-reactions relative to it some are positive and some are negative. Find the table of standard reduction potentials in your textbook. 

The two half reactions of any redox reaction together make up an electrochemical cell. This cell has a standard potential difference, E , which is the voltage of the reaction at 25 °C when all substances involved are at unit activity. E refers to the potential difference when the substances are not in the standard state. E for a particular reaction can be found by subtracting one half cell reaction from the other and also subtracting the corresponding voltages. For example for reduction of Fe to Fe by H2, E° = 0.77 - 0 = 0.77 V. A further example is the oxidation of Fe " by solid Mn02 in acid solution. The half cell reactions are. 

If the reactants and products were in their standard states of unit activity, then of course the voltage (E°) is the "standard cell potential," and the change in free energy is the change in "standard free energy" (AG°) ... 

The cell in the preceding problem is, in a sense, a pH meter. Suppose one half-cell contained 1.00 M H+, the standard state. Describe the relationship (at 25°C) between the pH of the other half-cell and the observed voltage (connecting the positive terminal of the meter to the standard half-cell). 

Calculate the voltage of this fuel cell (for the standard states). (Hint Use data from Table 16-1.)... 

Example 10 illustrates how thermochemical data for aqueous ions may be obtained from measurements in electrochemical cells. The problem of measuring cell potentials in the standard state, which is a hypothetical state, will be discussed in section 10.12. The temperature variation of the voltage of such cells would provide AHJ of aqueous ions, through the use of Eq. (48). 

Equations (47)-(50) indicate how thermodynamic quantities can be obtained from cell potentials measured under standard conditions. However, standard states are hypothetical states (e.g., infinitely dilute behavior at 1.0 m concentration), which cannot be prepared in the cell. As a result, an extrapolation procedure is used to find 8° from measured cell voltages as a function of concentration. From Eq. (47), we write the dependence of 8 on the concentration of the electrolyte in the form... 

If both electrode processes operate under standard conditions, this voltage is E°, the equilibrium standard electrode potential difference. Values of E and E° may be conveniently measured with electrometers of so large an internal resistance that the current flow is nearly zero. Figure 3.1.6 illustrates the measurement and the equilibrium state. The value of E° is a most significant quantity characterizing the thermodynamics of an electrochemical cell. Various important features of E and E° will be addressed in the following chapters. 

If the electrode reactants and products are not in the standard state, the equilibrium cell voltage will be the difference between the E values (i.e. the corresponding activity terms have to be included). Consider again the cell consisting of the half reactions Ag+/Ag and H+/H2. The equilibrium potential difference between the two electrodes, E - E(2) - E(l), is represented in Equation (20). Considering that czAg - 1 and 0(H+/H2) = 0 V, Equation (20) is identical to Equation (18). 

Subsequent deployment of the new catalyst in the cathode layer of small-area MEAs first, then large-area MEAs, and finally fuel cell stacks represents the typical series of performance tests to check the practical viability of novel ORR electrocatalyst materials. Figure 3.3.15A shows the experimental cell voltage current density characteristics (compare to Figure 3.3.7) of three dealloyed Pt-M (M = Cu, Co, Ni) nanoparticle ORR cathode electrocatalysts compared to a state-of-the-art pure-Pt catalyst. At current densities above 0.25 A/cm2, the Co- and Ni-containing cathode catalysts perform comparably to the pure-Pt standard catalyst, even though the amount of noble metal inside the catalysts is lower than that of the pure-Pt catalyst by a factor of two to three. The dealloyed Pt-Cu catalyst is even superior to Pt at reduced metal loading. 

Learning a few electrical variables and their nnits will enable us to do electrochemical calculations, both for voltaic cells and for electrolysis cells. These are presented in Table 17.1. In this section, potential, also called voltage, is the important unit. Potential is the tendency for an electrochemical half-reaction or reaction to proceed. In this section, we will be using the standard half-cell potential, symbolized e°. Standard half-cell potentials can be combined into standard cell potentials, also symbolized e°. The snperscript ° denotes the standard state of the system, which means that the following conditions exist in the cell ... 

Recall from Chapters 12 and 13 that the standard state of a substance means a pressure of 1 atm and a specified temperature. In addition, the standard state of a solute is that for which its concentration in ideal solution is 1 M. The standard free energy change AG° for a reaction in which all reactants and products are in their standard states can be calculated from a table of standard free energies of formation AG° of the substances taking part in the reaction (see Appendix D). For reactions that can be carried out in electrochemical cells, the standard free energy change AG° is related to a standard cell voltage A ° by... 

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