Standard-state cell potential

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. 

The standard state cell potential is simply the sum of the standard state potentials of the corresponding half reactions. The cell potential for a galvanic cell is always positive a galvanic cell always has chemical energy that can be converted to work. The real cell potential depends upon the half reactions, the concentrations of the reactants and products, and the temperature. 

The standard state cell potential for this reaction is ... 

Consequently, by measuring the zero-current cell potential we obtain the standard state Gibbs free energy change on reaction (if all the ions are in their standard states). Now if we continue further and measure how the zero-current standard state cell potential varies as a function of temperature, we have... 

Consequently by knowing the zero - current, standard state cell potential... 

The equation E° = InZ relates the standard state cell potential for a chemical... 

The standard-state cell potential difference of this cell is -0.2223 V, the negative of that of the cell of Figure 8.2. Hydrogen gas at the same pressure is fed into both hydrogen electrodes and the two HCI solutions are at the same concentration. A wire is connected between the two hydrogen electrodes and maintains them at the same electric potential. We can write... 

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. 

Substituting known values for the standard-state reduction potentials (see Appendix 3D) and the concentrations of Ag+ and gives a potential for the electrochemical cell in Figure 11.5 of... 

Thus far, we have based all of our calculations on the standard cell potential or standard half-cell potentials—that is, standard state conditions. However, many times the cell is not at standard conditions—commonly the concentrations are not 1 M. We may calculate the actual cell potential, Ecell, by using the Nemst equation ... 

Throughout this discussion we have considered cells in which the electrolytic solution is an aqueous solution. The same methods can be used to define standard half-cell potentials in any solvent system. However, it is important to remember that when the reference state is defined as the infinitely dilute solution of a solute in a particular solvent, the standard state depends upon that solvent. The values so obtained are not interchangeable between the different solvent systems. Only if the standard states could all be defined independently of the solvent would the values be applicable to all solvent systems. 

Standard half-cell potentials in aqueous solutions (T = 298 K, Standard state = 1 molal)... 

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 ... 

Therefore for a given reaction to take place, the cell potential must be positive. The cell potential is taken as the difference between the two half-cell reactions, the one at the cathode minus the one at the anode. The half-cell potential exists because of the difference in the neutral state compared to the oxidized state, such as Fe/Fe + or, at the cathode, the difference between the neutral state and the reduced state, as in These reduction-oxidation (redox) potentials are measured relative to a standard half-cell potential. The chart shown in Table 2 lists potentials relative to the which is set as zero. 

This equation allows one to compute the chemical equilibrium constant from measured standard-state electrochemical cell potentials (usually referred to as standard cell potentials). Some standard half-cell potentials are given in Table 14.6-1. The standard potential of an electrochemical cell is obtained by combining the two relevant half-cell potentials. 

The Nernst equation relates the reduction potential of an electrochemical cell to a standard-state reduction potential, along with the temperature, reaction quotient, and number of electrons transferred during the reaction in question. It was first developed by Walther Nernst, who won the Nobel Prize in Chemistry in 1920 for his influential work in physical chemistry. 

The dissipated heat is not the enthalpy differences, since the system is cyclic heat of reaction in forward and backward directions are balanced. As Eqn (e) shows that for an open biochemical network, fluxes and concentrations are important observable variables. Spectroscopic measurements show that concentrations of biochemical species in living cells are fluctuating. Concentrations and the standard state chemical potentials fi° yield the nonequilibrium chemical potentials. 

Despite the apparent ease of determining an analyte s concentration using the Nernst equation, several problems make this approach impractical. One problem is that standard-state potentials are temperature-dependent, and most values listed in reference tables are for a temperature of 25 °C. This difficulty can be overcome by maintaining the electrochemical cell at a temperature of 25 °C or by measuring the standard-state potential at the desired temperature. 

Another problem is that the Nernst equation is a function of activities, not concentrations. As a result, cell potentials may show significant matrix effects. This problem is compounded when the analyte participates in additional equilibria. For example, the standard-state potential for the Fe "/Fe " redox couple is +0.767 V in 1 M 1TC104, H-0.70 V in 1 M ITCl, and -H0.53 in 10 M ITCl. The shift toward more negative potentials with an increasing concentration of ITCl is due to chloride s ability to form stronger complexes with Fe " than with Fe ". This problem can be minimized by replacing the standard-state potential with a matrix-dependent formal potential. Most tables of standard-state potentials also include a list of selected formal potentials (see Appendix 3D). 

Standard Hydrogen Electrode The standard hydrogen electrode (SHE) is rarely used for routine analytical work, but is important because it is the reference electrode used to establish standard-state potentials for other half-reactions. The SHE consists of a Pt electrode immersed in a solution in which the hydrogen ion activity is 1.00 and in which H2 gas is bubbled at a pressure of 1 atm (Figure 11.7). A conventional salt bridge connects the SHE to the indicator half-cell. The shorthand notation for the standard hydrogen electrode is... 

Electrode Potential (E) the difference in electrical potential between an electrode and the electrolyte with which it is in contact. It is best given with reference to the standard hydrogen electrode (S.H.E.), when it is equal in magnitude to the e.m.f. of a cell consisting of the electrode and the S.H.E. (with any liquid-junction potential eliminated). When in such a cell the electrode is the cathode, its electrode potential is positive when the electrode is the anode, its electrode potential is negative. When the species undergoing the reaction are in their standard states, E =, the stan-... 

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 ... 

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 ... 

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