Cell potential temperature dependence

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. 

Fig. 6. 13 The variation of the standard potential of a cell with temperature depends on the standard entropy of the cell reaction.

In general, the cell potential also depends on the concentrations of the reactants and products in the ceU and the temperature (which we will assume to be 25 °C unless otherwise noted). Under standard conditions (1 M concentration for reactants in solution and 1 atm pressure for gaseous reactants), the cell potential is called the standard cell potential ( u) or standard emf. For example, the standard cell potential in the zinc and copper cell desalbed previously is 1.10 volts. 

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. 

The numerical values of cell potentials and half-cell potentials depend on various conditions, so tables of standard reduction potentials are true when ions and molecules are in their standard states. These standard states are the same as for tables of standard enthalpy changes. Aqueous molecules and ions have a standard concentration of 1 mol/L. Gases have a standard pressure of 101.3 kPa or 1 atm. The standard temperature... 

Electron movement across the electrode solution interface. The rate of electron transfer across the electrode solution interface is sometimes called k. This parameter can be thought of as a rate constant, although here it represents the rate of a heterogeneous reaction. Like a rate constant, its value is constant until variables are altered. The rate constants of chemical reactions, for example, increase exponentially with an increasing temperature T according to the Arrhenius equation. While the rate constant of electron transfer, ka, is also temperature-dependent, we usually perform the electrode reactions with the cell immersed in a thermostatted water bath. It is more important to appreciate that kei depends on the potential of the electrode, as follows ... 

It is of interest to consider the temperature dependence of the potential of an electrochemical cell. For an isothermal reaction [Equation (7.26)]... 

The overall rate of an electrochemical reaction is measured by the current flow through the cell. In order to make valid comparisons between different electrode systems, this current is expressed as cunent density,/, the current per unit area of electrode surface. Tire current density that can be achieved in an electrochemical cell is dependent on many factors. The rate constant of the initial electron transfer step depends on the working electrode potential, Tlie concentration of the substrate maintained at the electrode surface depends on the diffusion coefficient, which is temperature dependent, and the thickness of the diffusion layer, which depends on the stirring rate. Under experimental conditions, current density is dependent on substrate concentration, stirring rate, temperature and electrode potential. 

Work done with electrochemical cells, with particular reference to the temperature dependence of their potentials, has demonstrated that an accurate value for S (H h, aq) is — 20.9 J K mol-1. Table 2.15 gives the absolute molar entropies for the ions under consideration. The values of the absolute standard molar entropies of the ions in Table 2.15 are derived by using the data from Tables 2.13 and 2.14 in equations (2.51) and (2.57). 

Later in this chapter, we ll see that cell potentials, like free-energy changes, depend on the composition of the reaction mixture. The standard cell potential E° is the cell potential when both reactants and products are in their standard states—solutes at 1 M concentrations, gases at a partial pressure of 1 atm, solids and liquids in pure form, with all at a specified temperature, usually 25°C. For example, E° for the reaction... 

Cell potentials, like free-energy changes (Section 17.10), depend on temperature and on the composition of the reaction mixture—that is, on the concentrations of solutes and the partial pressures of gases. This dependence can be derived from the equation... 

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. 

Standard emf Values for the Cell H2/HCl/AgCl, Ag in Various Aqueous Solutions of Organic Solvents at Various Temperatures Temperature Dependence of the Standard Potential of the Silver Chloride Electrode Standard Electrode Potentials of Electrodes of the First Kind Standard Electrode Potentials of Electrodes of the Second Kind Polarographic Half-Wave Potentials (E1/2) of Inorganic Cations Polarographic E1/2 Ranges (in V vs. SCE) for the Reduction of Benzene Derivatives Vapor Pressure of Mercury... 

The numerical value of an electrode potential depends on the nature of the particular chemicals, the temperature, and on the concentrations of the various members of the couple. For the purposes of reference, half-cell potentials are taken at the standard states of all chemicals. Standard state is defined as 1 atm pressure of each gas (the difference between 1 bar and 1 atm is insignificant for the purposes of this chapter), the pure substance of each liquid or solid, and 1 molar concentrations for every nongaseous solute appearing in the balanced half-cell reaction. Reference potentials determined with these parameters are called standard electrode potentials and, since they are represented as reduction reactions (Table 19-1), they are more often than not referred to as standard reduction potentials (E°). E° is also used to represent the standard potential, calculated from the standard reduction potentials, for the whole cell. Some values in Table 19-1 may not be in complete agreement with some sources, but are used for the calculations in this book. 

This intermolecular potential for ADN ionic crystal has further been developed to describe the lowest phase of ammonium nitrate (phase V) [150]. The intermolecular potential contains similar potential terms as for the ADN crystal. This potential was extended to include intramolecular potential terms for bond stretches, bond bending and torsional motions. The corresponding set of force constants used in the intramolecular part of the potential was parameterized based on the ab initio calculated vibrational frequencies of the isolated ammonium and nitrate ions. The temperature dependence of the structural parameters indicate that experimental unit cell dimensions can be well reproduced, with little translational and rotational disorder of the ions in the crystal over the temperature range 4.2-250 K. Moreover, the anisotropic expansion of the lattice dimensions, predominantly along a and b axes were also found in agreement with experimental data. These were interpreted as being due to the out-of-plane motions of the nitrate ions which are positions perpendicular on both these axes. 

The emf of a cell or battery depends on the concentration of electrolyte. Calculate the emf of a charged and discharged lead-acid cell that has 29% by weight of sulfuric acid when it is fully charged. On discharge of this cell, the concentration of acid reduces to 21 % by weight. Assume that the temperature is 25 °C and the standard potential (E°) for both concentration is 2.0359 V. (Bhardwaj)... 

Professor S. Srinivasan and his team have studied the effect of pressure and characteristics of the current-potential relations in a hydrogen-oxygen fuel cell with a proton exchange membrane (Y. W. Rho, O. A. Velev, S. Srinivasan, and Y. T. Kho,./. Electrochem. Soc. 141 2084, 2089, 1994). In this problem, it is proposed to study the applicability of the theoretical dependence of the cell potential as a function of pressure. The temperature is 25 °C and it may be assumed that the pressure of the gas in each of the compartments, i.e., the anodic compartment (hydrogen) and the cathodic compartment (oxygen), are the same, Pn =Po P- For the formation of water in its standard state, the relevant thermodynamic quantities are ... 

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