Standard potential variation with temperature

The variation with temperature of the electrode potentials for pure water vapor and pure carbon dioxide at standard pressure is shown in Figure 25-1. 

The local conditions of temperature and pressure, as well as the new energy source in the form of the electrochemical gradient, can all be incorporated into the Gibbs free energy by adding new terms to the chemical potential. Variation of AG and AH with temperature are all standard thermodynamics, although we will resist the temptation to explore them here. 

For condensed phases (liquids and solids) the molar volume is much smaller than for gases and also varies much less with pressure. Consequently the effect of pressure on the chemical potential of a condensed phase is much smaller than for a gas and often negligible. This implies that while for gases more attention is given to the volumetric properties than to the variation of the standard chemical potential with temperature, the opposite is the case for condensed phases. 

Variation of the standard chemical potential with temperature... 

In general, the study of the variation of the formal electrode potential of a redox process with temperature has thermodynamic implications. Hence, one is interested in the measurement of AG°, AS° and AH° for the electron transfer process. It is recalled from thermodynamics that, under standard conditions, AE° is directly proportional to the free energy of the redox reaction according to the equation ... 

Variation of Reference Electrode Potentials with Temperature pH Values of Standard Solutions Used in the Calibration of Glass Electrodes Temperature vs. pH Correlation of Standard Solutions Used for the Calibration of Electrodes Solid Membrane Electrodes Liquid Membrane Electrodes... 

Standard electrode potentials of the Ag-AgI electrode were determined in the temperature range 5 °-35°C in 20-80 wt % ethylene glycol + diethylene glycol mixtures by emf measurements on the cell Pt-H2(g, 1 atm)/HOAC (mt), NaOAC (m2) KX (m3)/AgX-Ag in the solvent. The standard molal potentials Em°, in the various solvent mixtures have been expressed as a function of temperature. The various thermodynamic parameters for the transfer of hydrogen iodide from ethylene glycol to these media at 25° C are reported, and their variation with solvent composition is discussed. The transfer free energies of the proton and the iodide at 25°C, on the basis of the ferrocene reference method with ethylene glycol as the reference solvent, are also reported in the mixtures. 

The Variation of the Standard Potentials of Some Electrodes with the Temperature. In a number of cases the standard potentials of galvanic cells without liquid junctions have been determined over a range of temperatures. From these determinations it has been possible to prepare Table V, which gives the standard potentials of a number of electrodes at intervals of 12.5° from 0° to 50°. Some slight adjustments, of the order of 0.2 millivolt, of the original data have been necessary to bring the figures into accord with the Ho values at 25° adopted in this book. A more complete table of standard potentials of the elements at 25° will be found at the end of Chapter 14. 

Since every practical pH electrode can be regarded only as a somewhat imperfect tool that functions more or less unevenly over the whole pH range, and every practical pH reading involves a (possibly variable) liquid-junction potential, the NBS has adopted a series of six primary standard pH buffer solutions (Table 2.2). The pH of the standards is temperature dependent, primarily because of the variation of the Kg, of the buffer system with temperature. 

Based on the relation (2.50), the variation of the standard potential of an oxidation-reduction reaction with temperature and pressure is given by (2.51) and (2.52), respectively ... 

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

Despite its great potential, in the near future CFD will not completely replace experimental work or standard approaches currently used by the chemical engineering community. In this connection it is even not sure that CFD is guaranteed to succeed or even be an approach that will lead to improved results in comparison with standard approaches. For single-phase turbulent flows and especially for multiphase flows, it is imperative that the results of CFD analysis somehow be compared with experimental data in order to assess the validity of the physical models and the computational algorithms. In this connection we should mention that only computational results that possess invariance with respect to spatial and temporal discretization should be confronted with experimental data. A CFD model usually gives very detailed information on the temporal and spatial variation of many key quantities (i.e., velocity components, phase volume fractions, temperatures, species concentrations, turbulence parameters), which leads to in-... 

Here the point of reference is the chemical potential of i in pure form, at a pressure of one bar /l/(T, 1, x ) = jU,(T, l,c ) = fXi(T, 1, m ) = ixf(T, 1), known as the standard chemical potential for the pure material at temperature T. This is adopted regardless of the pressure under whieh the actual experiments are performed. The above expressions are self consistent. As usual, use of mole fractions for compositional variations offers the simplest formulation for the chemical potential. Also, in all three cases there are no problems with regard to units and dimensions. ... 

The equilibrium isotherms depend on the parameters that characterize the physical state of the system and the chemical potential of the compounds studied in this system selected, i.e., its temperature and pressure, the chemical compositions of the mobile and the solid phases. The last of these parameters is far more difficult to investigate than that of the other three. Suffice it to say that important variations of the isotherm parameters have been observed for different brands of Cig-bonded silica. However, the best isotherm model accormting for the adsorption data measured on these different brands remained the same [61] while the colmnn to column reproducibility of the data was excellent for at least one brand and probably for several others [11,121,122], with relative standard deviations for the parameters being of the order of a few percent [123]. 

Much has been written about the relative merits of standard free energies, enthalpies and entropies as fundamental properties to elucidate chemical processes (see, for example, Taft, 1956 Leffler and Grunwald, 1963 Hepler, 1963 Larsen and Hepler, 1969 Wells, 1968 Exner, 1964a, b Hammett, 1970 Bell, 1973). In our opinion this question can only be answered in terms of the use to which the data will be put. Since AG°, AH° and AS° at room temperature all contain kinetic energy (partition function) terms, none of these properties corresponds exactly to the potential energy. Physical organic chemists are not put off much by this fact since they are usually more concerned with how properties change in response to systematic variation of molecular structure or solvent than they arc in particular properties of individual compounds. 

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