The experimental data and results for [Fe (CN)6]-3/-4 system.
Thermoelectrochemistry (TEC) is a subject that combines the theories and techniques of both thermo- and electro-chemistry to investigate the cell and electrode reactions . That is, the parameters of thermodynamics [2-4] and kinetics  of the electrochemical reactions can be obtained by the simultaneous measurements and analysis of heat flow, electrode potential, electric current and time signals under the various conditions. Therefore, TEC can provide the availably and expansively additional information more for electrochemical reactions. It compensates the insufficiency for a single electrochemical study or a single thermochemical research to some extent. In earlier period, a lot of techniques and instruments used to research the heat effects of cell and half-cell was set up [6-30], such as thermoelectric power measurements [6,7], electrolytic calorimeter , controlled-potential and controlled-current polarizations , Kinetic method on the stationary heat effect , non-stationary temperature wave method , cyclic-voltammo-thermometry, Lumped-heat-capacity analysis , steady state electrolysis , differential voltammetric scanning thermometry , acoustic calorimetry, thermistor probe determination, potentiodynamic and galvanostatic transient techniques , non-isothermal cell , etc to obtain the electrochemical Peltier heat (EPH) of the electrode reactions.
In these researches, a mainly purpose is to acquire EPHs of cell or half-cell reactions. The EPH could be considered as a basic issue of TEC. Before the identification of this problem there had been two puzzled questions, one is that the heat effects for a reversible reaction,
In order to identify EPHs of the cell or electrode reactions from the experimental information, there had been two principal approaches of treatments. One was based on the heat balance under the steady state or quasi-stationary conditions [6, 11, 31]. This treatment considered all heat effects including the characteristic Peltier heat and the heat dissipation due to polarization or irreversibility of electrode processes such as the so-call heats of transfer of ions and electron, the Joule heat, the heat conductivity and the convection. Another was to apply the irreversible thermodynamics and the Onsager's reciprocal relations [8, 32, 33], on which the heat flux due to temperature gradient, the component fluxes due to concentration gradient and the electric current density due to potential gradient and some active components’ transfer are simply assumed to be directly proportional to these driving forces. Of course, there also were other methods, for instance, the numerical simulation with a finite element program for the complex heat and mass flow at the heated electrode was also used .
2. Electrochemical Peltier heat and the absolute scale
2.1. The electrochemical Peltier heat of cell reaction
The terminology of EPH originated from the thermoelectric phenomena in Physics. Dated back to more than 100 years ago, such as the Seebeck effect, the Peltier effect and the Thomson effect were successionally discovered. The Peltier heat was first found by the French physicist Peltier in 1834. The Peltier effect shows that the heat flow would be generated on the junction between two different metals in an electric current circumstance. The junction acts as a heat sink or as a heat source, which depends on the direction of the electric current. And the strength of the heat was found to be proportional to the current intensity. The Peltier effect can express as 
The Peltier effect is a reverse one of the Seebeck effect that was discovered by the German physicist Seebeck at earlier period (1822). Seebeck discovered that a potential difference will be resulted between two connection points in a loop composed of two dissimilar metals, if the two junctions are maintained at different temperatures. Thereafter, in 1854, the English physicist Lord Kelvin (W. Thomson) was to discover that a uniform conductor with electric current passing through will suck heat up from the surrounding when there has a temperature gradient in the conductor, which is called as the Thomson effect.
In 1877, Mill called the heat effects in the electrochemical reactions as the electrochemical Peltier heats. Later, Bouty and Jahn demonstrated experimentally the EPH effects. Subsequently, a few of experimental studies on the heat effects for the electrochemical cells had also been presented. However, the heat effects in physics are different from those in electrochemical reactions. No distinct definition for EPH was given in history, except it was defined as the heat effects observed when electric current passes through. Obviously, this definition is not precise.
Vetter has elegantly defined the EPH effect to be the heat arising out or the heat consumption in a reversible cell reaction, i.e.
Two features of this definition are worth noting. One is that EPH is defined as the heat of a reversible reaction, which essentially eliminates the various uncertainties arising from the irreversible factors such as overvoltage, Joule heat, thermal conductivity, concentration gradient and forced transfer of various particles like ions and electrons in electrical field, and makes the physical quantity more definite and comparable. This indicates that EPH is a characteristic measure of a cell reaction, because the term (∂ (
Another one is that the thermodynamic functions of the standard hydrogen electrode (SHE) are taken as the reference of Δ
This definition, where
2.2. The electrochemical Peltier heat of electrode reaction and the absolute scale
When applying the Vetter’s definition to a reversible electrode (or half-cell) reaction, it is no longer able to use the conventional scale as the reference of the free energy change and the electrode potential. Otherwise, for the SHE reaction itself, we will draw a conclusion that the heat effects of the reaction are always zero in all temperatures. Obviously this is not true, because even the SHE reaction, certainly there are the “old” chemical bond fracturing and a “new” chemical bond constructing process accompanied by the emergence of the heat effect . Then where does the problem come from? Look at the SHE reaction:
In the conventional scale, the entropy of the hydrogen ion and the change in entropy of this reaction are all arbitrarily set at zero, which would result in a bigger difference between these quantities and the “real” values. Just this entropy that is arbitrarily specified to the hydrogen ion is taken as reference point of the other ion entropies once again. This will also make the calculated entropy change differ from the “real” value for other electrode reaction. Therefore, the heat effect calculated based on the change in entropy of the reaction must differ from that obtained experimentally. In this case, in order to make the calculated result much approximate to the experimental data, we should adopt a new reference scale, i.e. the “absolute scale” as the reference, in which the enthalpy change, the entropy change, the free energy and its standard electrode potential for the SHE reaction are not able to be arbitrarily specified as zero. Define the reversible electrode potential of any electrode,
where the amount marked with an asterisk is on the “absolute scale” (the same below),
On this scale, the entropy change for a single-electrode reaction, Δ
When integrating Eq. (6), the integral constant, Δ
The resultant EPH of the electrochemical reaction,
The definition of EPH for the electrode reaction given by Eq. (7) or Eq. (8) is all similar to that of a cell reaction except on the absolute scale. These equations indicate that EPH of a half-cell, just like that of the cell reaction, is also a characteristic quantity that only relates to changes in the function of state, i.e. the entropies on the absolute scale, of substances taking part in the reaction. The heat effect occurs on the electrode-electrolyte interfaces. Evidently, when Eq. (7) or Eq.(8) is applied to a cell reaction, the terms,
The establishment of the absolute scale is dependent on determination of Δ
with the integral range from zero to a designated temperature
It should be pointed out that a specified reference is
Although the formula is confirmed to be correct in many cases, for the electrode reaction where the hydrated ions and the electrons would take part in it, the validity is to be confirmed. Even,
3. The basic equations for thermoelectrochemistry and experiments for determination of the entropy change of SHE on absolute scale
3.1. The basic equations for thermoelectrochemistry
It has been mentioned above that two methods, the heat balance under the steady state or quasi-stationary conditions, and the irreversible thermodynamics and Onsager's reciprocal relations, had been used to treat the heat effects in the electrochemical reactions. Although these methods can determine EPH of electrode reaction under some assumption, they are helpless to answer those problems presented in introduction.
Here a method based on the equilibrium thermodynamics will be introduced. In Eq.(5), a relationship between the electrode potentials on the absolute scale and the conventional scale is given. According to the relationship, the thermodynamic functions such as the entropy
For a reversible electrode reaction, on the absolute scale, we still have the following relationship
When a small electric current passes through, Eq. (17) can be approximately written, as
Being differential on both sides of Eq. (19) and letting
3.2. An experiment for evaluation of the entropy change of SHE on the absolute scale
As shown by Eq. (9), if Δ
The heat effects were determined by temperature-rise calorimetry. The experimental setup is shown by Fig. 1.
A three-electrode system with a platinum working (
controlled the isothermal surrounding with 0.001 K fluctuations. Another thermo-sensitive resistor (
The [Fe(CN)6]-3/-4+1mol.dm-3 K C l solutions were prepared with equal molar concentrations of the two negative ions being 0.075 mol.dm-3, 0.15 mol.dm-3, 0.2 mol.dm-3, 0.25 mol.dm-3and 0.3 mol.dm-3, respectively. The experiments were done at 298.15K. The experimental data are in table 1, and the typical experimental curves for electrode potentials against time and the potential signals for temperature difference against time for the 0.2 mol.dm-3 [Fe(CN)6]-3/-4 system are shown in Fig. 2.
3.3. Experimental data-processing and evaluation of entropy change of SHE on the absolute scale
The redox equation considered in this experiment is as follows:
When a small electric current passes through, Eq. (18) can be approximately written as
Noting that and at
Considering a thermodynamic principle which holds that the enthalpy of the solute at unlimited dilution is always equal to that at the standard state, when the standard state is designated to a hypothetical solution which obeys Henry’s law at unit molal concentration of solute , we can write
Consequently, Eq.(24) can be rewritten as
The values of Δ
|−ΔH Ø(c) / kJ. mol-1||86.67||93.75||98.17||102.07||106.96|
|−Π (c) / kJ. mol-1||39.97||46.57||50.51||54.70||58.98|
From table 2, plot Δ
3.4. Relationship between the quantities determined by TEC technology and those calculated with the current thermodynamic databank of ions
A mathematical expression of the first law of thermodynamics for an infinitesimal process is as follows
where the electric work done is appointed to the reference of SHE. This is an expression of the first law of thermodynamics.
When the law is used to an electrode reaction with the given electron transfer number at the given temperature, the enthalpy change calculated based on the electric work done and the heat effect obtained experimentally differs from that calculated by Eq.(30) on the current thermodynamic databank including the ion data. The difference between them is almost a constant. For this phenomenon it has been not yet explained reasonably so far, and this greatly influenced the development of thermoelectrochemistry.
It should be seen from Eq.(15) that the value on TEC experiments is the apparent enthalpy change, while the value calculated by Eq.(30) on the current thermodynamic databank is the enthalpy change of the electrode reaction on the conventional scale. They just differ by a constant that is z
In Eq. (30),
3.5. About the absolute value of thermodynamic function on the absolute scale
When these thermodynamic functions on the absolute scale are applied to a cell reaction, all terms concerning with SHE on the absolute scale, such as Δ
Here an issue is whether or not the potential of single electrode on the absolute scale is a “real” value? It should be said that the potential of electrode is not its “real” value in absolute sense, and the thermodynamic functions on the absolute scale like Δ
4. Some application of the basic equations for thermoelectrochemistry
4.1. The partial molal entropies of hydrogen ion and some other hydrated ions on the absolute scale
According to Eq.(4),
where and are the partial molal entropy of electron and hydrogen ion on the absolute scale, respectively. Substituting the corresponding data, 87.6, 65.29 and 0 for Δ
where Nz represents ion with the z valence of positive (z >0) or negative (z<0) ion. Table 3 gives the entropies for some hydrated ions on absolute scale based on the data for ion entropies from Ref. .
4.2. The electrochemical Peltier heats and the Peltier coefficients of the standard electrode reactions
Similar to the [Fe(CN)6]-3/-4 redox couple, EPH of an electrode reaction can directly be measured by the thermoelectrochemical experiments. However, it is hard to measure EPH of an electrode reaction at the standard state directly, because the standard state chosen usually in thermodynamics is even physically unrealizable in most cases. According to Eq.(8), EPH of a standard electrode reaction can be determined provided that Δ
Like this, the second problem mentioned in introduction, that is, how to seek a feasible method to calculate or predict the “real” heat effect of a standard reversible electrode reaction, is also resolved.
|H++ e- =0.5H2||87.6 ±1.0||0.271||26.1±0.3||Am3++3e-=Am||288.6±3.0||0.297||86.1±0.9|
|Ag++ e- = Ag||-8.6±1.0||-0.027||-2.6±0.3||Ce4++4e-=Ce||462.0±4.0||0.357||137.8±1.2|
|Sr2++2e-= Sr||132.2±2.0||0.204||39.4±0.6||Fe (CN) 6-3+e-= Fe (CN)6-4||-153.0±1.0||-0.473||-45.6±0.3|
4.3. Determination of the electric potentials of the standard electrode by Δ
The standard electrode potential of an electrode is a very important electrochemical quantity. Conventionally, it is determined by the extrapolating the electrode potentials of extremely dilute solution along the line predicted by the Debye-Hückel theory. Nevertheless, in the thermoelectrochemistry, it can be obtained by the measurement of the apparent enthalpy change. Based on a thermodynamic principle mentioned above (see Eq. (25)), Eq.(16) can be rewritten as
where the superscript “∅” represents the standard state. Therefore, if Δ
For the [Fe(CN)6]-3/-4 couple, when
4.4. The enthalpy change and entropy change at designated concentration
c, and diluted heats and diluted entropies of ions
The enthalpy change, Δ
According to the thermal cycle, the corresponding computing equations are following
Noting that Δ
|-ΔHØ(c) / kJ. mol-1||11.27||9.52||8.25||6.46||5.23|
Similarly, the dilute entropy, Δ
In a word, because the apparent enthalpy, Δ
5. Application to hydrometallurgy
The Seebeck effect has been used for the power generation practice. This is called as the thermoelectricity. Now, an application of thermoelectrochemistry to hydrometallurgy has been explored. The hydrometallurgy is a kind method that the valuable metals are separated and extracted from the corresponding ores or concentrates mainly by aqueous solution treatment. The leaching is a very important process in this method, by which the valuable metals are transformed into metallic or complex hydrated ions. By the subsequent purified and separated from impurity, the valuable components are extracted. In the direct leaching process, usually, the ores or concentrates are mixed with the acidic or the basic solution or the solution with the redox. A large amount of heats is suck up from surrounding or released out during the leaching. The heats are completely wasted except heating the leaching solution sometimes. The leaching heat effect,
For the wet-extraction of copper, the chalcopyrite (CuFeS2) is usually used as the raw materials, and the leaching reagent is the ferric sulphate. Its leaching reaction is
In the direct leaching, the released energy due to the disaggregation of the raw materials is educed as the heats. The energy that can do useful work could not be effectively released and functioned. If the power generation leaching is chosen, the galvanic cell could be constructed as shown by the following diagram,
The salt bridge or a kind of ionic membrane suited to the leaching system is located between the anodic and cathodic compartments. The electrode reactions are as follows,
The cell reaction is corresponding to Eq.(37). When the reaction progresses reversibly, the electric work could achieve about 100 kJ.mol-1 at room temperature.
Apparently, in the power generation leaching, a part of the energy due to the disaggregation of the ores or concentrates will be released as the electric work. Bockris had defined a coefficient as
In the leaching with the galvanic cell, the element sulfur produced due to its insolubility would cover the surface of ores or the concentrate particles, inhibiting the further progress of the chalcopyrite leaching. When a kind of microorganism,
The maximum electric work done could achieve about 1100 kJ.mol-1, when the reaction would be reversible at room temperature. That is to say, the power generation leaching would create a probability that the chemical energy of an electrochemical reaction transfers to the useful electric work.
In order to make the reaction progress under a high oxidation potential, the bacteria,
In a word, this power generation leaching not only can generate electricity, but also reduce the purified steps of the leaching solution and the reagents consumption as well as is able to adjust the reaction evolution by control of the power output. From the point of view of the economy and ecological protection, this is a worthy advocating method.
In this chapter, a very important thermodynamic quantity, the electrochemical Peltier heat of a single electrode process, and some concepts related to this quantity have been discussed. They include the definition about EPH and the Peltier coefficient for the electrode process, the absolute scale, and the fundamental equations on this scale for thermoelectrochemistry. The equations on this scale, actually, are a special depiction of the first and second laws of the thermodynamics used to the electrode reactions. Firstly, the energy conservation equation with a new form based on the classical equilibrium thermodynamics is set up. A new reference point for the heat effects and the enthalpy change is designated in the equation, that is both
That is, the stipulation of ΔS* T→0 = 0 would be also fit to the third law of thermodynamics.
To sum up, the set up of the absolute scale and the evaluation of the change in entropy of SHE on this scale are useful to resolve those two problems which are mentioned at the beginning of this chapter. From this, one can get the relationship between the thermodynamic functions on the conventional and the absolute scale, and obtain the changes in entropy on the absolute scale and EPHs for electrode reactions, as a result greatly enriching the thermodynamic database. This also provides a new scale to study the electrode reaction, being valuable to the further development of the thermoelectrochemistry.
Thermoelectrochemical applications have now been extended in many areas, especially in the surface-electrochemical treatment of the functional materials, electrode modifying, and the charge and discharge-control of the batteries. The application to hydrometallurgy has also been explored.
The author would like express his gratitude to the National Natural Science Foundation of China (No.50874119, No. 50374077) for the financial support.