Theoretical Electrochemistry

April 15, 2010

Fundamentals of Electrochemistry

Filed under: Electrochemistry — Murali Venkatraman @ 6:26 pm
1. The Electrochemical Interface and the potential difference
2. When a metal comes in contact with a solution, the double layer gets formed due to charge separation at the interface. This establishes a potential across the interface (Refer to Chapter 6 Bockris for more details). At equilibrium, the interface potential difference thus established due to the charge separation is termed the equilibrium potential difference given by the symbol $E_{eq}$ (Prof. Oldham prefers to call this $E_n$ or the null potential where there is no flow of charge). Experimentally this potential is immeasurable (see chapter 1 and 2 of Oldham for explanation on why it is immeasurable). When we say an interface is in equilibrium there is no net action. (The word net is important since such an equilibrium has been found to be dynamic and not static). Thus, this potential $E_{eq}$ by its own virtue, is incapable of causing a net transport of charges across the interface. Hence as with any system, if the interface is disturbed from the equilibrium, it would allow action which in our case is the transfer of electrons across the interface. This disturbance that the system experiences is called polarization. The disturbance could be natural (as in corrosion) or man-made (as in electrolysis). More scientifically natural is termed spontaneous and man-made is applied. As with any system in equilibrium, the disturbance or the polarization can be positive (anodic) or negative (cathodic). Hence if the polarization of the interface is performed to the extent that the potential difference across the interface has a value E, the departure of the interface from the equilibrium or null value is given by$E-E_{eq}$ which is also called the overpotential of the system and given by the symbol $\eta$. This overpotential could be a result of activation, concentration and/or ohmic (See Oldham book for more explanation). This departure from equilibrium of an electrode is characterized by a current flow through it, that is a net charge transfer across the interface.

3. Measuring $E_{eq}$
4. Note that $E_{eq}$ of an isolated electrode was deemed immeasurable. However, one can easily recognize that the value of $E_{eq}$ is dependent on the two materials, their physical state (for example, concentration) and other operating conditions like temperature, pressure etc. and hence is different for different interfaces. Thus there arises a need for quantifying $E_{eq}$ so that we can usefully compare interfaces. However, one also does recognize that there are infinite possibilities of having an interface even for the same 2 materials. For example, a solution of 1M $\rm Zn^{2+}$ ions in contact with a zinc electrode would have a much different $E_{eq}$ value than one in which say 0.01 M since charge separation characteristics would be different. Thus we have three issues concerning $E_{eq}$: They are:

1. $E_{eq}$ of an interface is not measurable
2. $E_{eq}$ of the interfaces differ considerably and depend strongly upon the materials that constitute the interface
3. Even with the same materials that make the interface, $E_{eq}$ depends strongly on the composition of the materials

But one recognizes that if at least the value of $E_{eq}$ for one system is known, the others can somehow be compared with it. Or in other words, the difference is what matters. Hence, to alleviate such difficulties, it was proposed to define the $E_{eq}$ of one of the interfaces, the constituents and the composition of which are known, to be zero arbitrarily. The value at other interfaces would then be obtained in reference to this chosen interface.

5. The Standard Hydrogen Electrode – Reference
6. This happens to be the Standard Hydrogen Electrode (SHE) in which 1M H+ ions are in equilibrium with hydrogen gas bubbled at 1 atm pressure at 25 deg C on a platinised platinum electrode. Note that this value is taken to be zero and not absolutely zero. However, electrochemistry concerns itself only with differences in potentials and hence this definition of reference $E_{eq}$comes extremely handy in calculations. (refer to Bockris for an interesting discussion on absolute value of potential of this interface). The reference $E_{eq}$ of the SHE is given a special symbol $E_{{{\rm{H}}^ + }/{{\rm{H}}_2}}^0$. However, one does recognize that the sign of$E_{eq}$depends on the spatial direction that whether the field is directed from the solution to the metal or from the metal to the solution. Hence, once again arbitrarily reduction direction is taken to be positive. That is at the metal/solution interface, the electric field is taken to be positive in that direction which favors the reduction of the ion in the solution. In case of H+ ions in the solution, the reaction can be written as:

$\rm{2H^{+} + 2e^{-}\underset{{{k_b}}}{\overset{{{k_f}}}{ \rightleftharpoons}} H_2}$

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