Question

Problem 1. (concept question) 1) What is the Nernst equation and how to define for the electrochemical reaction (aA bBcC dD)? 2) What is Formal potential and why it is useful? 3) What is the Faraday's law and how it is defined (i.e. its relation)? 4) What is the reference electrode and what is it used for? What is the desired characteristic of reference electrode? Show three examples of reference electrode 5) What is the electrochemical double layer and how it is formed? 6) What is the roughness factor? How is it defined? 7) What is the exchange current density? 8) Relationship between current and applied voltage (or overpotential) can be described by Butler-Volmer equation, and it can be simplified at the various limiting conditions. Simply the BV equation for η → +0。 η -oo, η 0, and when αα-Ac, respectively 9) What is the limiting current density and how it is defined (i.e. its relation) for the condition of linear- concentration distribution of ionic species in the diffuse layer (i.e. N, - D,Derive a relation to calculate surface concentration with operating current density and limiting current density

Answer 1

1.) In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half-cell or full-cell reaction) to the standard electrode potential, temperature and activities(often approximated by concentrations) of the chemical species undergoing reduction and oxidation. It was named after Walther Nernst, a German physical chemist who formulated the equation.

Let us consider the following chemical reaction :

$aA + bB \rightleftharpoons cC + dD$

If 'n' number of mole of electrons are involved in this reaction, then Nernst equation regarding cell potential is,

$\mathbf{E_{cell} = E^{0}_{cell} - \frac{RT}{nF} ln\frac{[C]^{c} [D]^{d}}{[A]^{a} [B]^{b}}}$

where, $E_{cell} =$ EMF of the cell, $E^{0}_{cell} =$ standard EMF of the cell, T= temperature (in Kelvin scale), F= faraday.

[A], [B], [C] and [D] are active masses or activities of A, B, C and D respectively.

If the solution is dilute, then active mass of a species in the solution is approximately equal to its concentration.

$\therefore E_{cell} = E^{0}_{cell} - \frac{2.303 \times RT}{nF} log \frac{[C]^{c} [D]^{d}}{[A]^{a} [B]^{b}} ;$

At    $25^{o}$C, $\frac{2.303RT}{F} = 0.059 V$

$\mathbf{\therefore E_{cell} = E^{0}_{cell} - \frac{0.059}{n} log \frac{[C]^{c} [D]^{d}}{[A]^{a} [B]^{b}} ;}$

Thus, the Nernst equation for the equation  $aA + bB\rightarrow cC + dD$ can be defined as,

$\mathbf{E_{cell} = E^{0}_{cell} - \frac{RT}{nF} ln\frac{[C]^{c} [D]^{d}}{[A]^{a} [B]^{b}}}$