Simplify the Nernst equation for standard laboratory conditions. For E = Eo – (RT/zF) Ln (aRed/aOx), we can treat RT/F as a constant where F = 298 degrees Kelvin (25 degrees Celsius). RT/F = (8.314 x 298) / 96,485 = 0.0256 Volts (V). Thus, E = Eo – (0.0256 V/z) Ln (aRed/aOx) at 25 degrees C.

The Nernst equation is used to determine the potential of a cell. n or z (from Zahl for “number”) is the number of moles of electrons transferred in the cell reaction.

2.303 is a conversion factor from natural log to log10. R = Gas constant, 8.135 J K-1 mol-1. T = temperature in K (273 + temp in oC)

The Nernst Equation empowers the assurance of cell potential under non-standard conditions and relates the measured cell potential to the reaction quotient and permits the exact measurement of equilibrium constants.

Here, two moles of electrons are transferred in the reaction. Therefore, n = 2. The reaction quotient (Q) is given by [Cd2+]/[Pb2+] = (0.02M)/(0.2M) = 0.1. Thus, the cell potential of this electrochemial cell at a temperature of 25oC is 0.3066 volts.

The Nernst Equation allows for cell potential determination under non – standard conditions. It relates the measured cell potential to the quotient of the reaction and allows the exact determination of constants of equilibrium (including constants of solubility).

2.303 is a conversion factor from natural log to log10. Log is commonly represented in base-10 whereas natural log or Ln is represented in base e. Now e has a value of 2.71828.

– nFE red = – nFE° red + RT ln [M]/ [M n+] = – nFE° red + 2.303 RT log [M] n / [M n+ ] The activity of the metal is, always considered as equal to unity. This relation connecting reduction potential measurable at conditions other than standard conditions to the standard electrode potential is the Nernst equation.

Limitations of Nernst Equation The activity of an ion in a very dilute solution is close to infinity and can, therefore, be expressed in terms of the ion concentration. However, for solutions having very high concentrations, the ion concentration is not equal to the ion activity.

The relationship between the Nernst equation, the equilibrium constant, and Gibbs energy change is illustrated below. Converting the natural logarithm into base-10 logarithm and substituting T=298K (standard temperature), the equation is transformed as follows.