The Nernst equation is used in electrochemistry and is named after physical chemist Walther Nernst. The general form of the Nernst equation determines the point at which an electrochemical half-cell reaches equilibrium. A more specific form determines the total voltage of a full electrochemical cell and an additional form has applications within a living cell. The Nernst equation uses the standard half-cell reduction potential, the activity of the chemical in the cell and the number of electrons transferred in the cell. It also requires values for the universal gas constant, the absolute temperature and the Faraday constant.

### Step 1

Define the components of the general Nernst equation. E is the half-cell reduction potential, Eo is the standard half-cell reduction potential, z is the number of electrons transferred, aRed is the reduced chemical activity for the chemical in the cell and aOx is the oxidized chemical activity. Furthermore, we have R as the universal gas constant of 8.314 Joules/Kelvin moles, T as the temperature in Kelvin and F as the Faraday constant of 96,485 coulombs/mole.

### Step 2

Calculate the general form of the Nernst equation. The form E = Eo - (RT/zF) Ln (aRed/aOx) provides the half-cell reduction potential.

### Step 3

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.

### Step 4

Convert the Nernst equation to use a base 10 logarithm instead of the natural logarithm for greater convenience. From the law of logarithms, we have E = Eo - (0.025693 V/z) Ln (aRed/aOx) = Eo - (0.025693 V/z) (Ln 10) log10 (aRed/aOx) = Eo - (0.05916 V/z) log10 (aRed/aOx).

### Step 5

Use the Nernst equation E = RT/zF ln (Co/Ci) in physiological applications where Co is the concentration of an ion outside a cell and Ci is the concentration of the ion inside the cell. This equation provides the voltage of an ion with charge z across a cell membrane.