Within electrochemistry, the *Nernst Equation* reveals the quantitative connection between the concentrations of compounds and cell potential.

**The Nernst Equation**

The Nernst Equation allows us to relate the reduction potential of an electrochemical reaction to the concentration, temperature and standard cell potential of a species. Its equation is:

**Standard Cell Potential (E ^{o}**

The variable of E^{o} represents the cell potential under standard state conditions. Standard state conditions are 1.0 M for concentration, 25^{o}C for temperature, pH = 7.0, and 1.0 atmosphere (atm) for pressure.

**Cell Potential (E _{Cell}) **

The variable of E_{Cell} represents the cell potential under non-standard conditions.

**Gas Constant (R)**

The variable of R represents the gas constant of the gas and is equal to 8.314 when incorporating joules (J) into its units.

**Temperature (T)**

The variable of T represents the absolute temperature of the gas. The units are in Kelvin.

**Moles of Electrons (n)**

The variable of n represents the number of electrons transferred during the oxidation-reduction process within an electrochemical cell.

**Faraday’s Constant (F)**

The variable of F represents the number of Coulombs (C) per mole of electron.

**Concentrations (A) **

The variable of A represents the activity or concentration of reacting species within an oxidation-reduction reaction of an electrochemical cell. The ratio itself is represented by the reaction quotient (Q).

**The Nernst Equation & Reaction Quotient **

The cell potential calculated from Nernst equation is the maximum potential at the instant the cell circuit is connected. At 25^{o}C (298.15 K) we can simplify the Nernst Equation as:

The units remaining are Joules per Coulomb, which is equal to volts (V).

**Conversion between ln and log**

By multiplying the natural log (ln) by 2.303 we can obtain the log function.

**The Nernst Equation & Equilibrium **

As an electrochemical cell discharges electricity and current flows, the electrolyte concentrations from both half-cells will change. The effect is that the reaction quotient (Q) will increase, the non-standard cell potential will decrease and the overall electrochemical cell will reach equilibrium.

**Introducing the equilibrium constant K**

As the non-standard cell potential approaches zero the variable of K can be incorporated into the formula.

**Introducing Gibbs Free Energy**

Gibbs Free Energy serves as one of the most important variables in our understanding of spontaneity under Chemical Thermodynamics. The relationship it shares with an electrochemical cell is expressed by the formula: