K_eq from Nernst Equation

The Equilibrium Constant for Nernst Equation calculator computes the constant based on the number of moles of electrons, standard cell potential, temperature, Faraday's constant and the Ideal gas law constant (R).

INSTRUCTIONS: Choose units and enter the following:

• (n) Number of Moles of Electrons
• (E_cell⁰) Standard Cell Potential
• (T) Temperature

Nerst Equation Equilibrium Constant (K_eq): The constant is returned as a real number.

The Math / Science

The relationship of E⁰_cell to ΔG⁰ and K_eq can be derived from the relationship between standard Gibbs Free Energy change, ΔG⁰, and the thermodynamic equilibrium constant, K_eq, as well as the relationship between ΔG⁰ and the standard cell potential E⁰_cell. This results in three equations:

nFE⁰_cell = RTlnK_eq  or E⁰_cell =  RTlnK_eq / nF   or lnK_eq = nFE⁰_cell / RT

These three equations can prove useful in different situations, however, the most useful is the last equation: lnK_eq = nFE⁰_cell / RT. This equation is usually much simpler to follow because K_eq is easier to find from electrochemical measurements than from measuring equilibrium concentrations directly.

The formula used in this equation is:

  Keq = e ^{( (n⋅F⋅E_cell0) / (R⋅T))}

where:

·      K_eq is the thermodynamic equilibrium constant

·      n is the number of moles of electrons that are transferred in the reaction

·      F is Faraday’s constant (96,485 J/V * mol e^-)

·      E⁰_cell is the standard cell potential (V)

·      R is the Ideal Gas Constant (8.3145 J/mol*K)

·      T is the temperature (in Kelvin, K) at which the reaction is taking place

For this equation, E⁰_cell must be entered in Volts (V) and temperature must be entered in Kelvin (K). This equation calculates the thermodynamic equilibrium constant for redox reactions at standard conditions.

Supplemental Materials

UCDavis ChemWiki: Connection between E_cell, ΔG, and K

UCDavis ChemWiki: Electrochemical Cells and Thermodynamics

Related Content

Nernst Equation for Reduction Half-reactions

Nernst Equation (at 25 degrees C)

References

Whitten, et al. "Chemistry" 10th Edition. Pp. 835