### Reduction Potentials, ΔG, and K

As you know, the standard reduction potential, E°, is measured at 298 Kelvin and with all solutions at 1M. However, redox reactions don't maintain this ideal state for very long; as soon as the reaction begins, the concentrations begin to change. To cope with this discrepancy, Walter Nernst, a German chemist and physicist, developed an equation in the early 1900's to relate reduction potential, temperature, concentration, and moles of electrons transferred. The Nernst equation, named in his honor, is:

E = E° - (RT/nF) ln Q

in which E is the corrected potential, the E° is the standard potential, R is the universal gas constant (joule units--8.3145 J/K * mol), T is the temperature in Kelvin, Q is the reaction quotient (the concentrations of all products, raised to the power of their coefficient, and multiplied together, over the concentrations of all reactants, raised to the power of their coefficient, and multiplied together--remember chapter 2?), n is the number of electrons transferred in the balanced equation, and F is the Faraday constant, 9.6485 x 104 J/V * mol. Since T is usually 298 Kelvin and R and F are constants, we can condense most of the Nernst equation into the following format:

E = E° - (0.0257V/n) ln Q

When the cell has reached equilibrium, there is no net voltage, and Q is equal to K, the equilibrium constant. Therefore, this form of the Nernst equartion becomes, at 298 kelvin:

ln K = nE° / 0.0257 V

This equation is quite powerful, because of its simplicity: the equilibrium constant can be determined for any redox reaction simply by knowing the standard reduction potential and the number of electrons transferred in the balanced equation.

Yet another important reaction-governing value is related to E°--the Gibbs free energy change. This can be derived using the K version of the Nernst equation and the equation relating K and ΔG, but we'll just give you the final version:

ΔG°reaction = -nFE°

where n is again the moles of electrons transferred in the balanced reaction, F is the Faraday constant, and E° is the standard cell potential.

Using these three powerful equations, you can find the real cell potential at any concentration state and temperature, find the equilibrium constant, and find the Gibbs free energy value for use in thermodynamic calculations. Note how similar all the reactions are, attesting to the fact that these branches of chemistry are tightly related.

This concludes the lesson portion of our "Redox Reactions" chapter; you now know everything you need to above oxidation-reduction reactions! The next page will include practice problems, or you can continue on to "Organic Chemistry" if you feel confident about your knowledge of redox reactions.

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