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Question

# When do we use the formula delta G=-nFE. and when do we use E=E0-0.059/nlogKc? Are there any specific conditions for using these two?

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Solution

## The Nernst Equation is derived from the emf and the Gibbs energy under non-standard conditions. Eo=Eo reduction−Eo oxidation When Eo is positive, the reaction is spontaneous. When Eo is negative, the reaction is not spontaneous. Since the change inGibbs free energy, ΔG, is also related to spontaneity of a reaction, therefore, ΔG and E are related. Specifically, ΔG=−nFE where, n is # of electrons transferred in the reaction, F is the Faraday constant (96500 C/mol) and E is potential difference. Under standard conditions, this equation is then ΔGo=−nFEo. Since, ΔG=ΔGo+RTlnQ(1) Substituting ΔG=−nFE and ΔGo=−nFEo into equation (1), we have: −nFE=−nFEo +RTlnQ Divide both sides of the equation above by −nF, we have E=Eo −RTnFlnQ(2) Equation (2) can be rewritten in the form of log base 10: E=Eo −2.303RTnFlogQ(3) At standard temperature T = 298K, the 2.303RTF equals .0592 V, so equation (3) turns into: E = Eo −.0592VnlogQ The equation above indicates that the electrical potential of a cell depends upon the reaction quotient Q of the reaction. As the redox reaction proceeds, reactants are consumed, thus concentration of reactants decreases. Conversely, the products concentration increases due to the increased in products formation. As this happens, cell potential gradually decreases until the reaction is atequilibrium, at which ΔG =0.

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