Nernst Equation, Equlibrium and Potential

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nernst.mcd 6/12/97 Nernst Equation, Equlibrium and Potential Starting with the Nernst Equation for the equlibrium; Ox + n e- <--> Red : R.T C ox E E .ln Typical form of Nernst Equation cell std_cell . n F C red n.F C ox Rearange E E . ln cell std_cell . R T C red n.F E E . C ox cell std_cell . e R T Gives the ratio of oxidized to C red reduced form of redox pair. n.F ( DE). C ox . e R T Reduced variables to DE, the C red difference between the equlibrium potential and the applied potential. This function describes how the equlibrium ration of oxidized and reduced form depend upon the applied potential. Notice that if DE = 0 Where the applied potential is the same as the standard cell potential. Then the exponent is 0, so the ratio of Cox/Cred = 1. This is the conditions for the standard state. If DE > 0 Where the applied potential is positive of Eo. Now the exponent is greater than 0 so the ratio of Cox/Cred >1. The concentration of the oxidized form is greater than the concentration of the reduced form. This is consistent with the half reaction because an applied potential positive of Eo pulls e-'s off and causes oxidation. If DE < 0. Where the applied potential is negative of Eo. Now the exponent is less than 0 so the ratio of Cox/Cred < 1. The concentration of the oxidized form is less than the concentration of the reduced form. This is consistent with the half reaction because an applied potential negative of Eo pushes e-'s on and causes reduction. nernst.mcd 6/12/97 Now let's take a graphical look at this function. Look at a range of applied potentials for a reaction with 1 electron exchanged: DE 0.4.volt, 0.39.volt.. 0.4.volt n 1 Some Constants for electrochemistry: R 8.31441.joule.K 1.mole 1 T 298.K F 96484.6.coul.mole 1 The functions to describe a (the ratio of oxidzied over reduced) and the concentration of each species (assuming a total concentration of 1. n.F DE. R.T 1 a(DE, n) e C red(DE,n) C ox(DE, n) 1 C red(DE, n) 1 a(DE, n) Nernst Relationships 1 C red( DE,n) C ox( DE, n) 0.5 Concentration 0 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 DE Cell Potential a Nernst Relationships 0 5 ln C red( DE, n) ln C ox( DE,n) 10 Concentration 15 20 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 DE Cell Potential nernst.mcd 6/12/97 Now, let's see what happens if the number of electrons changes: n 2 Nernst Relationships 1 C red( DE,n) C ox( DE, n) 0.5 Concentration 0 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 DE Cell Potential a Nernst Relationships 0 10 ln C red( DE, n) ln C ox( DE,n) 20 Concentration 30 40 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 DE Cell Potential n 3 Nernst Relationships 1 C red( DE, n) C ox( DE, n) 0.5 Concentration 0 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 DE Cell Potential.

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