Handout12-ElectroPotentiaJKl

Handout12-ElectroPotentiaJKl - CEM 834 ELECTROCHEMICAL...

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CEM 834 ELECTROCHEMICAL POTENTIAL FALL 2005 I. Potential Difference between Dissimilar Conducting Media with a Common Charge Carrier The work required to move a charge Q from infinite distance, where the electrostatic potential is zero, to a point at electrostatic potential Ψ is Ψ = Q w The work is independent of the path, therefore w w w ∞→ ∞→ + = 1 1 2 2 To move the charge Q from a point at Ψ 1 to a point at Ψ 2 , w Q ( ) 2 1 = - Ψ Ψ and for an infinitesimal increment of charge dQ, dw dQ ( ) 2 1 = - Ψ Ψ Consider two spheres, S 1 and S 2 , composed of the same metal that have electrostatic potentials of Ψ 1 and Ψ 2 , respectively. The work done on the system to move dQ from S 1 to S 2 is dw dQ ( ) rev 2 1 = - Ψ Ψ For reversible work at constant temperature and pressure, the change in Gibbs free energy is dV p dA dG - = where the change in Helmholtz energy is given by dA dw rev = Since there is no p dV work involved, dG dQ ( ) 2 1 = - Ψ Ψ To transfer dn moles of electrons from S 1 to S 2 , dG can also be written as ( 29 ( 29 ( 29 dG dn e 2 e 1 = - - - μ μ
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2 where (1) e - μ is the chemical potential of the electron in S 1 . The charge on dn moles of electrons is dn F dQ - = where F is the Faraday constant. By equating the expressions for dG, we obtain ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 1 e 2 e 1 2 1 e 2 e Ψ Ψ F μ μ dn F Ψ Ψ dn μ μ - - = - - = - - - - - If Ψ 1 is taken as a reference point of zero potential, then ( 29 ( 29 potential electrical Ψ F potential chemical μ potential
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Handout12-ElectroPotentiaJKl - CEM 834 ELECTROCHEMICAL...

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