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MIT10_626S11_lec08 - II Equilibrium Thermodynamics Lecture...

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II. Equilibrium Thermodynamics Lecture 8: The Nernst Equation MIT Student (and MZB) 0.1 Chemical Activity Let µ i be the chemical potential. δ G µ i = = k B T log( a i ) + z i e Φ (per particle) (1) δ N i N j ,T,P, Φ Alternatively, we can consider the chemical activity per mole, in which case: µ i = RT log( a i ) + z i F Φ (per mole) (2) R = universal gas constant = k B N A (3) J = 8 . 31 ( N A = 6 × 10 23 particles) K mol F = Faraday’s constant = N A e = 96 , 487 C (4) k B T = RT = thermal voltage = at 25 C 26mV (5) e F a i is the activity of species i, γ i is the molal activity coe ffi cient and f i is the molar activity coe ffi cient. In a dilute solution a i c i x i , where x i is the mole fraction and c i is the concentration number i . In a dilute solution, γ i = f i = 1. volume In a concentrated solution, a i contains all ”chemical” contributions to µ i and is expressed in terms of activity coe ffi cients , γ i or f i . 1
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Lecture 7: Nernst equation 10.626 (2011) Bazant moles i mol m i = molality of solution = = (6) moles of solvent kg i a = γ i m i = f i c i = γ i x i = p i for an ideal gas (7) i 0 0 0 a 0 m i c i p i 0 0 0 0 In the reference state: µ i = kT log ( a i ) + z i e φ 0 or µ i = RT log ( a i ) + z i F φ 0 . Reference states are usually defined in terms of a standard concen­ tration, temperature (25 C) and pressure (1atm).
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