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The Nernst Equation

The Nernst Equation. Thermodynamics of the relationship of D E and D G - electrical work - relating D G and D E: D G = - n F D E - finding the equilibrium constant from measured cell potentials.

lilah-buckner
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The Nernst Equation

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  1. The Nernst Equation Thermodynamics of the relationship of DE and DG - electrical work - relating DG and DE: DG = - n F DE - finding the equilibrium constant from measured cell potentials. Dependence of the cell potential on activity - the Nernst Equation - the calomel electrode The calomel electrode The pH meter - the glass electrode

  2. Relationship of Cell Potential and DG DG = DH - TDS (const T) = DE + pDV - TDS (const P) = (qrev + w) + pDV - qrev (reversible, const T) w = - pDV + wel,rev expansion work electrical work wel = - Q DE work = charge * (potential difference) = - n F DE Joules Volts Coulombs DG = wel,rev = - n F DE (const T, P, reversible)

  3. Concentration Effects and The Nernst Equation DG° is the standard DG - all solute concentrations must be 1 M and partial pressures must be 1 atm. DG = DG° + RT ln Q - this allows you to calculate DG at non-standard concentrations and partial pressures. DG = - n F DEcell - this is always true; the cell potential is a very fundamental quantity, just like DG DEcell = DE°cell - (RT/nF) lne Q- the Nernst equation. It allows you to calculate DG at non-standard conditions

  4. DE° = (RT/nF) lne K - For reactions in solution, K and can be measured from a standard cell potential. DG°, Measuring Equilibrium Constants DG° = - RT lne K - K can be calculated from DG°, which for many compounds can be obtained from thermodynamic tables. DG = - n F DEcell - this is always true; the cell potential is a very fundamental quantity, just like DG DEcell = DE°cell - (RT/nF) lne Q- The Nernst equation relates DEcell to DE°cell = DE°cell - 2.303 (RT/nF) log10 Q = DE°cell - (0.0152/n) log10 Q (at T=25°C)

  5. PbO2(s) + SO42-(aq) + 4 H3O+(aq) + 2 e- PbSO4(s) + 6 H2O(l) E°=+1.685 V 1 E = E° - (.0592/2) log10 [H3O+]4 [SO42-] The Nernst Equation DEcell = DE°cell - (0.0592/n) log10 Q at T = 25°C Pt(s) The cell potential changes by 0.118 V for each pH unit or by 0.0296 V for each factor of 10 change in [SO42-]: SO42-(aq) slurry of PbO2(s) + PbSO4(s) pH = 0 E = +1.685 V pH = 4 E = +1.211 V H3O+(aq)

  6. pH measurement Standard Hydrogen Electrode: 2 H3O+(aq, 1M) + 2 e- H2(g) + 2 H2O(l) E = +0.241 V - (.0592/2) log10 [H3O+]2 = +0.241 + .0592 * pH Calomel Electrode: Hg2Cl2(s) + 2 e- 2Hg(l) + 2 Cl-(sat’d) Pt(s) Pt(s) H2(g) salt bridge sat’d KCl(aq) paste of Hg(l) and Hg2Cl2(s) H3O+(aq) KCl(s) standard hydrogen electrode calomel reference electrode E° = +0.000 V E° = +0.241 V

  7. 0.0592 V [H+]out2 Ecell = E°cell - log10 2 [H+]in2 The Glass Electrode and the pH Meter The glass electrode is non-metallic electrode composed of a special glass that is porous to H3O+. A diffusion potential develops across the membrane in response to a pH gradient. The potential varies by 59.6 mV for each unit change in pH. Notice that Ecell is uniformly sensitive to pH over 14 orders of magnitude!! Ecell = constant + (0.0592 v) * pH

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