## Sunday, October 20, 2019

### Equilibrium Constant of Electrochemical Cell Reaction

Equilibrium Constant of Electrochemical Cell Reaction The equilibrium constant of an electrochemical cells redox reaction can be calculated using the Nernst equation and the relationship between standard cell potential and free energy. This example problem shows how to find the equilibrium constant of a cells redox reaction. Problem The following two half-reactions are used to form an electrochemical cell:Oxidation:SO2(g) 2 H20(Ã¢â€žâ€œ) Ã¢â€ â€™ SO4-(aq) 4 H(aq) 2 e-Ã‚  Ã‚  EÃ‚ °ox -0.20 VReduction:Cr2O72-(aq) 14 H(aq) 6 e- Ã¢â€ â€™ 2 Cr3(aq) 7 H2O(Ã¢â€žâ€œ)Ã‚  Ã‚  EÃ‚ °red 1.33 VWhat is the equilibrium constant of the combined cell reaction at 25 C? Solution Step 1: Combine and balance the two half-reactions. The oxidation half-reaction produces 2 electrons and the reduction half-reaction needs 6 electrons. To balance the charge, the oxidation reaction must be multiplied by a factor of 3.3 SO2(g) 6 H20(Ã¢â€žâ€œ) Ã¢â€ â€™ 3 SO4-(aq) 12 H(aq) 6 e- Cr2O72-(aq) 14 H(aq) 6 e- Ã¢â€ â€™ 2 Cr3(aq) 7 H2O(Ã¢â€žâ€œ)3 SO2(g) Cr2O72-(aq) 2 H(aq) Ã¢â€ â€™ 3 SO4-(aq) 2 Cr3(aq) H2O(Ã¢â€žâ€œ)By balancing the equation, we now know the total number of electrons exchanged in the reaction. This reaction exchanged six electrons. Step 2: Calculate the cell potential.This electrochemical cell EMF example problem shows how to calculate cell potential of a cell from standard reduction potentials.**EÃ‚ °cell EÃ‚ °ox EÃ‚ °redEÃ‚ °cell -0.20 V 1.33 VEÃ‚ °cell 1.13 VStep 3: Find the equilibrium constant, K.When a reaction is at equilibrium, the change in free energy is equal to zero. The change in free energy of an electrochemical cell is related to the cell potential of the equation:ÃŽâ€G -nFEcellwhereÃŽâ€G is the free energy of the reactionn is the number of moles of electrons exchanged in the reactionF is Faradays constant (96484.56 C/mol)E is the cell potential. The cell potential and free energy example shows how to calculate free energy of a redox reaction.If ÃŽâ€G 0:, solve for Ecell0 -nFEcellEcell 0 VThis means, at equilibrium, the potential of the cell is zero. The reaction progresses forward and backward at the same rate, meaning there is no net electron flow. With no electron flow, there is no current and the potential is equal to zero.Now there is enough information known to use the Nernst equation to find the equilibrium constant.The Nernst equation is:Ecell EÃ‚ °cell - (RT/nF) x log10QwhereEcell is the cell potentialEÃ‚ °cell refers to standard cell potentialR is the gas constant (8.3145 J/molÃ‚ ·K)T is the absolute temperaturen is the number of moles of electrons transferred by the cells reactionF is Faradays constant (96484.56 C/mol)Q is the reaction quotient**The Nernst equation example problem shows how to use the Nernst equation to calculate cell potential of a non-standard cell.**At equilibrium, the reaction quotient Q i s the equilibrium constant, K. This makes the equation:Ecell EÃ‚ °cell - (RT/nF) x log10KFrom above, we know the following:Ecell 0 VEÃ‚ °cell 1.13 VR 8.3145 J/molÃ‚ ·KT 25 degC 298.15 KF 96484.56 C/moln 6 (six electrons are transferred in the reaction)Solve for K:0 1.13 V - [(8.3145 J/molÃ‚ ·K x 298.15 K)/(6 x 96484.56 C/mol)]log10K-1.13 V - (0.004 V)log10Klog10K 282.5K 10282.5K 10282.5 100.5 x 10282K 3.16 x 10282Answer:The equilibrium constant of the cells redox reaction is 3.16 x 10282.