Electrochemistry Calculations Using the Nernst Equation

Electrochemistry Calculations Using the Nernst Equation The Nernst equation is used to calculate the voltage of an electrochemical cell or to find the concentration of one of the components of the cell. The Nernst Equation The Nernst equation relates the equilibrium cell potential (also called the Nernst potential) to its concentration gradient across a membrane. An electric potential will form if there is a concentration gradient for the ion across the membrane and if selective ions channels exist so that the ion can cross the membrane. The relation is affected by temperature and whether the membrane is more permeable to one ion over others. The equation may be written: Ecell E0cell - (RT/nF)lnQ Ecell cell potential under nonstandard conditions (V)E0cell cell potential under standard conditionsR gas constant, which is 8.31 (volt-coulomb)/(mol-K)T temperature (K)n number of moles of electrons exchanged in the electrochemical reaction (mol)F Faradays constant, 96500 coulombs/molQ reaction quotient, which is the equilibrium expression with initial concentrations rather than equilibrium concentrations Sometimes it is helpful to express the Nernst equation differently: Ecell E0cell - (2.303*RT/nF)logQ at 298K, Ecell E0cell - (0.0591 V/n)log Q Nernst Equation Example A zinc electrode is submerged in an acidic 0.80 M Zn2 solution which is connected by a salt bridge to a 1.30 M Ag solution containing a silver electrode. Determine the initial voltage of the cell at 298K. Unless youve done some serious memorizing, youll need to consult the standard reduction potential table, which will give you the following information: E0red: Zn2aq 2e- → Zns -0.76 V E0red: Agaq e- → Ags 0.80 V Ecell E0cell - (0.0591 V/n)log Q Q [Zn2]/[Ag]2 The reaction proceeds spontaneously so E0 is positive. The only way for that to occur is if Zn is oxidized (0.76 V) and silver is reduced (0.80 V). Once you realize that, you can write the balanced chemical equation for the cell reaction and can calculate E0: Zns → Zn2aq 2e- and E0ox 0.76 V 2Agaq 2e- → 2Ags and E0red 0.80 V which are added together to yield: Zns 2Agaq → Zn2a 2Ags with E0 1.56 V Now, applying the Nernst equation: Q (0.80)/(1.30)2 Q (0.80)/(1.69) Q 0.47 E 1.56 V - (0.0591 / 2)log(0.47) E 1.57 V