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Unformatted text preview: II. Equilibrium Thermodynamics Lecture 9: Fuel Cells and Lead-Acid Batteries MIT Student (and MZB) Were going to calculate the open circuit voltage of two types of elec- trochemical system: polymer electrolyte membrane (PEM) fuel cells and lead-acid batteries. To do this, were going to make use of two equations from the last lecture. The first is the Nernst equation, which describes the potential difference between the electrode and electrolyte in the half-cell reaction s i M z i i n e . (1) i The potential difference, which is always defined to be the potential of the electrode minus the potential of the electrolyte, is = k B T ln( a s i i ) . (2) ne i is the potential difference of this half-cell reaction in a particular refer- ence state. The values of the activity a i , are then scaled so that the activity of species i in the reference state is 1. Reference states are set to be 1 in convenient units, such as 1 atmosphere of pressure for gases. The second equation is for open circuit voltage, and comes from combin- ing the Nernst equation at each electrode. The total open circuit voltage of a cell is V O = c a s j = k B T ln cathode a j . (3) c a s i ne anode a i This describes the open circuit voltage in terms of the half-cell reactions at the cathode and anode, but we can also describe it in terms of the full cell 1 Lecture 8: Fuel cells and lead-acid batteries 10.626 (2011) Bazant reaction, s i R i s j P j . (4) i j Since the reaction at the anode is going forwards in order to produce elec- trons, s i for reactants in the half-cell reaction is the same as s i in the full cell reaction, while the value of s i for products is defined to be negative in the half-cell reaction but positive in the full cell reaction. The situation is the opposite for the cathode, because the half-cell reaction proceeds backwards, in order to accept electrons. This means that we can rewrite equation 3 in the form s j k B T products a j V O = V ln , (5) s i ne a reactants i using the stoichiometric coecients defined for the full cell reaction. Here we have made the definition V = , (6) c a the open circuit voltage of the reaction under reference conditions. 1 Polymer Electrolyte Membrane Fuel Cells 1.1 Hydrogen concentration cell A hydrogen concentration cell has a porous electrode situated in hydrogen gas for both the anode and the cathode, the difference being the pressure of the hydrogen. The two electrodes are separated by a polymer membrane that permits the ow of hydrogen ions but not hydrogen gas. The reactions are anode: H 2 2H + + 2e (7) cathode: 2H + + 2e H 2 (8)...
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