3. You are responsible for approximating the current-voltage characteristics for an individual SOFC fuel cell stack. As a first approximation, you assume that the cathode side of the fuel cell dominates both the kinetic losses and the transport losses. Also assume that the open-circuit potential of the cell is 1 V. The fuel cell operates at 700 oC (973 Kelvin) and the cathode input is air at 1 atm pressure. a. Write the cathode half reaction for this fuel cell (as a 4-electron process). b. Your first step is to determine the kinetics at the cathode. You find that the catalyst exchange current density is 0.01 mA/cm2 and that the symmetry factor or transfer coefficient is 0.5. Use the Butler-Volmer equation to plot the kinetic data over the overpotential range of 0 to -0.4 V. c. Your next step is to determine the transport at the cathode. The diffusion coefficient of O2 in N2 is 0.22 cm2 /s at room temperature, and increases with absolute temperature (Kelvin) to the 1.5 power: !! #$ %!, '! = !! #$ %!, '" % ( ) ' */( What is the diffusion coefficient of O2 in N2 at 700 oC? If the porosity of the gas diffusion layer is 35%, the tortuosity is 16, the thickness of the gas diffusion layer is 400 micrometers, and ambient heated air is used as the feed, what is the maximum limiting current density? d. As an approximation, assume that the limiting current density is the same at all voltages. Use the Kouteck-Levich equation (lecture 2D) to make a current densityvoltage plot for t