Tafel Equation—Simplified Activation Kinetics

We have seen that the BV equation is dependent on several parameters, and when applying it to fuel cell reaction kinetics, some simplifications are 

For small values of r (typically less than 15 mV at room temperature), the exponential term can be approximated using Taylor series expansion as e 1 + X, for small x. For small n, then Equation 5.77 can be written as 

For small n, the net current density varies linearly with the overpotential in a narrow range of potential near equilibrium potential It should be noted that the current density is independent of the charge transfer coefficient a for small values of overpotential. The ratio -x]/j has the dimensions of resistance and is called the charge transfer resistance, R,., and is given as 

Theoretically, the exchange current density Jq can be obtained by measuring i versus q for a low range of q. Unfortunately, this measurement is not practical because of large experimental errors introduced by other fuel cell losses arising from ohmic resistances, mass transport effects, and reactant and product crossover effects. These losses are discussed in the next section. 

Determine for what values of q the linear form of the BV equation is a good approximation. 

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