Fuel Cell Reaction Question - is this right?

[JoeMama]

Homework Statement

Consider a Fuel cell working via reaction: H_2 + (1/2)O_2 -> H_2 O Derive an expression for the quantity (dE_dP)_T assuming that all the working fluid streams into and out of the fuel cell are at a pressure of 20 bar.
Note this is the rate of change of the EMF with respect to pressure at constant temperature. State clearly your assumptions

Relevant Equations

NA

The quantity (dE_dP)_T can be derived using the Gibbs-Helmholtz equation which states that dE = TdS - PdV + μdN where E is the internal energy of the system, S is the entropy, V is the volume, N is the number of particles and μ is the chemical potential. Differentiating this equation with respect to pressure at constant temperature gives (dE_dP)_T = T(d^2S/dPdT) - V.

For a fuel cell working via reaction H2 + 0.5O2 -> H2O, we can use the Nernst equation to calculate the cell potential Ecell = E°cell - (RT/nF)ln(Q) where E°cell is the standard cell potential, R is the gas constant, T is temperature in Kelvin, n is the number of electrons transferred in the reaction and F is Faraday’s constant. Q is the reaction quotient which can be calculated as Q = (PH2O)0.5/(PH2)(PO2)0.5 where PH2O, PH2 and PO2 are partial pressures of water vapor, hydrogen and oxygen respectively.

The change in cell potential with pressure at constant temperature can be calculated using (dEcell/dP)_T = -(RT/nF) [(dlnQ/dP)_T] where Q depends on partial pressures of reactants and products.

Substituting Q into this equation and simplifying gives (dEcell/dP)_T = -(RT/nF) [(1/4)(dln(PH2O)/dP)_T - (1/2)(dln(PH2)/dP)_T - (1/4)(dln(PO2)/dP)_T]

For a fuel cell operating at a pressure of 20 bar, we can substitute PH2O = 20 bar and PH2 = PO2 = 10 bar into this equation to obtain (dEcell/dP)_T = -0.059 V/bar.

 

[member38644]

Yes, this appears to be a correct derivation of the change in cell potential with pressure at constant temperature for a fuel cell operating via the reaction H2 + 0.5O2 -> H2O. The Nernst equation and the Gibbs-Helmholtz equation are both important in understanding the behavior of fuel cells, and your explanation of how they are used in this context is clear and accurate. Good job!