Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Fuel Cells The chemical thermodynamics of SOFCs

# The chemical thermodynamics of SOFCs

The reactant properties and fuel cell condition determines the electrical potential difference between the anode and the cathode electrode. The following analysis assumes quasi-static equilibrium and a steady flow of gas and ions.

At the cathode-electrolyte interface, the following half reaction occurs:

(1)      ½O2 + 2e ↔ O2–

In equilibrium the sum of the chemical potentials is zero:

(2)     $${\textstyle{1 \over 2}}{\mu _{{O_2}}} + 2({\mu _{{e^ - }}} - F \cdot {\Phi _C}) = ({\mu _{{O^{2 - }}}} - 2F \cdot {\Phi _E})$$

Rearranging equation (2) gives:

(3)     $${\Phi _C} - {\Phi _E} =$$$${\textstyle{1 \over {2F}}}$$$$({\textstyle{1 \over 2}}{\mu _{{O_2}}} + 2{\mu _{{e^ - }}} - {\mu _{{O^{2 - }}}})$$

At the anode-electrolyte interface, the following half reaction occurs:

(4)     H2 + O2– ↔ H2O + 2e

In equilibrium the sum of the chemical potentials is zero:

(5)     $${\mu _{{H_2}}} + ({\mu _{{O^{2 - }}}} - 2F \cdot {\Phi _E}) = {\mu _{{H_2}O}} + 2({\mu _{{e^ - }}} - F \cdot {\Phi _A})$$

Rearranging equation (5) gives:

(6)     $${\Phi _A} - {\Phi _E} =$$$${\textstyle{1 \over {2F}}}$$$$({\mu _{{H_2}O}} + 2{\mu _{{e^ - }}} - {\mu _{{H_2}}} - {\mu _{{O^{2 - }}}})$$

Hence we can calculate the electric potential difference between the anode and the cathode:

(7)     $${\Phi _C} - {\Phi _A} =$$$${\textstyle{1 \over {2F}}}$$$$({\mu _{{H_2}}} + {\textstyle{1 \over 2}}{\mu _{{O_2}}} + {\mu _{{H_2}O}})$$

Assuming that the gases behave like ideal gases, we can write for the chemical potential:

(8)     $$\mu (T,p) = {\mu ^o}(T) + RT \cdot \ln ({\textstyle{p \over {{p_o}}}}) + RT \cdot \ln ({x_i})$$

xi is the mole fraction of component i, mo(T) is the chemical potential per mole of an ideal gas at po = 1 bar.

Substituting (8) in (7), we can write:

(9)     $${\Phi _C} - {\Phi _A} = {\textstyle{1 \over {2F}}}({\mu _{{H_2}}}^o + {\textstyle{1 \over 2}}{\mu _{{O_2}}}^o - {\mu _{{H_2}O}}^o) + {\textstyle{{RT} \over {2F}}} \cdot \ln ({\textstyle{{{x_{{H_2}}}\sqrt {{x_{{O_2}}}} } \over {{x_{{H_2}O}}}}}) + {\textstyle{{RT} \over {4F}}} \cdot \ln ({\textstyle{p \over {{p_0}}}})$$