A hydrogen fuel cell operates at 25°C and pressure of 100 kPa, using a supply of pure hydrogen and oxygen from ambient air. The partial pressure of the water that forms from the hydrogen and oxygen is 30 kPa. (a) What is the voltage drop across the fuel cell? (b) If the supply of air is replaced

Question

A hydrogen fuel cell operates at 25°C and pressure of 100 kPa, using a supply of pure hydrogen and oxygen from ambient air. The partial pressure of the water that forms from the hydrogen and oxygen is 30 kPa. (a) What is the voltage drop across the fuel cell? (b) If the supply of air is replaced with a supply of pure oxygen, and nothing else changes, what is the new voltage drop?

Accepted Answer

(a) Given the initial data, partial pressures for each of the components of the reaction are [latex]P_{\mathrm{H}_{2}}=1[/latex] , [latex]P_{\mathrm{O}_{2}}=0.21[/latex] , and [latex]P_{\mathrm{H}_{2} \mathrm{O}}=0.3[/latex] Substituting into Eq. (13-10) gives

[latex]E=E^{0}+\frac{R T}{2 F} \ln \left(\frac{P_{\mathrm{H}_{2}} P_{\mathrm{O}_{2}}{ }^{0.5}}{P_{\mathrm{H}_{2} \mathrm{O}}} ight)[/latex] (13-10)

[latex]E=1.23+\frac{8.314(298)}{2(96400)} \ln \left(\frac{1(0.21)^{0.5}}{0.3} ight)=1.23+0.0054=1.24 \mathrm{~V}[/latex]

(b) If the fuel cell is operated with pure oxygen, [latex]P_{\mathrm{O}_{2}}=0.21[/latex] Thus [latex]\beta^{ ext {new }}=1[/latex] while [latex]\beta^{ ext {old }}=0.21[/latex]. Rewriting Eq. (13-12) to include only nonzero terms gives

[latex]\Delta E=E^{ ext {new }}-E^{ ext {old }}=E\left(\alpha^{ ext {new }}, \beta^{ ext {new }}, \delta^{ ext {new }}, P^{ ext {new }} ight)-E\left(\alpha^{ ext {old }}, \beta^{ ext {old }}, \delta^{ ext {old }}, P^{ ext {old }} ight) [/latex](13-12)

[latex]\Delta E=E^{ ext {new }}-E^{ ext {old }}=\frac{R T}{2 F}\left[\ln \left(\left(\beta^{ ext {new }} ight)^{0.5} ight)-\ln \left(\left(\beta^{ ext {old }} ight)^{0.5} ight) ight][/latex]

[latex]=(0.5) \frac{R T}{2 F}[\ln (1)-\ln (0.21)]=0.01[/latex]

Thus [latex]E^{n e w}=E^{o l d}+\Delta E=1.24+0.01=1.25 \mathrm{~V}[/latex]

Question 13.5: A hydrogen fuel cell operates at 25°C and pressure of 100 kP...

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