Chapter 10, Problem 10.13P

Solar Energy Capture: Water Splitting. Hydrogen and O₂ can be combined in fuel cells to generate electricity. Solar energy can be used to split water to generate the raw reactants H₂ and O₂ for fuel cells. One method of solar thermal reduction is with NiFe₂O₄ in the sequence

Step (1)     $\text{Solar Energy}+\stackrel{\text{Surface (}S\text{)}}{\stackrel{︷}{{\text{NiFe}}_2{\text{O}}_4}}\to \stackrel{\text{Solid Solution}(S^{\prime })}{\stackrel{︷}{1.2\text{FeO}+0.4{\text{Fe}}_2{\text{O}}_3+\text{NiO}}}+0.3{\text{O}}_2\uparrow$

Step (2)     $\stackrel{\text{Solid Solution}(S^{\prime })}{\stackrel{︷}{1.2\text{FeO}+0.4{\text{Fe}}_2{\text{O}}_3+\text{NiO}}}+0.6{\text{H}}_2\text{O}\to \stackrel{\text{Surface (}S\text{)}}{\stackrel{︷}{{\text{NiFe}}_2{\text{O}}_4}}+0.6{\text{H}}_2\uparrow$

We note NiFe₂O₄ is regenerated in this process.³³

1. (a) Derive a rate law for Step (2), assuming that water adsorbs on the solid solution as a single-site mechanism and that the reaction is irreversible.
2. (b) Repeat (a) when the reaction is reversible and the solid solution adsorption site for water is (S′) different than the NiFe₂O₄ site for the adsorption of H₂, (S).

$\begin{array}{l}{\text{H}}_2\text{O}+{\text{S}}^{\prime }\rightleftarrows {\text{S}}^{\prime }\cdot {\text{H}}_2\text{O}\\ {\text{S}}^{\prime }\cdot {\text{H}}_2\text{O}\rightleftarrows \text{S}\cdot {\text{H}}_2\text{+}\frac{1}{2}{\text{O}}_2\\ {\text{H}}_2\cdot \text{S}\rightleftarrows \text{S}+{\text{H}}_2\end{array}$

1. (c) How would your rate law change if we included Step 1?

$\begin{array}{l}S+hv\rightleftarrows S^{\prime }\cdot {\text{O}}_2\\ S^{\prime }\cdot {\text{O}}_2\rightleftarrows S^{\prime }+{\text{O}}_2\end{array}$