DOI: 10.1002/ente.201700605 Response to Rebuttal to “Theoretical and Experimental Investigation of Solar Methane Reforming through the Nonstoichiometric Ceria Redox Cycle” Kent J. Warren, Julie Reim, Kelvin Randhir, Benjamin Greek, Richard Carrillo, David W. Hahn, and Jonathan R. Scheffe* [a] We appreciate the rebuttal from Krenzke and Davidson re- garding the thermodynamic analysis presented in our paper entitled “Theoretical and Experimental Investigation of Solar Methane Reforming through the Nonstoichiometric Ceria Redox Cycle”. In the original work, [1] we attempted to differentiate the results of our “simultaneous” approach and their “sequential” approach. [2] It is now apparent that the CH 4 /O 2 ratio used in our original approach was not consis- tent with their reported ratio; thus, the direct comparison made in Figure 2 of our manuscript [1] is not applicable. How- ever, as detailed in the following, we do not agree with the assertion by Krenzke and Davidson that each method is “fundamentally identical”; rather, we show that equivalency holds only under a limiting set of assumptions. We recalculated the reduction oxygen non-stoichiometry (d red ) using the same 2:1 CH 4 /O 2 ratio as Krenzke and David- son, and the results using either approach agree well under most of the temperatures considered in Figure 2 of the origi- nal work. Near-perfect agreement is only observed when H 2 and CO comprise the majority of the products at equilibrium (e.g., higher temperatures). In a derivation below, we show that if the methane partial oxidation reaction is constrained to only produce H 2 and CO, the sequential and simultaneous methods are indeed mathematically identical. However, if another degree of freedom is introduced, such as the forma- tion of H 2 O from the oxidation of H 2 , the approaches are not mathematically equivalent, and the results begin to di- verge under conditions where this reaction becomes favora- ble. To elucidate the differences between each model, we present the two aforementioned cases. First, we will consider methane-driven ceria reduction when H 2 and CO are the predominant products at equilibri- um. The fundamental reactions for this scenario are shown below. 1 Dd CeO 2d ox ! 1 Dd CeO 2d red þ 1 2 O 2 ðR0Þ CH 4 þ 1 2 O 2 ! COþ2H 2 ðR1Þ Using the reaction coordinate method [3] and assuming the system pressure (p system ) is equal to 1 bar, the equilibrium constant K of Reaction (R1) is mathematically described ac- cording to Equation (1): K R1 ¼ p CO p H 2 2 p CH 4 p O 2 1=2 ¼ e 1 n i;CH 4 þ2e 1 2e 1 n i;CH 4 þ2e 1 2 n i;CH 4 e 1 n i;CH 4 þ2e 1 p O 2 1=2 ð1Þ where n i,CH 4 refers to the initial molar amount of methane. The reaction coordinate of Reaction (R1), e 1 , is equivalent to Dd, the amount of oxygen released in the reduction of ceria (Reaction R0). Furthermore, adopting the methodology de- scribed by Krenzke and Davidson, n i,CH 4 can be related to Dd as shown in Equation (2). n i;CH 4 e 1 ¼ n i;CH 4 Dd ¼ C ð2Þ Per the sequential method, the CH 4 /O 2 ratio is set equal to a constant (C). For Reaction (R1), C is equal to 2, but the con- clusion derived from this derivation is applicable for any CH 4 /O 2 ratio. Simplifying and combining Equations (1) and (2) yields the following result for p O 2 , the partial pressure of oxygen at equilibrium. K R1 ¼ e 1 Ce 1 þ2e 1 2e 1 Ce 1 þ2e 1 2 Ce 1 e 1 Ce 1 þ2e 1 p O 2 1=2 ¼ Dd CDdþ2Dd 2Dd CDdþ2Dd 2 CDdDd CDdþ2Dd p O 2 1=2 ¼ 4 C 1 ð Þ C þ 2 ð Þ 2 p O 2 1=2 p O 2 1=2 ¼ 4 C 1 ð Þ C þ 2 ð Þ 2 K R1 ð3Þ [a] K. J. Warren, J. Reim, K. Randhir, B. Greek, R. Carrillo, Prof. D. W. Hahn, Prof. J. R. Scheffe Department of Mechanical and Aerospace Engineering University of Florida 231 MAE-A Building Gainesville, FL 32611-6250 (USA) E-mail: jscheffe@ufl.edu Homepage: http ://www.scheffelab.com/ The ORCID identification number(s) for the author(s) of this article can be found under: https://doi.org/10.1002/ente.201700605. Energy Technol. 2017, 5, 1 – 4 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim &1& These are not the final page numbers! ÞÞ