Zero-order systems provide an interesting opportunity for students to think about the underlying mechanism behind the physical phenomena being modeled. The work reported here is part of a larger study that seeks to characterize how students integrate chemistry and mathematics in the context of chemical kinetics. Thirty-six general chemistry students, five physical chemistry students, and three chemical engineering students were asked to think aloud as they responded to an interview prompt about the half-life of a catalyst-driven zero-order reaction. Our findings revealed that students often described zero-order in mathematical terms (i.e., the zero-order rate law, integrated rate law, and graphical representation), but lacked a clear understanding of the particulate nature of zero-order systems. Results also indicated students have productive discipline-specific conceptions of catalysts but less productive ideas regarding half-life, expressing a limited view that seemed restricted to first-order decay reactions. Analysis of student problem solving further revealed patterns among this type of half-life reasoning. Our work suggests the need for instruction that varies context to promote a more holistic understanding of chemical kinetics concepts.