Anaerobic respiration reactions are of fundamental importance to global biogeochemical cycling of elements. Yet, the idea that cellular respiration can occur not only in the absence of oxygen but also involve the oxidation of inorganic substrates (e.g., AsO[subscript 3 superscript 3-], Fe[superscript 2+], H[subscript 2], H[subscript 2]S, Mn[superscript 2+], NH[subscript 3], and S[superscript 0]) is often foreign to many undergraduate students. This article describes a problem-solving exercise where students are introduced to the thermodynamic fundamentals of respiration with a particular focus on the role of redox (reduction-oxidation) potentials (E[subscript 0]'). In the exercise, the students investigate how the difference in redox potential ([delta]E[subscript 0]') between different pairs of reductants and oxidants affects the range of permissible microbial metabolic reactions in natural environments when oxygen is absent.