Infrared observations probe the warm gas in the inner regions of planet-forming disks around young sun-like, T Tauri stars. In these systems, H$_2$O, OH, CO, CO$_2$, C$_2$H$_2$, and HCN have been widely observed. However, the potentially abundant carbon carrier CH$_4$ remains largely unconstrained. The James Webb Space Telescope (JWST) will be able to characterize mid-infrared fluxes of CH$_4$ along with several other carriers of carbon and oxygen. In anticipation of the JWST mission, we model the physical and chemical structure of a T Tauri disk to predict the abundances and mid-infrared fluxes of observable molecules. A range of compositional scenarios are explored involving the destruction of refractory carbon materials and alterations to the total elemental (volatile and refractory) C/O ratio. Photon-driven chemistry in the inner disk surface layers largely destroys the initial carbon and oxygen carriers. This causes models with the same physical structure and C/O ratio to have similar steady state surface compositions, regardless of the initial chemical abundances. Initial disk compositions are better preserved in the shielded inner disk midplane. The degree of similarity between the surface and midplane compositions in the inner disk will depend on the characteristics of vertical mixing at these radii. Our modeled fluxes of observable molecules respond sensitively to changes in the disk gas temperature, inner radius, and the total elemental C/O ratio. As a result, mid-infrared observations of disks will be useful probes of these fundamental disk parameters, including the C/O ratio, which can be compared to values determined for planetary atmospheres.
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