  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.
