  We explore the transmission spectrum of the Neptune-class exoplanet GJ 436b,
including the possibility that its atmospheric opacity is dominated by a
variety of non- equilibrium chemical products. We also validate our
transmission code by demonstrating close agreement with analytic models that
use only Rayleigh scattering or water vapor opacity. We find broad disagreement
with radius variations predicted by another published model. For GJ 436b, the
relative coolness of the planet's atmosphere, along with its implied high
metallicity, may make it dissimilar in character compared to "hot Jupiters."
Some recent observational and modeling efforts suggest low relative abundances
of H2O and CH4 present in GJ 436b's atmosphere, compared to calculations from
equilibrium chemistry. We include these characteristics in our models and
examine the effects of absorption from methane-derived higher order
hydrocarbons. Significant absorption from HCN and C2H2 are found throughout the
infrared, while C2H4 and C2H6 are less easily seen. We perform detailed
simulations of JWST observations, including all likely noise sources, and find
that we will be able to constrain chemical abundance regimes from this planet's
transmission spectrum. For instance, the width of the features at 1.5, 3.3, and
7 microns indicates the amount of HCN versus C2H2 present. The NIRSpec prism
mode will be useful due to its large spectral range and the relatively large
number of photo-electrons recorded per spectral resolution element. However,
extremely bright host stars like GJ 436 may be better observed with a higher
spectroscopic resolution mode in order to avoid detector saturation. We find
that observations with the MIRI low resolution spectrograph should also have
high signal-to-noise in the 5 - 10 micron range due to the brightness of the
star and the relatively low spectral resolution (R ~ 100) of this mode.
