We explore how well James Webb Space Telescope (JWST) spectra will likely
constrain bulk atmospheric properties of transiting exoplanets. We start by
modeling the atmospheres of archetypal hot Jupiter, warm Neptune, warm
sub-Neptune, and cool super-Earth planets with clear, cloudy, or high mean
molecular weight atmospheres. Next we simulate the $\lambda = 1 - 11$ $\mu$m
transmission and emission spectra of these systems for several JWST instrument
modes for single transit and eclipse events. We then perform retrievals to
determine how well temperatures and molecular mixing ratios (CH$_4$, CO,
CO$_2$, H$_2$O, NH$_3$) can be constrained. We find that $\lambda = 1 - 2.5$
$\mu$m transmission spectra will often constrain the major molecular
constituents of clear solar composition atmospheres well. Cloudy or high mean
molecular weight atmospheres will often require full $1 - 11$ $\mu$m spectra
for good constraints, and emission data may be more useful in cases of
sufficiently high $F_p$ and high $F_p/F_*$. Strong temperature inversions in
the solar composition hot Jupiter atmosphere should be detectable with $1 -
2.5+$ $\mu$m emission spectra, and $1 - 5+$ $\mu$m emission spectra will
constrain the temperature-pressure profiles of warm planets. Transmission
spectra over $1 - 5+$ $\mu$m will constrain [Fe/H] values to better than 0.5
dex for the clear atmospheres of the hot and warm planets studied.
Carbon-to-oxygen ratios can be constrained to better than a factor of 2 in some
systems. We expect that these results will provide useful predictions of the
scientific value of single event JWST spectra until its on-orbit performance is
known.