  JWST$'$s large aperture and wide wavelength coverage will enable it to
collect the highest quality transit spectra observed so far. For exoplanetary
atmospheres we expect to retrieve the abundance of the most abundant molecules,
such as H$_2$O, CO, and CH$_4$. Other molecules, such as H$_2$S and PH$_3$,
have been observed in Jupiter and Saturn but their chemistry and detectability
in strongly irradiated planets is highly unknown. In this paper, we make the
first effort to study their spectral features in solar composition atmospheres,
and evaluate their detectability with JWST. We model the chemistry of
phosphorus and sulfur in solar composition atmospheres. Our model includes the
effect of vertical transport. Photochemistry effects are not included in our
calculations. Using the abundance profiles, we model the JWST transmission and
emission spectra for K=6.8 G-type star and for planets with cloud-free solar
composition atmospheres. We find PH$_3$ is detectable at 3 sigma from
transmission spectra of the simulated atmosphere with $T_{\rm eq}$ $<$ 500K
using the NIRCam LW grism F444W mode with a total observing time of 28.8 hrs.
H$_2$S is detectable at 3 sigma in the transmission and emission spectra for
the simulated planet with $T_{\rm eq}$ $>$ 1500K using the NIRCam LW grism
F322W2 mode with a total observing time of 24.0 hrs. Our results specifically
highlight the importance of including H$_2$S for future abundances retrieval
with JWST. The presence of clouds and hazes challenges the detections of PH$_3$
and H$_2$S, but H$_2$S features are still expected to be present in the
emission spectra.
