$s large aperture and wide wavelength coverage will enable it to collect the highest quality transit spectra observed so far. For exoplanetary atmospheres we expect to retrieve the abundance of the most abundant molecules, such as H$_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 $T_{\rm eq}$ %CONTENT%lt;$ 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 $T_{\rm eq}$ %CONTENT%gt;$ 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.