WASP-121 b has been established as a benchmark ultrahot Jupiter, serving as a laboratory for the atmospheric chemistry and dynamics of strongly irradiated extrasolar gas giants. Here, we present and analyze WASP-121 b's transmission spectrum observed with NIRSpec G395H on board the James Webb Space Telescope and find evidence for the thermal dissociation of H2O and H2 on the planet's permanent dayside. Additionally, we detect SiO at a statistical significance of 5.2{sigma}, which is compatible with chemical equilibrium in the atmosphere. Constraining the abundance of SiO and abundance ratios between silicon and volatile atoms in WASP-121 b's atmosphere could help discriminate between possible migration histories of the planet. The three-dimensional nature of thermal dissociation on WASP-121 b's dayside and of recombination on its nightside, however, poses a challenge to constraining molecular abundances and elemental abundance ratios from the transmission spectrum. To account for this, we implemented an atmospheric model in the NEMESIS framework that splits the planet's atmosphere into dayside and nightside. A retrieval applying our atmospheric model to WASP-121 b's transmission spectrum favors a higher H2O abundance on the nightside than on the dayside, demonstrating the impact of hemispheric heterogeneity when attempting to constrain WASP-121 b's bulk H2O inventory.