Earth system models (ESM) demand significant hardware resources and energy consumption to solve atmospheric chemistry processes. Recent studies have shown improved performance from running these models on GPU accelerators. Nonetheless, there is room for improvement in exploiting even more GPU resources. This study proposes an optimized distribution of the chemical solver's computational load on the GPU, named Block-cells. Additionally, we evaluate different configurations for distributing the computational load in an NVIDIA GPU. We use the linear solver from the Chemistry Across Multiple Phases (CAMP) framework as our test bed. An intermediate-complexity chemical mechanism under typical atmospheric conditions is used. Results demonstrate a 35x speedup compared to the single-CPU thread reference case. Even using the full resources of the node (40 physical cores) on the reference case, the Block-cells version outperforms them by 50%. The Block-cells approach shows promise in alleviating the computational burden of chemical solvers on GPU architectures.