The key idea and contribution of this study are to present the innovative functional matrix approach for solving the two chemical, mathematical problems such as the absorption of into phenyl glycidyl ether (PGE) and the chemical kinetic problem. These chemical problems are characterized as a system of nonlinear ODEs with initial and boundary conditions. Numerical outcomes are obtained to establish the simplicity and efficacy of the developed scheme. Graphs and tables show how consistently and effectively the developed strategy works. Results obtained show that the newly adopted technique is more precise and effective than other methods such as Adam–Bashforth–Moultan method (ABM), Runge–Kutta method (RK4), Adomian Decomposition method (ADM), and residual method (RM). Mathematical software called Mathematica 11.3 has been used to perform all calculations. Theorems explain the convergence of this approach.