We proposed a novel technique to obtain highly accurate solution to the problem of an irreversible exothermic chemical reaction occurring in an adiabatic tubular chemical reactor. The study also delves into the convergence behavior and error analysis of this technique. Furthermore, we investigate the approximation of the steady-state temperature of the reaction under various scenarios involving the Peclet and Damkohler numbers, and the dimensionless adiabatic temperature rise. To validate our findings, we compare our results with those obtained using several other established methods, including the Taylor and B-Spline Wavelet Methods, Adomian Method, Shooting Method, Contraction Mapping Principle, Sinc-Galerkin Method, and Chebyshev Finite Difference Method. These comparisons affirm that our proposed technique yields solutions that are not only accurate but also stable and efficient when applied to the specified model.