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In the present work, a study involving a spectral method to solve the reactive Euler and Navier-Stokes equations is performed. The Euler and Navier-Stokes equations, in conservative and finite volume contexts, employing structured spatial discretization, on a condition of chemical non-equilibrium, are studied. The spectral method presented in this work employs collocation points and variants of Chebyshev and Legendre interpolation functions are analyzed. High-order studies are performed to verify the accuracy of the spectral method. The “hot gas” hypersonic flows around a blunt body, around a double ellipse, and around a reentry capsule in two-dimensions are performed. The Van Leer and the Liou and Steffen Jr. flux vector splitting algorithms are applied to accomplish the numerical experiments. The Euler backward integration method is employed to march the schemes in time. The convergence process is accelerated to steady state condition through a spatially variable time step procedure, which has proved effective gains in terms of computational acceleration (see Maciel). The reactive simulations involve Earth atmosphere chemical model of five species and seventeen reactions, based on the Saxena and Nair model. N, O, N2, O2, and NO species are used to perform the numerical comparisons. The results have indicated that the Chebyshev collocation point variants are more accurate in terms of stagnation pressure estimations, whereas the Legendre collocation point variants are more accurate in terms of the lift coefficient estimations. Moreover, the Legendre collocation point variants are more computationally efficient and cheaper.