The paper presents an all-time analysis of unsteady convective diffusion of solute undergoing an irreversible first-order chemical reaction at the bounding walls of a parallel-plate channel. The heterogeneous chemical reaction significantly influences the convective and diffusive coefficients. A new coefficient arises exclusively due to the incorporation of wall reaction. The effects of wall-catalysed reaction and power-law index 'N' on dispersion are investigated against the background of the no -reaction problem. The analytical result on dispersion of solute with wall catalysed reaction at long times is compared with the analytical solution when reaction is absent, The Taylor [1] and Aris [2] regimes of dispersion for the present problem are obtained as limiting cases from the study. The graphical results of the study serve as a jury on any numerical study that might be undertaken considering non-asymptotic all-time analysis.