The influence of interphase mass transfer on dispersion of solute in a tube flow of a power-law fluid is examined at all times after the injection of the solute. Three important dispersion mechanisms are shown to arise in the study in place of two in classical studies. This is true in channel flows also (see Siddheshwar et al. [1]). The present 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 [2] and Aris [3] regimes of dispersion are obtained as limiting cases from the study. The graphical results of the study serve as a jury on any numerical treatment of the present problem that might be undertaken considering non-asymptotic all-time analysis.