Longitudinal dispersion of passive tracer molecules released in a pulsatile flow through an annular pipe with a reactive outer wall is studied by employing the method of integral moments. It is shown how the spreading of tracers is influenced by the shear flow due to a periodic pressure pulsation in the pipe and a first-order reaction at the wall. The behaviour of the dispersion coefficient due to variation of the aspect ratio (the ratio of the inner radius to the outer radius of the annular pipe) for periodic flow with and without a non-zero mean is examined. It is shown that an increase of aspect ratio, Womersley parameter or reaction at the outer wall of the annular pipe inhibits the dispersion of tracers. The axial distribution of the mean concentration is approximated using a Hermite polynomial representation from the first four central moments for a range of different aspect ratios and frequencies of the pressure pulsation. It is interesting to note that for low frequencies of pulsation, an increase of aspect ratio leads to a significant effect on the concentration distribution, whereas for large frequencies, this effect tends to diminish. The results of this study are of great importance in understanding the dispersion process in a catheterized artery with a reactive arterial wall.