Density fingering arising in the acid-catalyzed chlorite-tetrathionate reaction is investigated experimentally in Hele-Shaw cells of various thickness. Upward propagating chemical fronts are stable for all gapwidths examined. The initial evolution of the downward propagating planar fronts resulting in a cellular structure has been characterized by dispersion curves and it is found that the convectively unstable regime increases as the gapwidth increases. From the dispersion curves, the change in the characteristics of the most unstable mode and in the marginal wave number, separating the stable and unstable modes, is determined quantitatively.