Mercurous Bromide ($Hg_2Br_2$) crystals hold promise for many acousto-optic and opto-electronic applications. This material is prepared in closed ampoules by the physical vapor transport (PVT) growth method. We investigate the effects of solutal convection on the crystal growth rate in a horizontal configuration for diffusive-convection conditions and purely diffusion conditions achievable in a low gravity environment. Our results show that the growth rate is decreased by a factor of one-fourth with a ten reduction of gravitational acceleration near y = 2.0 cm. For 0.1 $g_O$ the growth rate pattern exhibits relatively flat which is intimately related to diffusion-dominated processes. The growth rate nonuniformity is regardless of aspect ratio across the interfacial positions from 0 to 1.5. Also, the effect of a factor of the ten reduction in the gravitational acceleration is same to both Ar = 5 and 2. The enlargement in the molecular weight of B from 50 to 500 by a factor 4 causes a decrease in the maximum growth rate by the same factor, indicative of the effect of solutal gradients.