Single crystals of Bi_2 Rh _3S _2 and Bi_2 Rh _3.5S _2 were synthesized by solution growth and the crystal structures, thermodynamic and transport properties of both compounds were studied. In the case of Bi_2 Rh _3S _2, a structural first-order transition at around 165 K is identified by single crystal diffraction experiments, with clear signatures visible in resistivity, magnetization and specific heat data. No superconducting transition for Bi_2 Rh _3S _2 was observed down to 0.5 K. In

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... st, no structural phase transition at high temperature was observed for Bi_2 Rh _3.5S _2, however bulk superconductivity with a critical temperature, T_c≈ 1.7 K was observed. The Sommerfeld coefficient γ and the Debye temperature(_D) were found to be 9.4 mJ mol^-1 K^-2 and 209 K respectively for Bi_2 Rh _3S _2, and 22 mJ mol^-1 K^-2 and 196 K respectively for Bi_2 Rh _3.5S _2. Study of the specific heat in the superconducting state of Bi_2 Rh _3.5S _2 suggests that Bi_2 Rh _3.5S _2 is a weakly coupled, BCS superconductor.