In this paper, we study the achievable rate region of 1-layer rate splitting (RS) in the presence of hardware impairment (HWI) and improper Gaussian signaling (IGS) for a single-cell reconfigurable intelligent surface (RIS) assisted broadcast channel (BC). We assume that the transceivers may suffer from an imbalance in in-band and quadrature signals, which is known as I/Q imbalance (IQI). The received signal and noise can be improper when there exists IQI. Therefore, we employ IGS to compensate for IQI as well as to manage interference. Our results show that RS and RIS can significantly enlarge the rate region, where the role of RS is to manage interference while RIS mainly improves the coverage.