In this paper, we investigate the physical layer security capabilities of reconfigurable intelligent surface (RIS) empowered wireless systems. In more detail, we consider a general system model, in which the links between the transmitter (TX) and the RIS as well as the links between the RIS and the legitimate receiver are modeled as mixture Gamma (MG) random variables (RVs). Moreover, the link between the TX and eavesdropper is also modeled as a MG RV. Building upon this system model, we derive the probability of zero-secrecy capacity as well as the probability of information leakage. Finally, we extract the average secrecy rate for both cases of TX having full and partial channel state information knowledge.