Rate Splitting Multiple Access (RSMA) relies on multi-antenna rate splitting (RS) at the transmitter and successive interference cancellation (SIC) at the receiver. In RS the users' messages are split into a common message and private messages, where the common part is first decoded by the all users, while the private part is decoded only by the intended user using SIC technique. This split of the users' signals into common and private parts raises some interesting tradeoffs between maximizing sum rate versus secrecy rate. In this work we consider the secrecy performance of RSMA in multi-user multiple-input single-output (MU-MISO) systems, where secrecy is defined by the ability of any user to decode the signal intended for user k in the system. To that end, new analytical expressions for the ergodic sum-rate and ergodic secrecy rate are derived for two closed-form precoding techniques of the private messages, namely, 1) zero-forcing (ZF) precoding approach, 2) minimum mean square error (MMSE) approach. Then, based on the analytical expressions of the ergodic rates, novel power allocation strategies that maximize the sum-rate subject to a target secrecy rate for the two precoding schemes are presented and investigated. Our Monte Carlo simulations show a close match with our theoretical derivations. They also reveal that, by tuning the split of the messages, our power allocation approaches provide a scalable tradeoff between rate benefits and secrecy.