One of the interests in studying the intercalation phenomenon of Li-ion is to explain the hystereses which are observed on the open circuit voltage curve of the graphite electrode during the charge and discharge. We investigated a potentiometric method to obtain the equilibrium curve and entropy change curve of the graphite electrode in charge and discharge. These curves lead to the analysis of the intercalation compounds in the graphite electrode. The results show a high hysteresis between the lithiation and delithiation in region II on the entropy curve. We do not observe the formation of LiC18 compound which would be observed at filling fraction x = 0.33 and there is no clear evidence of the LiC27 at x = 0.22. Based on our observations, we propose an intercalation model of Li into graphite in an attempt to explain the hysteresis phenomenon which was observed during charge and discharge in region II due to the possible presence of the compound LiC24. We have also observed a possible compound for the LiC24 by XRD post-mortem analysis.