Purdue: first year engineering students apply to their majors after completing some college course work. 3.2 college GPA automatically admits to major, otherwise competitive (apparently not that competitive for most engineering majors, but the school has not been transparent about past admission GPAs). Transition to Major - School of Engineering Education - Purdue University and Enrollment Management Policy for FYE Students - College of Engineering - Purdue University
UIUC: if you were directly admitted to the MSE major, then you can stay in the major. Changing to chemical engineering is described at On-Campus Transfer to SCS Majors | School of Chemical Sciences at Illinois . Changing major to popular majors can be difficult at UIUC due to many majors being filled to capacity by direct admission (e.g. ME and CS require a 3.75 college GPA just to enter a competitive admission process).