Hello @johnbaker I’m very glad to know your interest to replace this 2013 Education iMac original processor Core i3-3225 with Core i7-3770S. Yes, you may do it, Remember one thing that Apple officially does not intend for the processor in any Intel-based iMac models to be upgraded that's why you must do this process following with the proper guideline. Actually, I’m a professional educational advisor and I have also used this same model: iMac Intel 21.5" EMC 2545 (Edu) for the last few years. Now I also gonna prepare to replace the original processor with the i7-3770S very soon. Thanks!