I installed the program for molecular mass calculator but I can't seem to open it. Does anyone have a solution to this? Please and thank you

If you are talking about mine, it should be pretty straightforward, it will simply ask you to input a chemical formula and once you do, it will calculate the molar mass...

I'm using the Ti-84 plus CE and yesterday I installed ATOMI, ELECONFG, and STOICHIOMETRY and every time I try to open the programs I get error:archived

You need to go and Unarchive the program. I'm a bit fuzzy on the steps but it should be doable from the Memory menu. Press [2nd] then [+] to open the Memory Menu. From there look for Unarchive or Archive, maybe they're on the same line? Then select what you want to take actions on.

Be careful, Unarchived programs are susceptible to memory resets. So, if you ever intentionally reset your RAM, anything unarchived will be deleted. Memory Resets can also happen due to an error so it can happen accidentally as well.

Alternatively, you can download Cesium and transfer that over to your calculator. You'll then be able to run Archived programs without going through that menu.