I donate to my university, I do it to fund scholarships and programs that I benefited from when attending. I don't donate to the 'general fund'. Although the bulk of my donations to my alma mater go to cancer treatment center at the university medical center which relies on fundraising for research and other programs which I believe will benefit all. I would never donate to revamp a student union as I believe that should be paid for by the University.
Money is fungible. Every dollar donated to the medical center is a dollar freed up from the general fund (until the medical center is totally funded with earmarked donations, of course).