They mean different things.
Originally Posted by eleanordsouza
Sentence 1 asks if the library will open for the first time ever today. Perhaps there will be a ceremony where someone will open the doors for the first time. Maybe it's the first time there has been a library in the town.
Sentence 2 simply asks if the library will be open for people to come in and borrow books today. Will it be open, not closed?
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.