How do you calculate the weight capacity of a shelf?
There is a cool site for this:  The "sagulator" for computing this. It's intended more for freespan shelves (like a book case), but you might be able to use it to answer your question.  Hope it meets your needs. Ed makes a good point about support as well. With that weight it will need to be fastened to studs with multiple brackets. 

Edit:  Forgot the link, here it is:  https://www.woodbin.com/calcs/sagulator/