Can you determine a compounds structural formula if you are given the molecular formula?

You might be able to do so in a few cases. If you take CH4 or O3, and know the bonds that those elements form, you'll see those can only be arranged one way.

But if you take C4H10, this can be arranged in different ways. The four carbon atoms could be in a chain of four, which is known as Butane. Or you could have one central Carbon atom with all three of the others attached to it, this is called Isobutane. You don't know which you are talking about from just saying C4H10 alone.