As stated already, it is impossible to have an object at a distance beyond infinity, unless you have made some mathematical/theoretical physics breakthrough and have successfully calculated the value of (infinity + 42). If not, go find a dictionary, look up the definition of infinity, and be aware that everyone reading this thread is having a laugh at your expense.
If, on the other hand, the subject distance merely approaches infinity (distant mountains, stars, etc.) there are two things to keep in mind:
1: As focus distance approaches infinity, so does depth of field, regardless of aperture. You can't use selective focus on objects in deep space.
2: Aperture's effect on exposure level is completely independent of focus distance. You'll get a 1-stop exposure difference between f/8 and f/5.6 regardless of focus distance, as long as shutter speed and ISO remain constant.