What is the standard distance between bars in a slab?
There is no STANDARD distance. Concrete slab design, both in thickness, and in reinforcement requirements, are based upon the use of the slab. The heavier that the load on the slab will be, the thicker the concrete, and also either the thicker the rebar will be, or the closer the spacing of the rebar will be, or both.
That being said, rebar is often spaced at either 12in or 16in on center. For instance, a slab with just pedestrian traffic on it may have #4 rebar at 16in on center. A slab requiring the ability to bear slightly more loading may require #4 at 12in on center.
Then, a slab requiring still more loading may call for #5 rebar at 16 inch on center, and from there maybe up to #5 at 12in on center. That being said, it is not unheard of to have rebar at 8in, 10in, or even 18in on center.
Engineers determine how much weight of rebar steel is required, either per cubic yard or per square foot of a given slab thickness, based on the load that is going to be expected. Based on that number, they can specify different sizes of rebar in combination with different spacing to achieve the weight per unit that they are looking for.
Again, 12in and 16in on center are very common but they are not necessarily standard and there are other considerations to be dealt with