They move (on average) at 500m/s but they are bouncing back and forth randomly. On average a molecule moves away from it's starting location at the square root of time. So if it takes 1 us to move 1 um then it takes 4 us to move 2 um, 1e6 us to move 1e3 um and 1e12 us to move 1e6 um (or 1 million seconds to move 1 meter).

I pulled those numbers out of my ass but if you know the root mean velocity (your 500m/s number) and the root mean path (average distance until collision) you can use the two numbers to derive the diffusion coefficient from first principles.