Where is the first track of Toaru Kagaku no Railgun S OST 2 first played?
this song was featured on the Railgun S OST but it first appeared in "a certain magical index", episode 14 which was actually titled the same as the song, "strongest vs weakest", viewable here https://www.youtube.com/watch?v=7NV2fR2cdRQ
but since your post does request when it appears in relevance to the Railgun series that would be episode 4 when Touma is fighting Misaka under the bridge at night. here's a clip of it directly from funimation's official channel https://www.youtube.com/watch?v=-lEtG-CJ9IY 
in the Railgun S series it was swapped for the soundtrack from OST volume 2 #16 "Ketsui to kakugo" in the Touma vs Accelerator fight which took place in episode 15.