One of the easiest things to do would be to go to the Arkansas site.
Then right there on the upper right hand corner is the Gerdes site.
The Gerdes site lists every known man and the Arkansas unit each served in during the Civil War.
Some CSA units had such poor record keeping that unless a man filed for a pension, died in a prison, or perhaps a wife filed for a widow's pension, no one knows if that individual was there or not.
If by chance your person died in a Federal Prison, you may be in luck and actually find out where he went to. Now finding a grave would be like winning the lottery.
I am not trying to sound unkind, but just being honest with you, at least that is the way it has been for me.