mix for black tank using calgon water softner

I just usually give it a couple of Glugs down the toilet after a tank flush. I believe its about a cup or so, just enough to soften the water as it fills, My thought being that after a flush I add about five gallons of water to the black tank and a cup or so also,, the splashing and sloshing on the way camping will coat the sides and censors to help make thing flow smoothly..
Wall mart sells the quarts and half gallons of Calgon, I think I have a half of a half left over.. Probably splash half of that in next trip..