how do you find the concentration of an ion remaining after a reaction is complete???

Answer 1

There are two or three methods but each is a little different and each depends upon the reaction. There is no general way to do it.
If you have a limiting reagent problem (limiting reagent problems are those in which amounts are given for BOTH reactants) you do them this way. There are shorter ways but this method is easier to explain.
"What amount of NaCl remains unreacted after 5g NaCl reacts with 5g AgNO3?"

AgNO3 + NaCl ==> AgCl + NaNO3
1. First determine the limiting reagent (LR).
mols NaCl =- 5/58.5 = about 0.085 but you need to do it more accurately.
mols AgNO3 = 5/170 = about 0.029

Convert mols NaCl to mols AgCl (any product will do, however). That is 0.085.
Convert mols AgNO3 to mols AgCl (always use the same product though). 0.029

You can see one gives you 0.085 and the other 0.029; both can't be right. The correct answer in LR problems is ALWAYS the smaller value and the reagent producing that value is the limiting reagent (LR). The other reagent is called the excess reagent (ER), other reagent, or non-limiting reagent. You can determine grams, if that's what you wanted, for AgCl by mols AgCl x molar mass AgCl or about 4.2 g. Again, these are estimates. So far this is just a glorified stoichiometry problem.

How do we find how much NaCl is left? That's just another stoichiometry problem.
mols AgNO3 (LR) = 0.029
Using the coefficients in the balanced equation convert mols AgNO3 to mols NaCl. That's 0.029 mols NaCl used. We had 0.085 mols initially, we've used 0.029 mols so we must have 0.085-0.029 = 0.056 mols NaCl left. That will be 0.056 x 58.5 = about 3.3g remaining unreacted. You can see this is the excess reagent (ER).