You mix 1.00 L of 2.00 M BaCl2 with 1.00 L of 2.00 M AgNO3. What compounds remain in solution, and what are their concentrations?

There is no compound in solution. You will produce 2 moles AgCl solid. Everything else is in solution as ions.

To determine the compounds that remain in solution and their concentrations, we need to consider the chemical reaction that occurs between BaCl2 and AgNO3. BaCl2 is a soluble compound, so it dissociates into its ions when it dissolves in water:

BaCl2 (aq) → Ba2+ (aq) + 2Cl- (aq)

AgNO3 is also a soluble compound and dissociates into its ions:

AgNO3 (aq) → Ag+ (aq) + NO3- (aq)

Now, we need to determine if there is a reaction occurring between the ions. By looking at the balanced chemical equation, it can be seen that there is a possibility for precipitation because both the Ba2+ and the Cl- ions can react to form an insoluble compound, BaCl2.

Ba2+ (aq) + 2Cl- (aq) → BaCl2 (s)

To determine if a reaction will occur, we need to check if there is a net ionic equation. In this case, both compounds are strong electrolytes, meaning they fully dissociate into ions. Therefore, we can write the net ionic equation:

Ba2+ (aq) + 2Cl- (aq) + 2Ag+ (aq) + 2NO3- (aq) → BaCl2 (s) + 2Ag+ (aq) + 2NO3- (aq)

From the net ionic equation, we can see that BaCl2 forms a precipitate while AgNO3 remains in solution. Therefore, the compound that remains in the solution is AgNO3.

As for the concentrations, both the Ba2+ and Cl- ions are consumed in the reaction, forming the precipitate BaCl2. Hence, the concentrations of Ba2+ and Cl- ions will decrease to zero.

On the other hand, the Ag+ and NO3- ions remain in solution as AgNO3. Since the initial concentration of AgNO3 is 2.00 M, the concentrations of Ag+ and NO3- ions will still be 2.00 M.

To summarize:
The compound that remains in the solution is AgNO3, and its concentration remains at 2.00 M.
The compounds that form a precipitate are Ba2+ and Cl-, and their concentrations reduce to zero.