An aqueous solution that 2.00 M in AgNO3 is slowly added from a buret to an aqueous solution that is 1.00×10−2 M in Cl− and 0.260 M in I−. When the second ion begins to precipitate, what is the remaining concentration of the first ion?

I know that the first ion to ppt is I- , however I can't figure out the remaining concentration.

When AgNO3 is added drop wise to the solution, the one with Qsp greater than Ksp will ppt first. You're correct, that is AgI. More drops of AgNO3 results in AgI continuing to ppt until Ksp for AgCl is met. What is (Ag^+) then?

Ksp = (Ag^+)(Cl^-). You know Ksp and you know Cl^-, solve for Ag^+. At that point with Ag^+ that value, what is I^-?
Ksp = (Ag^+)(I^-). You know Ksp and (Ag^+), solve for I^-. That is I^- at that point.

To determine the remaining concentration of the first ion (Cl-), we need to identify the point at which the second ion (I-) begins to precipitate.

Since Ag+ and Cl- ions form a sparingly soluble salt (AgCl) with a low solubility product (Ksp), we can use this information to determine when the precipitation of AgCl starts.

The precipitation reaction can be written as follows:
Ag+ (aq) + Cl- (aq) -> AgCl (s)

The solubility product constant expression for AgCl is:
Ksp = [Ag+][Cl-]

Given that the initial concentration of Cl- is 1.00×10−2 M, we can assume that it contributes negligibly to the equilibrium expression initially (because it is much smaller than the concentration of Ag+).

Thus, at the point when the precipitation of AgCl starts, the concentration of Ag+ will be equal to the solubility product constant, Ksp, of AgCl (because all Ag+ ions will react with the Cl- ions to form AgCl):

[Ag+] = Ksp / [Cl-] = Ksp / (1.00×10−2 M)

We can calculate the value of Ksp for AgCl using the solubility product constant:

Ksp = [Ag+][Cl-] = (2.00 M) * (1.00×10−2 M) = 2.00×10−2

Substituting this value into the equation, we get:

[Ag+] = (2.00×10−2) / (1.00×10−2) = 2.00 M

Therefore, when the second ion begins to precipitate (I-), the remaining concentration of the first ion (Cl-) is still 1.00×10−2 M.