Sodium sulfate is slowly added to a solution containing 0.0500 M Ca2 (aq) and 0.0210 M Ag (aq). What will be the concentration of Ca2 (aq) when Ag2SO4(s) begins to precipitate?

Ksp=1.20×10^–5 silver sulfate
ksp=4.93x 10 ^-5 calcium sulfate

To find out the concentration of Ca2+ when Ag2SO4(s) begins to precipitate, we need to determine the point at which the concentration of Ag+ ions in the solution reaches the solubility product constant (Ksp) of silver sulfate (Ag2SO4).

The balanced equation for the precipitation reaction is:
Ag+(aq) + SO4^2-(aq) ⇌ Ag2SO4(s)

Let's assume x M is the concentration of Ag+ ions that will precipitate and form Ag2SO4(s). This means the equilibrium concentrations of Ag+ and SO4^2- ions will become x M.

Using the solubility product constant (Ksp) equation for Ag2SO4:
Ksp = [Ag+]^2[SO4^2-]

Plugging in the values:
1.20 × 10^–5 = (x)^2(x)

Simplifying the equation:
1.20 × 10^–5 = x^3

Taking the cube root of both sides:
x = (1.20 × 10^–5)^(1/3)

Calculate the value of x:
x ≈ 0.0508 M (rounded to four significant figures)

Now, we know that when the concentration of Ag+ ions in the solution reaches approximately 0.0508 M, Ag2SO4(s) will begin to precipitate.

Since we know the total concentration of Ag+ ions before the addition of sodium sulfate is 0.0210 M, we can subtract the concentration of Ag+ ions that precipitate to find the concentration of Ca2+ ions remaining in the solution.

Concentration of Ca2+ = Initial concentration - Concentration of Ag+ that precipitates
Concentration of Ca2+ = 0.0500 M - 0.0508 M

Concentration of Ca2+ ≈ -0.0008 M or 0 M (rounded to four significant figures)

So, the concentration of Ca2+ when Ag2SO4(s) begins to precipitate is practically zero, since the negative concentration is not physically meaningful.

Ksp Ag2SO4 = 1.2E-5 = (Ag^+)^2(SO4^2-)

Ksp CaSO4 = 4.93E-5 = (Ca^2+)(SO4^2-)

So CaSO4 ppts first. How do you know that. Calculate the (SO4^2-) when each bgins to ppt.
Ag2SO4. (SO4^2-) = Ksp/(Ag^+)^2
(SO4^2-) = you do it. I get approx 2.7E-2M
CaSO4. (SO4^2-) = Ksp/(Ca^2+) = you do it but I have approx 1E-3. So if you are adding Na2SO4 slowly to the mix, the 1E-3 level will be reached before the 3E-2.

Visualize what is happening. Na2SO4 is being added slowly to a mix of Ag^+ and Ca^2+. As soon as the Ksp for CaSO4 is exceeded it starts to ppt and it will continue to ppt until (even after) the Ksp for Ag2SO4 is exceeded. When will that be. With a (Ag^+) = 0.021, Ksp will be exceeded when SO4^2- = that 2.7E-2 we calculated above. So slip 2.7E-2 (that's an aprox remember so go through the work to get a good number). Then calculate (Ca^2+).