What is the Cl concentration just as Ag2CrO4 begins to precipitate when 1.0 M AgNO3 is slowly added to a solution containing 0.015 M Cl and 0.015 M CrO4^2?
To find the concentration of Cl- just as Ag2CrO4 begins to precipitate, we need to determine the solubility product constant (Ksp).
The balanced equation for the precipitation reaction is:
Ag2CrO4(s) ⇌ 2Ag+(aq) + CrO4^2-(aq)
The Ksp expression for this reaction is:
Ksp = [Ag+]^2 [CrO4^2-]
The solubility product constant for Ag2CrO4 is 1.1 x 10^-12.
Given that the initial concentrations of Cl- and CrO4^2- are the same (0.015 M), and assuming the formation of Ag2CrO4 is small (x), we can write the Ksp expression as:
1.1 x 10^-12 = (2x)^2 (x)
Simplifying, we get:
1.1 x 10^-12 = 4x^3
Now, solve for x:
x^3 = (1.1 x 10^-12) / 4
x = [(1.1 x 10^-12) / 4]^(1/3)
Calculating this, we find that x ≈ 2.63 x 10^-5 M.
Therefore, the concentration of Cl- just as Ag2CrO4 begins to precipitate is approximately 2.63 x 10^-5 M.