Solid Na2SO4 is added to a solution which is 0.020 M in Pb(NO3)2 and 0.045 M in AgNO3. Assume the volume remains constant. Ksp = 2.0 10-8 for PbSO4 and Ksp = 1.2 10-5 for Ag2SO4.
What is the concentration of the first ion precipitated when the second ion starts to precipitate?
Ksp = 2E-8 = (Pb^2+)(SO4^2-)
(SO4^2-) = 2E-8/0.02 = 1E=6M
Ksp = 1.2E-5 = (Ag^+)^2(SO4^2-)
(SO4^2-) = 1.2E-5/(0.045)^2 = 5.9E-3
When Na2SO4 is added incrementally, the first Ksp exceeded will begin to ppt. Ksp for PbSO4 is smaller; therefore, it will be the first ppt. It will continue to ppt as Na2SO4 is added until the Ksp for Ag2SO4 is exceeded. When will that be? When the (SO4^2-) becomes 5.9E-3M (and not before). So what will (Pb^2+) be when SO4^2- is 5.9E-3. Go back to the PbSO4 Ksp, plug in SO4^2- = 5.9E-3 and calculate the (Pb^2+).
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To find the concentration of the first ion precipitated when the second ion starts to precipitate, we need to compare the solubility products (Ksp) of the two precipitates (PbSO4 and Ag2SO4).
First, let's determine which ion is the first to precipitate. We compare the solubility product (Ksp) values for PbSO4 and Ag2SO4.
Given:
Ksp for PbSO4 = 2.0 × 10^(-8)
Ksp for Ag2SO4 = 1.2 × 10^(-5)
Ksp is an equilibrium constant that describes the solubility of a compound in a solution. When the product of the concentrations of the ions in a saturated solution exceeds the Ksp, precipitation occurs.
For PbSO4:
PbSO4 (s) ⇌ Pb^2+ (aq) + SO4^2- (aq)
For Ag2SO4:
Ag2SO4 (s) ⇌ 2Ag^+ (aq) + SO4^2- (aq)
To determine the concentration of the first ion precipitated, we compare the Ksp values. The ion with the larger Ksp will reach its saturation point first. In this case, PbSO4 has a smaller Ksp than Ag2SO4, so PbSO4 will precipitate first.
To find the concentration of the first ion precipitated, we need to find the concentration of Pb^2+ when PbSO4 starts to precipitate. We can assume that the concentration of SO4^2- will be twice the concentration of Pb^2+ due to the balanced equation.
Let's assume the concentration of Pb^2+ when precipitation of PbSO4 just starts is x M.
Thus, the concentration of SO4^2- is 2x M.
Using the expression for the solubility product (Ksp) for PbSO4:
Ksp = [Pb^2+][SO4^2-]
Ksp = (x)(2x)
2.0 × 10^(-8) = 2x^2
Solving for x:
x^2 = (2.0 × 10^(-8)) / 2
x^2 = 1.0 × 10^(-8)
x = √(1.0 × 10^(-8))
x ≈ 1.0 × 10^(-4)
Therefore, the concentration of Pb^2+ when the precipitation of PbSO4 starts is approximately 1.0 × 10^(-4) M.