Solid Na2SO4 is added to a solution which is 0.014 M in Pb(NO3)2 and 0.041 M in AgNO3. Assume the volume remains constant. Ksp = 2.0 10-8 for PbSO4 and Ksp = 1.2 10-5 for Ag2SO4.
(a) Which compound precipitates first?
1 PbSO4
(b) What is the concentration of the first ion precipitated when the second ion starts to precipitate?
I NEED HELP WITH PART B THANK YOU!
Divide Ksp of one by the other.
[KspPbSO4/KspAg2SO4]=[(Pb^+2)(SO4^=)/(Ag^+)^2(SO4^=)].
Note (SO4^=) cancels and you are left with
2*10^-8/1.2*10^-5 = (Pb^+2)(Ag^+)^2
Plug in (Ag^+)^2 and solve for (Pb^+2), Check my thinking.
To determine the concentration of the first ion precipitated when the second ion starts to precipitate, we need to compare the solubility products of the two compounds. The compound with a smaller solubility product will precipitate first.
The solubility product (Ksp) expression for each compound is as follows:
For PbSO4: Ksp = [Pb2+][SO4^2-]
For Ag2SO4: Ksp = 4[Ag+][SO4^2-]
Given that Ksp for PbSO4 is 2.0×10^-8 and Ksp for Ag2SO4 is 1.2×10^-5, we can compare the two expressions:
2.0×10^-8 = [Pb2+][SO4^2-]
1.2×10^-5 = 4[Ag+][SO4^2-]
From the second equation, we can rearrange it to find the concentration of Ag+ when the second ion starts to precipitate:
[Ag+] = (1.2×10^-5)/(4[SO4^2-])
Now, we need to determine the concentration of the sulfate ion (SO4^2-) at this point. Initially, there is no sulfate ion in the solution, but when the first ion precipitates, it reacts with the available sulfate ions to form the precipitate. Thus, the concentration of sulfate ion at the point when the second ion starts to precipitate can be calculated by using stoichiometry.
To do this, we need to determine the stoichiometric coefficients of the ions precipitation reaction between the first and second compound. The balanced equation for the precipitation of PbSO4 is:
Pb2+ + SO4^2- → PbSO4
According to the equation, the stoichiometric coefficient for sulfate ion (SO4^2-) is 1.
Therefore, the concentration of sulfate ion (SO4^2-) at the point when the second ion (Ag+) starts to precipitate is the same as the initial concentration of sulfate ion in the solution, which is 0 (zero).
Now, we can substitute the concentration of sulfate ion (SO4^2-) into the equation for [Ag+]:
[Ag+] = (1.2×10^-5)/(4×0) = undefined
Therefore, the concentration of the first ion precipitated when the second ion starts to precipitate is undefined as there is no sulfate ion (SO4^2-) remaining in the solution.