In: Chemistry
Sodium phosphate is added to a solution that contains 0.0099 M aluminum nitrate and 0.021 M calcium chloride. The concentration of the first ion to precipitate (either Al3+ or Ca2+) decreases as its precipitate forms. What is the concentration of this ion when the second ion begins to precipitate? Hint: Note that well over 99% of the first ion has precipitated before the second ion starts to precipitate. Correct Answer: 2.613e-7 (I need an "EXPERT" to show me how to arrive at this answer that I gave above with full work). *Ok there is no sodium phosphate concentration given, but somehow still you should be able to solve this without it.. Maybe you chem experts know another way of going about this and arriving at that answer or what are your conclusions or methods you guys are planning on using to solve this problem. Anything is appreciated! (If you are not too sure on how to solve this problem, then give me a good reasoning at least on why this problem cannot be solved but it should be solvable according to my general chem 2 college professor, but all i can tell you is that there is other similar questions to this getting some kind of answer here on chegg.
Aluminum phosphate dissolves according to
AlPO₄(s) ⇄ Al³⁺(aq) + PO₄³⁻(aq)
=>
Ksp = [Al³⁺]∙[PO₄³⁻]
with Ksp = 9.84×10⁻²¹
Calcium phosphate dissolves according to
Ca₃(PO₄)₂(s) ⇄ 3 Ca²⁺(aq) + 2 PO₄³⁻(aq)
=>
Ksp = [Ca²⁺]³∙[PO₄³⁻]²
with Ksp = 2.07×10⁻³³
By addition of sodium phosphate increases while the metal ion
concentrations are constant. When the product of the ion
concentrations reaches the value of Ksp. When you solve the
equilibrium equation of each salt for [PO₄³⁻] you get the level of
phosphate concentration at which the salt starts to
precipitate:
- aluminum phosphate
[PO₄³⁻] = Ksp / [Al³⁺] = 9.84×10⁻²¹ / 0.0099 = 9.93×10⁻19 M
- calcium phosphate
[PO₄³⁻] = √(Ksp / [Ca²⁺]²) = √(2.07×10⁻³³ / 0.021³) = 1.495 ×10⁻14
M
Because [PO₄³⁻] is smaller for Al³⁺, aluminum phosphate
precipitates first. After this point solution is saturated with
aluminum phosphate. Further addition of sodium phosphate increases
the phosphate concentration, so aluminum ion concentration
decreases due precipitation such that solubility equilibrium
equation is always satisfied. So at the instant when calcium
phosphate starts to precipitate the aluminum ion concentration has
decreased to:
[Al³⁺] = Ksp / [PO₄³⁻] = 9.84×10⁻²¹ / 1.495 ×10⁻¹⁴ = 6.58×10⁻⁷
M