Question

Sodium phosphate is added to a solution that contains 0.0070 M aluminum nitrate and 0.052 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?

Answer 1

Answer:

The answer to the question is;

The first ion to precipitate out is the Al³⁺ ion and the concentration of the Al³⁺ ion when the Ca²⁺ ion begins to precipitate is 1.12 × 10⁻⁵ M.

Explanation:

To solve the question, we note that

aluminum nitrate, Al(NO₃)₃ will dissociate as follows

Al(NO₃)₃ → Al³⁺ (aq) + 3NO₃⁻ (aq)

Therefore when sodium phosphate is added to a solution that contains aluminum nitrate  we have the following system  of aluminium phosphate which is

AlPO₄(s) ⇄ Al³⁺(aq) + PO₄³⁻(aq)

The solubility product for the above reaction is

Ksp = [Al³⁺][PO₄³⁻] = 9.84×10⁻²¹

The solubility product for calcium phosphate is expressed as

Ca₃(PO₄)₂(s) ⇄ 3 Ca²⁺(aq) + 2 PO₄³⁻(aq)

With Ksp =  [Ca²⁺]³[PO₄³⁻]² = 2.07×10⁻³³

From the solubility product, we can find the concentration of [PO₄³⁻] at which precipitation starts as follows

The phosphate concretion for Al³⁺ when precipitation starts is

[PO₄³⁻] = $\frac{K_{sp}}{[Al^{3+}]}$= 9.84×10⁻²¹ / 0.007 = 1.406×10⁻¹⁸ M

The phosphate concretion for Ca²⁺ when precipitation starts is

[PO₄³⁻] =$\sqrt{\frac{K_{sp}}{[Ca^{2+}]^2}}$  = $\sqrt{\frac{2.07\times10^{-33}}{[0.052]^2}}$ = 8.75×10⁻¹⁶ M

(Aluminium phosphate precipitates out first)

The reaction favors the precipitation of the aluminum phosphate first due to the lower concentration of the [PO₄³⁻]  ions in the [Al³⁺][PO₄³⁻] system which  is lower than the relative [PO₄³⁻] in the [Ca²⁺]³[PO₄³⁻]².

Therefore, the more sodium phosphate added serves to precipitate the remaining aluminium phosphate.

The process continues and the concentration of Al³⁺ decreases as more precipitates form. The process continues until the equilibrium conditions satisfies the precipitation threshold level for the calcium phosphate system concentration whereby the concentration of the Al³⁺ in the solution is given by.

[Al³⁺] = $\frac{K_{sp}}{[PO_4^{3-}]} = \frac{9.84\times 10^{-21}}{8.75\times 10^{-16}}$  = 1.12 × 10⁻⁵ M

Therefore the concentration of this aluminium ion when the calcium ion begins to precipitate =  1.12 × 10⁻⁵ M.