Question

I have 1.01 of a solution that is 0.100M Fe(NO₃)₂ and 0.200M Cu(NO₃)₂​. I want to seperate the metal ions. I gradually add a solution that is 0.100M in K₃PO₄, 0.100 M in KOH, and 0.100 M in K₂CO_3.What volume of the solution do I need to add to get the first metal to begin to precipitate?

Answer 1

We need to ascertain what metal salts can possibly precipitate out from the solution.

We have the following options.

Fe₃(PO₄)₂ (s) <=====> 3 Fe²⁺ (aq) + 2 PO₄^3- (aq); K_sp = 1.0*10^-36

Fe(OH)₂ (s) <=====> Fe²⁺ (aq) + 2 OH^- (aq); K_sp = 7.9*10^-16

FeCO₃ (s) <======> Fe²⁺ (aq) + CO₃^2- (aq) ; K_sp = 2.1*10^-11

Cu₃(PO₄)₂ (s) <=====> 3 Cu²⁺ (aq) + 2 PO₄^3- (aq); K_sp = 1.40*10^-37

Cu(OH)₂ (s) <=====> Cu²⁺ (aq) + 2 OH^- (aq); K_sp = 4.8*10^-20

CuCO₃ (s) <=====> Cu²⁺ (aq) + CO₃^2- (aq); K_sp = 1.40*10^-10

We see that both the metal ions are divalent and form salts that solubilize in the same way. Hence, we can compare the K_sp values to predict which metal ion will precipitate out first. Since Fe₃(PO₄)₂ and Cu₃(PO₄)₂ have comparable K_sp values, either one of them will precipitate out first.

Find out the concentration of PO₄^3- required to precipitate out both.

Fe₃(PO₄)₂: K_sp = [Fe²⁺]³[PO₄^3-]²

===> 1.0*10^-36 = (0.100)³*[PO₄^3-]²

===> [PO₄^3-]² = 1.0*10^-33

===> [PO₄^3-] = 3.162*10^-17

The concentration of PO₄^3- required to precipitate out Fe₃(PO₄)₂ is 3.162*10^-17 M. Since the concentration of PO₄^3- is extremely low, we can assume the total volume of the solution to stay constant at 1.0 L.

Use the dilution equation to find out the volume of K₃PO₄ required.

M₁*V₁ = M₂*V₂

===> (1.0 L)*(3.162*10^-17 M) = (0.100 M)*V₂

===> V₂ = 3.162*10^-16 L (ans).

Cu₃(PO₄)₂: K_sp = [Cu²⁺]³[PO₄^3-]²

===> 1.40*10^-37 = (0.200)³*[PO₄^3-]²

===> [PO₄^3-]² = 1.75*10^-35

===> [PO₄^3-] = 4.183*10^-18

The concentration of PO₄^3- required to precipitate out Cu₃(PO₄)₂ is 4.183*10^-18 M. Since the concentration of PO₄^3- is extremely low, we can assume the total volume of the solution to stay constant at 1.0 L.

Use the dilution equation to find out the volume of K₃PO₄ required.

M₁*V₁ = M₂*V₂

===> (1.0 L)*(4.183*10^-18 M) = (0.100 M)*V₂

===> V₂ = 4.183*10^-17 L (ans).

Since it requires a lower volume of PO₄^3- to precipitate out Cu₃(PO₄)₂, hence it will take 4.183*10^-17 L of the solution to precipitate out the first salt.