Question

a) A solution contains 1.18×10^-2 M sodium hydroxide and 7.66×10^-3 M ammonium sulfide.
Solid silver acetate is added slowly to this mixture.

1. What is the formula of the substance that precipitates first?

2. What is the concentration of silver ion when this precipitation first begins?
[Ag⁺] = ------- M

b) A solution contains 9.85×10^-3 M calcium acetate and 5.76×10^-3 M silver nitrate.
Solid sodium sulfide is added slowly to this mixture.

1. What is the formula of the substance that precipitates first?

2. What is the concentration of sulfide ion when this precipitation first begins?
[S^2-] = ------- M

Answer 1

a) 1. When silver acetate is added to a solution containing sodium hydroxide and ammonium sulphide, the following reactions occur

Silver hydroxide (AgOH) has a Ksp value=2.0x10^-8

Silver sulphide (Ag₂S) has Ksp=1.0x10^-49

Since the Ksp of Ag₂​​​​​​S is less than that of AgOH, this means Ag₂S is less soluble in water than AgOH. So Ag₂S will precipitate first.

2. Concentration of ammonium sulphide (NH₄)₂S=7.66x10^-3 M

So concentration of sulphide ions (S^2-)=7.66x10^-3 M

(As 1 mol ammonium sulphide gives 1 mol sulphide ion in solution as per its chemical formula)

Ksp of Ag₂S=[Ag⁺]²[S^{​​​​​​2-}]=1.0x10^-49 (1 mol Ag ₂S contains 2 mol Ag⁺ and 1 mol S^2-)

[Ag⁺]²x7.66 x 10^-3=1.0 x 10^-49

[Ag⁺]²=1.0x10^-49/7.66 x10^{​​​​-3}=0.13x10^-46

[Ag⁺]=0.36x10^-23 M

So concentration of Ag⁺ when precipitation of Ag₂S begins=0.36x10^-23 M

b) 1. When sodium sulphide is added to a solution containing calcium acetate and silver nitrate, the following reactions occur

Calcium sulphide (CaS) has a Ksp value=8.0x10^-6

Silver sulphide (Ag₂S) has Ksp=1.0x10^-49

Since the Ksp of Ag₂​​​​​​S is less than that of CaS, this means Ag₂S is less soluble in water than CaS. So Ag₂S will precipitate first.

2. Concentration of silver nitrate (AgNO₃)=5.76x10^-3 M

So concentration of silver ions (Ag⁺)=5.76x10^-3 M

(As 1 mol silver nitrate gives 1 mol silver ion in solution as per its chemical formula)

Ksp of Ag₂S=[Ag⁺]²[S^{​​​​​​2-}]=1.0x10^-49 (1 mol Ag ₂S contains 2 mol Ag⁺ and 1 mol S^2-)

5.76x10^-3 x [S^2-]=1.0 x 10^-49

[S^{​​​​​​2-}]=1.0x10^-49/5.76 x10^{​​​​-3}=0.17x10^-46 M

So concentration of sulphide ion when precipitation of Ag₂S begins is 0.17x10^-46 M.