Question

Argentometric titrations can be used to determine the concentration of a number of halides (see Table 7-1 in the book). However, if the sample contains a mixture of halides they will precipitate in certain order. Considering that information, which of the following will preferentially form during a titration with AgNO₃?

A .Silver acetate (Ksp = 2.0 x 10-3)

B. Silver bromide (Ksp = 5.3 x 10-13)

C. Silver chloride (Ksp = 1.8 x 10-10)

D. AgF (very soluble)

E. Silver carbonate (Ksp = 8.1 x 10-10)

Answer 1

Given the K_sp values, we need to determine the solubility of the halides to answer the question.

a) Silver acetate, AgAc.

=

AgAc (s) <====> Ag⁺ (aq) + Ac^- (aq)

K_sp = [Ag⁺][Ac^-] = 2.0*10^-3

===> (x).(x) = 2.0*10^-3 (the solubilities of Ag⁺ and Ac^- are the same due to 1:1 nature of the dissociation).

===> x² = 2.0*10^-3

===> x = 0.0447

The solubility of Ac^- is 0.0447 M (ans).

b) Silver Bromide, AgBr.

AgBr (s) <=====> Ag⁺ (aq) + Br^- (aq)

K_sp = [Ag⁺][Br^-] = 5.3*10^-13

===> (x).(x) = 2.0*10^-3 (the solubilities of Ag⁺ and Br^- are the same due to 1:1 nature of the dissociation).

===> x² = 5.3*10^-13

===> x = 7.280*10^-7

The solubility of Br^- is 7.280*10^-7 M (ans).

c) Silver Chloride, AgCl.

AgCl (s) <=====> Ag⁺ (aq) + Cl^- (aq)

K_sp = [Ag⁺][Cl^-] = 1.8*10^-10

===> (x).(x) = 1.8*10^-10 (the solubilities of Ag⁺ and Cl^- are the same due to 1:1 nature of the dissociation).

===> x² = 1.8*10^-10

===> x = 1.342*10^-5

The solubility of Cl^- is 1.342*10^-5 M (ans).

d) Silver fluoride, AgF is soluble in water.

e) Silver Carbonate, Ag₂CO₃.

Ag₂CO₃ (s) <======> 2 Ag⁺ (aq) + CO₃^2- (aq)

K_sp = [Ag⁺]²[CO₃^2-] = 8.1*10^-10

====> (2x)².(x) = 8.1*10^-10 (the solubilities of Ag⁺ and CO₃^2- are in the ratio 2:1 due to the nature of dissociation).

====> 4x³ = 8.1*10^-10

====> x = 1.423*10^-5

The solubility of CO₃^2- is 1.423*10^-5 M (ans).

We note that Br^- is the least soluble when a source of Ag⁺ is added and hence, AgBr will preferentially form when a solution of AgNO₃ is added (ans).

When all the Br^- is replenished, AgCl will start forming (ans).