Question

As a sodium chloride solution is added to a solution of silver nitrate, a white precipitate forms. Ammonia is added to the mixture and the precipitate dissolves. When potassium bromide solution is then added, a pale yellow precipitate appears. When a solution of sodium thiosulfate is added, the yellow precipitate dissolves. Finally, potassium iodide is added to the solution and a yellow precipitate forms. Write reactions for all the changes mentioned above. What conclusions can you draw concerning the sizes of the Kop values for AgCl, AgBr, and AgI? What can you say about the relative values of the formation constants of $\mathit{A}\mathit{g}{\left(N{H}_3\right)}_{\mathbf{2}}^{\mathbf{+}}$and $\mathit{A}\mathit{g}{\mathbf{\left(}{\mathbf{S}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{\right)}}_{\mathbf{2}}^{\mathbf{3}\mathbf{-}}$?

Short answer

Answer

Thereactions for all the changesare

$$\begin{gathered} \mathit{N}\mathit{a}\mathit{C}\mathit{l}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{+}\mathit{A}\mathit{g}\mathit{N}{\mathit{O}}_{\mathbf{3}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{\to }\mathit{A}\mathit{g}\mathit{C}\mathit{l}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathit{N}\mathit{a}\mathit{N}{\mathit{o}}_{\mathbf{3}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{w}\mathit{h}\mathit{i}\mathit{t}\mathit{e}\mathbf{}\mathit{p}\mathit{p}\mathit{t}\mathbf{.} \\ \mathit{A}\mathit{g}\mathit{C}\mathit{l}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathit{N}{\mathit{H}}_{\mathbf{3}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{A}\mathit{g}{\mathbf{\left(}\mathbf{N}{\mathbf{H}}_{\mathbf{3}}\mathbf{\right)}}_{\mathbf{2}}^{\mathbf{+}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{}\mathbf{}\mathbf{+}\mathbf{}\mathbf{}\mathbf{}\mathit{C}{\mathit{l}}^{\mathbf{-}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)} \\ \mathit{A}\mathit{g}{\left(N{H}_3\right)}^{\mathbf{2}\mathbf{+}}\left(aq\right)\mathbf{}\mathbf{+}\mathbf{}\mathit{B}{\mathit{r}}^{\mathbf{-}}\left(aq\right)\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{A}\mathit{g}\mathit{B}\mathit{r}\left(s\right)\mathbf{}\mathbf{+}\mathbf{}\mathbf{2}\mathit{N}{\mathit{H}}_{\mathbf{3}}\left(aq\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\left(KBr\right)\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{p}\mathit{a}\mathit{l}\mathit{e}\mathbf{}\mathit{y}\mathit{e}\mathit{l}\mathit{l}\mathit{o}\mathit{w} \\ \mathit{A}\mathit{g}\mathit{B}\mathit{r}\left(s\right)\mathbf{+}\mathbf{2}{\mathit{S}}_{\mathbf{2}}{{\mathit{O}}_{\mathbf{3}}}^{\mathbf{2}\mathbf{-}}\left(aq\right)\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{A}\mathit{g}{{\left(S_2{O}_3\right)}_{\mathbf{2}}}^{\mathbf{3}\mathbf{-}}\left(aq\right)\mathbf{+}\mathit{B}{\mathit{r}}^{\mathbf{-}}\left(aq\right) \\ \mathit{y}\mathit{e}\mathit{l}\mathit{l}\mathit{o}\mathit{q}\mathbf{}\mathit{p}\mathit{p}\mathit{t}\mathbf{.} \\ \mathit{d}\mathit{i}\mathit{s}\mathit{s}\mathit{o}\mathit{l}\mathit{v}\mathit{e}\mathit{s} \\ \mathit{A}\mathit{g}{{\left(S_2{O}_3\right)}_{\mathbf{2}}}^{\mathbf{3}\mathbf{-}}\left(aq\right)\mathbf{+}{\mathit{I}}^{\mathbf{-}}\left(aq\right)\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{A}\mathit{g}\mathit{l}\left(s\right)\mathbf{+}\mathbf{2}{\mathit{S}}_{\mathbf{2}}{{\mathit{O}}_{\mathbf{3}}}^{\mathbf{2}\mathbf{-}}\left(aq\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\left(KI\right)\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{y}\mathit{e}\mathit{l}\mathit{l}\mathit{o}\mathit{w}\mathbf{}\mathit{p}\mathit{p}\mathit{t}\mathbf{.} \end{gathered}$$

The order of ${\mathit{K}}_{\mathbf{s}\mathbf{p}}$values are

${\mathit{K}}_{\mathbf{s}\mathbf{p}}\left(AgCl\right)\mathbf{>}{\mathit{K}}_{\mathbf{s}\mathbf{p}}\left(AgBr\right)\mathbf{>}{\mathit{K}}_{\mathbf{s}\mathbf{p}}\left(Agl\right)$

Therelative values of the formation constants

$\left(K_f\left[Ag{{\left(S_2{O}_3\right)}_2}^{3-}\right]>K_f\left[Ag{{\left(N{H}_3\right)}_2}^{+}\right]\right)$

Step-by-step solution

Formation of white precipitate.

The reaction when NaCl is added,

$$\begin{gathered} \mathit{N}\mathit{a}\mathit{C}\mathit{l}\left(aq\right)\mathbf{+}\mathit{A}\mathit{g}\mathit{N}{\mathit{O}}_{\mathbf{3}}\left(aq\right)\mathbf{\to }\mathit{A}\mathit{g}\mathit{C}\mathit{l}\left(s\right)\mathbf{+}\mathit{N}\mathit{a}\mathit{N}{\mathit{O}}_{\mathbf{3}}\left(aq\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{w}\mathit{h}\mathit{i}\mathit{t}\mathit{e}\mathbf{}\mathit{p}\mathit{p}\mathit{t}\mathbf{.} \end{gathered}$$

AgCl is a white precipitate.

Formation of the pale-yellow precipitate.

The reaction of ammonia and KBr is added,

$$\begin{gathered} \mathit{A}\mathit{g}\mathit{C}\mathit{l}\left(s\right)\mathbf{}\mathbf{}\mathbf{}\mathbf{+}\mathbf{}\mathbf{}\mathbf{}\mathbf{2}\mathit{N}{\mathit{H}}_{\mathbf{3}}\left(aq\right)\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{A}\mathit{g}{{\left(N{H}_3\right)}_{\mathbf{2}}}^{\mathbf{+}}\left(aq\right)\mathbf{}\mathbf{}\mathbf{+}\mathbf{}\mathbf{}\mathit{C}{\mathit{l}}^{\mathbf{-}}\left(aq\right) \\ \mathit{p}\mathit{p}\mathit{t}\mathbf{.}\mathbf{}\mathit{d}\mathit{i}\mathit{s}\mathit{s}\mathit{o}\mathit{l}\mathit{v}\mathit{e}\mathit{s} \end{gathered}$$

The white colored precipitate dissolves.

$$\begin{gathered} \mathit{A}\mathit{g}{\mathbf{\left(}{\mathbf{NH}}_{\mathbf{3}}\mathbf{\right)}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{}\mathbf{}\mathbf{}\mathbf{+}\mathbf{}\mathbf{}\mathbf{}\mathit{B}{\mathit{r}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{A}\mathit{g}\mathit{B}\mathit{r}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{}\mathbf{}\mathbf{+}\mathbf{}\mathbf{}\mathbf{2}\mathit{N}{\mathit{H}}_{\mathbf{3}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\left(}\mathbf{KBr}\mathbf{\right)}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{p}\mathit{a}\mathit{l}\mathit{e}\mathbf{}\mathit{y}\mathit{e}\mathit{l}\mathit{l}\mathit{o}\mathit{w} \end{gathered}$$

AgBr is a pale-yellow precipitate.

Formation of yellow precipitate

The reaction ofsodium thiosulfateand KI is added,

$$\begin{gathered} \mathit{A}\mathit{g}\mathit{B}\mathit{r}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{}\mathbf{+}\mathbf{2}{\mathit{S}}_{\mathbf{3}}{{\mathit{O}}_{\mathbf{3}}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{A}\mathit{g}{{\mathbf{\left(}{\mathbf{S}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{\right)}}_{\mathbf{2}}}^{\mathbf{3}\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathit{B}{\mathit{l}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)} \\ \mathit{y}\mathit{e}\mathit{l}\mathit{l}\mathit{o}\mathit{w}\mathbf{}\mathbf{}\mathit{p}\mathit{p}\mathit{t}\mathbf{.} \\ \mathbf{}\mathbf{}\mathit{d}\mathit{i}\mathit{s}\mathit{s}\mathit{o}\mathit{l}\mathit{v}\mathit{e}\mathit{s} \end{gathered}$$

The yellow colored AgBr dissolves.

Also, with the addition of potassium iodide.

$$\begin{gathered} \mathit{A}\mathit{g}{{\mathbf{\left(}{\mathbf{S}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{\right)}}_{\mathbf{2}}}^3\mathbf{}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathit{I}\mathbf{}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{A}\mathit{g}\mathit{l}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{}\mathbf{+}\mathbf{}\mathbf{2}{\mathit{S}}_{\mathbf{2}}{{\mathit{O}}_{\mathbf{3}}}^{\mathbf{2}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\left(}\mathbf{Kl}\mathbf{\right)}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{y}\mathit{e}\mathit{l}\mathit{l}\mathit{o}\mathit{w}\mathbf{}\mathbf{}\mathit{p}\mathit{p}\mathit{t}\mathbf{.} \end{gathered}$$

Here, AgI is a yellow precipitate.

Order of the formation constants.

The least soluble salt is AgI, it leads to the presence of $\mathit{B}{\mathit{r}}^{\mathbf{-}}$and $\mathit{C}{\mathit{l}}^{\mathbf{-}}$ions.

The highest soluble salt is AgCl.

Therefore, the order of ${\mathit{K}}_{\mathbf{sp}}$values are

${\mathit{K}}_{\mathbf{s}\mathbf{p}}\left(AgCl\right)\mathbf{>}{\mathit{K}}_{\mathbf{s}\mathbf{p}}\left(AgBr\right)\mathbf{>}{\mathit{K}}_{\mathbf{s}\mathbf{p}}\left(Agl\right)$

The relative values of the formation constants.

The precipitation of AgBr dissolution by the addition of thiosulfate because of the presence of ammonia cannot be prevented.

The order of formation constant is therefore,

${\mathit{K}}_{\mathbf{f}}\mathbf{\left[}\mathbf{Ag}{{\left(S_2{O}_3\right)}_{\mathbf{2}}}^{\mathbf{3}\mathbf{-}}\mathbf{\right]}\mathbf{>}{\mathit{K}}_{\mathbf{f}}\mathbf{\left[}\mathbf{Ag}{{\left({\mathrm{NH}}_3\right)}_{\mathbf{2}}}^{\mathbf{+}}\mathbf{\right]}$