Question

A solution contains $\left[I^{-}\right]=\left[B{r}^{-}\right]=\left[C{l}^{-}\right]=0.2M$ each.
Then which of the following statements regarding precipitation of sparingly soluble salts $AgCl$, $AgBr$ and $AgI$ is correct:
Given :
$Salt{K}_{sp}(mol{L}^{-1}{)}^2$
$AgCl1.8\times {10}^{-10}$
$AgBr5\times {10}^{-13}$
$AgI8.3\times {10}^{-17}$

• A. For, $\left[A{g}^{+}\right]>4.15\times {10}^{-16}M$, precipitation of $AgI$ occurs.
• B. For $\left[A{g}^{+}\right]>2.5\times {10}^{-12}M$, precipitation of $AgBr$ occurs.
• C. For $\left[A{g}^{+}\right]>9\times {10}^{-9}M$, precipitation of $AgCl$ occurs.
• D. For $\left[A{g}^{+}\right]<4.15\times {10}^{-16}M$, precipitation of $AgI$ occurs.

Answer 1

Answer: (A), (B)

For $\left[A{g}^{+}\right]>2.5\times {10}^{-12}M$, precipitation of $AgBr$ occurs.

For precipitation, $Q_{sp}>K_{sp}$
(i) The minimum concentration required for the precipitation of $AgI$ is:
$(K_{sp}{)}_{AgI}<[A{g}^{+}\left]\right[I^{-}]$
$\left[A{g}^{+}\right]>\frac{(K_{sp}{)}_{AgI}}{\left[I^{-}\right]}$ $=\frac{8.3\times {10}^{-17}}{0.2}$
$[A{g}^{+}{]}_{minimum}=4.15\times {10}^{-16}M$ is required for precipitation of $AgI$.

For, $\left[A{g}^{+}\right]>4.15\times {10}^{-16}M$ precipitation of $AgI$ occurs.

(ii) The minimum concentration required for the precipitation of $AgBr$ is:
$(K_{sp}{)}_{AgBr}<[A{g}^{+}\left]\right[B{r}^{-}]$
$\left[A{g}^{+}\right]>\frac{(K_{sp}{)}_{AgBr}}{\left[B{r}^{-}\right]}$ $=\frac{5\times {10}^{-13}}{0.2}$
$[A{g}^{+}{]}_{minimum}=2.5\times {10}^{-12}M$ is required for precipitation of $AgBr$.

For ,$\left[A{g}^{+}\right]>2.5\times {10}^{-12}M$ precipitation of $AgBr$ occurs.

(iii) The minimum concentration required for the precipitation of $AgCl$ is:

$(K_{sp}{)}_{AgCl}<[A{g}^{+}\left]\right[C{l}^{-}]$
$\left[A{g}^{+}\right]>\frac{(K_{sp}{)}_{AgCl}}{\left[C{l}^{-}\right]}=\frac{1.8\times {10}^{-10}}{0.2}$
$[A{g}^{+}{]}_{minimum}=9\times {10}^{-10}M$ is required for precipitation of $AgCl$ .

For $\left[A{g}^{+}\right]>9\times {10}^{-10}M$ , precipitation of $AgCl$ occurs.