Question

Calculate simultaneous solubility of AgCNS and AgBr in a solution of water.

[Ksp of $AgBr=5\times {10}^{-13}$ and Ksp of $AgCNS=1\times {10}^{-12}$].

• A. $8.16{10}^{-7}M,4.08{10}^{-7}M$
• B. $5.78\times {10}^{-8}M,0.037M$
• C. $0.04M,6.25\times {10}^{-8}M$
• D. $1.58\times {10}^{-3}M,1.26\times {10}^{-5}M$

Answer 1

The correct option is A $8.16{10}^{-7}M,4.08{10}^{-7}M$

Let a M and b M represents the solubility of AgCNS and AgBr respectively.

$\left[A{g}^{+}\right]=a+b,\left[CN{S}^{-}\right]=a,\left[B{r}^{-}\right]=b$

$K_{sp,AgCNS}=\left[A{g}^{+}\right]\left[CN{S}^{-}\right]$

$1\times {10}^{-12}=(a+b)a$......(i).

$K_{sp,AgBr}=\left[A{g}^{+}\right]\left[B{r}^{-}\right]$

$5\times {10}^{-13}=(a+b)b$......(ii).

Divide equation (i) by (ii) to obtains $a=2b$ or $b=0.5a$

Substitute the value of a in (i).

$(a+b)a={10}^{-12}$

$b=4.08\times {10}^{-7}M$

Substitute the value of b in (ii).

$(a+b)a={10}^{-12}$

$a=8.16\times {10}^{-7}M$