Question

At 25⁰C, the solubility product values of AgCl and AgCNS are 1.8 x 10-10 and 1.6 x 10-11 respectively. When a solution is saturated with both solids, calculate the ratio [Cl-]/[CNS-] and also [Ag+] in the solution.

• A. 1.125, 4 × 10-6 M
• B. 11.25, 1.4 × 10-5 M
• C. 1.25, 4 ×10-5 M
• D. 1.25, 4 × 10-6 M

Answer 1

Answer: (B)

11.25, 1.4 × 10-5 M

Answer 2

AgCI $\longrightarrow$ Ag+ + CI– AgCNS $\longrightarrow$ Ag+ + CNS–

(x + y) x (x + y) y

$\frac{K_{SP}(AgCl)}{K_{SP}(AgCNS)} = \frac{x}{y} = \frac{\lbrack Cl^{-}\rbrack}{\lbrack CNS^{-}\rbrack}$

So $\frac{\lbrack Cl^{-}\rbrack}{\lbrack CNS^{-}\rbrack}$ = $\frac{x}{y}$ = $\frac{1.8 \times 10^{- 10}}{1.6 \times 10^{- 11}}$

= 1.125 × 10 = 11.25

$\Rightarrow$ $\frac{x}{y}$= 11.25 x = 11.25

KSP (AgCI) = [Ag+] [CI–] = (x + y) x = 1.8 × 10–10

12.25 y × 11.25 y = 1.8 × 10–10

y2 = $\frac{1.8 \times 10^{- 10}}{12.25 \times 11.25}$

y2 = $\frac{180 \times 10^{- 12}}{12.25 \times 11.25}$

y2 = 1.3 × 10–12

y = 1.14 × 10–6

x = 11.25 × 1.14 × 10–6 = 12.83 × 10–6

[Ag+] = [x + y] = 12.83 × 10–6 + 1.14 × 10–6 = 13.97 × 10–6 = 1.4 × 10–5 M