Question

A saturated solution of AgCl was treated with 1.5 M $N{a}_{2}C{O}_3$ solution giving $A{g}_{2}C{O}_3$. The remaining solution contained 0.0026 gm of Cl per liter $[K_{sp}ofA{g}_{2}C{O}_3=8.2\times {10}^{-12}{M}^3]$ Which of the following statements is/are correct?

• A. The concentration of NaCl at equilibrium is $7.32\times {10}^{-1}M$
• B. The concentration of $A{g}^{+}$ at equillibrium is $2.33\times {10}^{-6}M$
• C. $K_{sp}$ of AgCl from the above data is $1.71\times {10}^{-10}{M}^2$
• D. The equilibrium concentration of $C{O}_3^{-2}$ is $8.2\times {10}^{-12}M$

Answer 1

Answer: (A), (B), (C)

The correct options are
A The concentration of $A{g}^{+}$ at equillibrium is $2.33\times {10}^{-6}M$
B $K_{sp}$ of AgCl from the above data is $1.71\times {10}^{-10}{M}^2$
C The concentration of NaCl at equilibrium is $7.32\times {10}^{-1}M$

$\left[C{O}_3^{2-}\right]=\left[N{a}_{2}C{O}_3\right]=1.5M$

At equilibrium $\left[Cl\right]=\left[NaCl\right]=\frac{0.0026}{35.5}=7.32\times {10}^{-5}M$

$2AgCl\left(s\right)+N{a}_{2}C{O}_3\rightleftharpoons A{g}_{2}C{O}_3\left(s\right)+2NaCl$

Intital

at equilibrium $(1.5-7.32\times {10}^{-5})M7.32\times 2NaCl$

$\left[A{g}^{+}{]}^2\right[C{O}_3^{2-}]=K_{5p}[A{g}_{2}C{O}_3]$

$\therefore \left[A{g}^{+}\right]=\sqrt{\frac{8.2\times {10}^{-12}}{1.5}}=2.33\times {10}^{-6}M$

$\therefore K_{sp}ofAgCl=\left[A{g}^{+}\right]\left[Cl\right]=(2.338\times {10}^8)\times (7.32\times {10}^{-5})=1.71\times {10}^{-10}$