Applications of Solubility Product and Common Ion Effect

Derive expression for the $\mathrm{pH}$ of a basic buffer mixture.

Given that the solubility product of radium sulphate $\left({\mathrm{RaSO}}_4\right)$ is $4\times {10}^{-11}$. Calculate the solubility in $0.10 \mathrm{M} {\mathrm{Na}}_2{\mathrm{SO}}_4$.

Using the Gibb's free energy change,

$∆\mathrm{G}° = + 63.3 \mathrm{kJ}$ for the following reaction

${\mathrm{Ag}}_2{\mathrm{CO}}_3 \left(\mathrm{s}\right) \iff 2 {\mathrm{Ag}}^{+} \left(\mathrm{aq}\right) + {{\mathrm{CO}}_3}^{2-} \left(\mathrm{aq}\right)$

the ${\mathrm{K}}_{\mathrm{sp}}$ of ${\mathrm{Ag}}_2{\mathrm{CO}}_3$ in water at $25°\mathrm{C}$ is $(\mathrm{R} = 8.314 {\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1})$ 

The ${\mathrm{K}}_{\mathrm{sp}}$ of ${\mathrm{Ag}}_2{\mathrm{CrO}}_4$ is $1.1\times {10}^{-12}$ at $298 \mathrm{K}$. The solubility (in $\mathrm{mol}/\mathrm{L}$) of ${\mathrm{Ag}}_2{\mathrm{CrO}}_4$ in $0.1 \mathrm{M} {\mathrm{AgNO}}_3$ solution is

Passing ${\mathrm{H}}_2\mathrm{S}$ gas into a mixture of ${\mathrm{Mn}}^{2+}, {\mathrm{Ni}}^{2+}, {\mathrm{Cu}}^{2+} \mathrm{and} {\mathrm{Hg}}^{2+}$ ions in an acidified aqueous solution precipitates

The ${\mathrm{K}}_{\mathrm{sp}}$ of ${\mathrm{Ag}}_2{\mathrm{CrO}}_4, \mathrm{AgCl}, \mathrm{AgBr} \mathrm{and} \mathrm{Agl}$ are respectively $1.1\times {10}^{-12} , 1.8\times {10}^{-10}, 5.0\times {10}^{-13} \mathrm{and} 8.3\times {10}^{-17}$. Which one of the following salts will precipitate last if ${\mathrm{AgNO}}_3$ solution is added to the solution containing equal moles of $\mathrm{NaCl}, \mathrm{NaBr}, \mathrm{Nal} \mathrm{and} {\mathrm{Na}}_2{\mathrm{CrO}}_4$?

The solubility product $\left({\mathrm{K}}_{\mathrm{sp}}\right)$ of the following compounds are given at $25°\mathrm{C}$

The most soluble and least soluble compounds are respectively

The solubility product of a sparingly soluble metal hydroxide ${\mathrm{M}(\mathrm{OH}{)}_2}_{}$ at $298 \mathrm{K}$is $5\times {10}^{-16} {\mathrm{mol}}^3 {\mathrm{dm}}^{-9}$. The pH value of its aqueous and saturated solution is

For which of the following sparingly soluble salt, the solubility $\left(\mathrm{S}\right)$ and solubility product $\left({\mathrm{K}}_{\mathrm{sp}}\right)$ are related by the expression

$\mathrm{S} = ({\mathrm{K}}_{\mathrm{sp}}/4{)}^{1/3}$ ?

Equal volumes of the following ${\mathrm{Ca}}^{2+} \mathrm{and} {\mathrm{F}}^{-}$ solutions are mixed. In which of the solutions will precipitation occur ? (${\mathrm{K}}_{\mathrm{sp}}$ of ${\mathrm{CaF}}_2$ = $1.7\times {10}^{-10}$)

 $$\begin{gathered} 1. {10}^{-2} \mathrm{M} {\mathrm{Ca}}^{2+} + {10}^{-5} \mathrm{M} {\mathrm{F}}^{-} \\ 2. {10}^{-3} \mathrm{M} {\mathrm{Ca}}^{2+} + {10}^{-3} \mathrm{M} {\mathrm{F}}^{-} \\ 3. {10}^{-4} \mathrm{M} {\mathrm{Ca}}^{2+} + {10}^{-2} \mathrm{M} {\mathrm{F}}^{-} \\ 4. {10}^{-3} \mathrm{M} {\mathrm{Ca}}^{2+} + {10}^{-3} \mathrm{M} {\mathrm{F}}^{-} \end{gathered}$$

${\mathrm{PbCl}}_2$ has a solubility product of $1.7\times {10}^{-8}$. Will a precipitate of ${\mathrm{PbCl}}_2$ form when $0.010$ mole of lead nitrate and $0.010$ mole of potassium chloride are mixed and water added upto $1$ litre?

$0.03 \mathrm{mole}$ of ${\mathrm{Ca}}^{2+}$ ions are added to a litre of $0.01 \mathrm{M} {\mathrm{SO}}_4^{2-}$ solution. Will it cause precipitation of ${\mathrm{CaSO}}_4$? ${\mathrm{K}}_{\mathrm{sp}}$ for ${\mathrm{CaSO}}_4= 2.4\times {10}^{-5}$.

If $20 \mathrm{mL}$ of $2\times {10}^{-5} {\mathrm{BaCl}}_2$ solution is mixed with $20 \mathrm{mL}$ of $1\times {10}^{-5} \mathrm{M} {\mathrm{Na}}_2{\mathrm{SO}}_4$ solution, will a precipitate form? $({\mathrm{K}}_{\mathrm{sp}}$ for ${\mathrm{BaSO}}_4$ is $1.0\times {10}^{-10})$

Predict whether a precipitate will be formed or not on mixing $20 \mathrm{mL}$ of $0.001 \mathrm{N} \mathrm{NaCl}$ solution with $80 \mathrm{mL}$ of $0.01 \mathrm{N} {\mathrm{AgNO}}_3$ solution. ${\mathrm{K}}_{\mathrm{sp}}$ for $\mathrm{AgCl}=1.5\times {10}^{-10}$.

Given that the solubility product of radium sulphate $\left({\mathrm{RaSO}}_4\right)$ is $4\times {10}^{-11}$. Calculate the solubility in pure water.

Calculate the molar solubility of $\mathrm{Ni}(\mathrm{OH}{)}_2$ in $0.10 \mathrm{M} \mathrm{NaOH}$. The ionic product of $\mathrm{Ni}(\mathrm{OH}{)}_2$ is $2.0\times {10}^{-15}$.

The values of ${\mathrm{K}}_{\mathrm{sp}}$ of two sparingly soluble salts, $\mathrm{Ni}(\mathrm{OH}{)}_2$ and $\mathrm{AgCN}$ are $2.0\times {10}^{-15}$ and $6.0\times {10}^{-17}$, respectively. Which salt is more soluble? Explain.

Calculate the solubility of ${\mathrm{A}}_2{\mathrm{X}}_3$ in pure water, assuming that neither kind of ion reacts with water. The solubility product of ${\mathrm{A}}_2{\mathrm{X}}_3, {\mathrm{K}}_{\mathrm{sp}}=1.1\times {10}^{-23}$.

How many moles of $\mathrm{AgBr} ({\mathrm{K}}_{\mathrm{sp}}=5\times {10}^{-13} {\mathrm{mol}}^2 {\mathrm{L}}^{-2})$ will dissolve in $0.01 \mathrm{M} \mathrm{NaBr}$ solution?

Give reason for the following:
The precipitation of $\mathrm{Mg}(\mathrm{OH}{)}_2$ is prevented by the addition of ${\mathrm{NH}}_4\mathrm{Cl}$ prior to the addition of ${\mathrm{NH}}_4\mathrm{OH}$ but its precipitation by $\mathrm{NaOH}$ is not prevented by the prior addition of $\mathrm{NaCl}$.