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Question: In a saturated solution of the sparingly soluble strong electrolyte \[{\text{AgI}}{{\text{O}}_3}\lef...

In a saturated solution of the sparingly soluble strong electrolyte AgIO3(molecular mass=283){\text{AgI}}{{\text{O}}_3}\left( {{\text{molecular mass}} = 283} \right) the equilibrium which sets in is AgIO3(s)⇔Ag+(aq)+IO3−(aq){\text{AgI}}{{\text{O}}_{\text{3}}}\left( {\text{s}} \right) \Leftrightarrow {\text{Ag}} + \left( {{\text{aq}}} \right) + {\text{I}}{{\text{O}}_3}^ - \left( {{\text{aq}}} \right)
if the solubility product constant, Ksp of AgIO3{{\text{K}}_{{\text{sp}}}}{\text{ of AgI}}{{\text{O}}_3} at a given temperature is 1.0×10−81.0 \times {10^{ - 8}} . What is the mass of AgIO3{\text{AgI}}{{\text{O}}_3} contained in 100mL of its saturated solution?

Explanation

Solution

Using the formula for solubility product we will get the solubility in terms of mol per litre. Using the molar mass we will calculate the mass in 1000 mL solution.

Complete step by step answer:
AgIO3{\text{AgI}}{{\text{O}}_3} is a strong electrolyte but it does not completely dissociate in aqueous medium.
We have been given the dissociation of the sparingly soluble salt as:
AgIO3(s)⇔Ag+(aq)+IO3−(aq){\text{AgI}}{{\text{O}}_{\text{3}}}\left( {\text{s}} \right) \Leftrightarrow {\text{Ag}} + \left( {{\text{aq}}} \right) + {\text{I}}{{\text{O}}_3}^ - \left( {{\text{aq}}} \right)
Let the solubility of the ions formed is S. Ksp{{\text{K}}_{{\text{sp}}}} is the solubility product of product of ion raised to the power equal to their stoichiometric coefficient. The solubility product of the above reaction with solubility S of each ion will be:
Ksp=[Ag][IO3−]{{\text{K}}_{{\text{sp}}}} = \left[ {{\text{Ag}}} \right]\left[ {{\text{IO}}_3^ - } \right]
Ksp=S.S=S2{{\text{K}}_{{\text{sp}}}} = {\text{S}}{\text{.S}} = {{\text{S}}^2}
Now the value of solubility constant is known to us as:
1.0×10−8=S21.0 \times {10^{ - 8}} = {{\text{S}}^2}
Taking the square root both sides we will get the solubility as:
10−4=S{10^{ - 4}} = {\text{S}}
The solubility of AgIO3{\text{AgI}}{{\text{O}}_3} is 10−4{10^{ - 4}} mol per litre.
In 1 litre or 1000 mL solution, 10−4{10^{ - 4}} moles of AgIO3{\text{AgI}}{{\text{O}}_3} is present.
We need to calculate the mass present in 100 mL solution.
In 100 mL solution, 10−41000×100=10−5\dfrac{{{{10}^{ - 4}}}}{{1000}} \times 100 = {10^{ - 5}} moles of AgIO3{\text{AgI}}{{\text{O}}_3} is present.
Number of moles=massMolar mass{\text{Number of moles}} = \dfrac{{{\text{mass}}}}{{{\text{Molar mass}}}}
We have been given the molar mass. Substituting the known variable:
10−5=mass283{\text{1}}{{\text{0}}^{ - 5}} = \dfrac{{{\text{mass}}}}{{{\text{283}}}}
The mass of AgIO3{\text{AgI}}{{\text{O}}_3} contained in 100 mL solution is:
283×10−5 g or 2.83×10−3 g{\text{283}} \times {\text{1}}{{\text{0}}^{ - 5}}{\text{ g or }}2.83 \times {\text{1}}{{\text{0}}^{ - 3}}{\text{ g}}

Note:
A sparingly soluble salts are those salts which do not completely dissociate in the solution. They exist in equilibrium with their ions. The saturated solution is formed when no more solute is dissolved in the solution at a particular temperature. Silver chloride and silver nitrate are also sparingly soluble salts. We can increase the solubility of the sparingly soluble salt by increasing the temperature. A supersaturated solution will form when temperature is raised.