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Question: In a saturated of the sparingly soluble strong electrolyte \[Agl{O_3}\]​ (molecular mass = 283), the...

In a saturated of the sparingly soluble strong electrolyte AglO3Agl{O_3}​ (molecular mass = 283), the equilibrium which sets in is
AgIO3(s)⇆Ag+(aq)+IO−(aq)AgI{O_3}\left( s \right)\underset {} \leftrightarrows A{g^ + }\left( {aq} \right) + I{O^ - }\left( {aq} \right)
If the solubility product constant Ksp{K_{sp}}​ ofAglO3Agl{O_3}​ at a given temperature is1.0×10−81.0 \times {10^{ - 8}}, what is the mass of AglO3Agl{O_3} contained in 100 mL of its saturated solution?
A.1.0×10−71.0 \times {10^{ - 7}}
B.1.0×10−41.0 \times {10^{ - 4}}
C.28.3×10−228.3 \times {10^{ - 2}}
D.2.83×10−32.83 \times {10^{ - 3}}

Explanation

Solution

Hint: To solve these types of questions you should know the basic principles and the basic formula of the solubility product constant i.e. [My+]x[Ax−]y{\left[ {{M^{y + }}} \right]^x}{\left[ {{A^{x - }}} \right]^y}to find the correct option.

Complete answer:
According to the question we are given,
The solubility product constant Ksp{K_{sp}} of AglO3Agl{O_3} = 1.0×10−81.0 \times {10^{ - 8}}
And we know the molecular mass of AglO3Agl{O_3} which is 283.
We have to calculate the mass of AglO3Agl{O_3} contained in 100ml of its saturated solution.
We know that Ksp{K_{sp}} equation is written as: [My+]x[Ax−]y{\left[ {{M^{y + }}} \right]^x}{\left[ {{A^{x - }}} \right]^y}
So,
Let us consider the solubility of AglO3Agl{O_3} as “s”.
Then, Ksp{K_{sp}} =[Ag]+[LO3]−{\left[ {Ag} \right]^ + }{\left[ {L{O_3}} \right]^ - }
Ksp{K_{sp}}=1.0×10−81.0 \times {10^{ - 8}}
So, 1.0×10−8=s21.0 \times {10^{ - 8}} = {s^2}
Then s =10−4{10^{ - 4}} mol/liter
Now, formula of solubility is “Solubility in gram ×100Solubility{\text{ }}in{\text{ }}gram{\text{ }} \times 100”
Substituting the value in the formula of solubility
\Rightarrow $$${10^{ - 4}} \times \dfrac{{283}}{{1000}} \times 100$$ \Rightarrow 283 \times {10^{ - 5}} \Rightarrow 2.83 \times {10^{ - 3}}$g/100 ml
Hence, the correct option is D.

NOTE: In the above formulation we used a term the solubility of product constant Ksp that can be defined as it is the constant of equilibrium for a solid substance that dissolves in an aqueous solution. The more soluble a substance is, the higher its Ksp value will become. Its equation is: [My+]x[Ax−]y{\left[ {{M^{y + }}} \right]^x}{\left[ {{A^{x - }}} \right]^y}