In a saturated solution of the sparingly soluble strong electrolyte AgIO_{3}\left ( molecular\: mass = 283 \right )the equilibrium which sets in is   AgIO_{3(s)}\rightleftharpoons Ag^{+}_{(aq)}+IO^{-}_{3(aq)} . If the solubility product constant   K_{sp}  of  AgIO_{3}    at a given temperature is  1.0 x 10-8 , what is the mass of AgIO_{3} contained in 100 ml of its saturated solution?

  • Option 1)

    1.0\times 10^{-4}\; g

  • Option 2)

    28.3\times 10^{-2}\; g

  • Option 3)

    2.83\times 10^{-3}\; g

  • Option 4)

    1.0\times 10^{-7}\; g

 

Answers (1)

As we learnt in 

General expression of solubility product -

M_{x}X_{y}\rightleftharpoons xM^{p+}(aq)+yX^{2-}(aq)


(x.p^{+}=y.\bar{q})

- wherein

Its solubility product is 
 

K_{sp}=[M^{p+}]^{x}\:[X^{2-}]^{y}

 

 

K_{sp}= 1\times 10^{-8}=S^{2},S=\sqrt{10^{-8}}=10^{-4}moleL^{-1}

Concentration in mole L1=\frac{Mass\ in\ gm}{Molar\ mass \times Volume\ in\ L}

10^{-4}=\frac{Mass\ in\ gm\times 1000}{283 \times 100}

Mass in gm = 283\times 10^{-5}gm=2.83\times 10^{-3}gm

Correct option is 3.


Option 1)

1.0\times 10^{-4}\; g

This option is incorrect.

Option 2)

28.3\times 10^{-2}\; g

This option is incorrect.

Option 3)

2.83\times 10^{-3}\; g

This option is correct.

Option 4)

1.0\times 10^{-7}\; g

This option is incorrect.

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