Equilibrium Question 752
Question: In a saturated solution of the sparingly soluble strong electrolyte $ AgIO_3 $ (molecular mass = 283) the equilibrium which sets in is $ AgIO_3(s)\rightarrow A{g^{+}}(aq)+I{O^{-}}_3(aq) $ If the solubility product constant $ K _{sp} $ of $ AgIO_3 $ , at a given temperature is $ 1.0\times {10^{-8}} $ , what is the mass of, $ AgIO_3 $ contained in 100 mL of its saturated solution'
Options:
A) $ 28.3\times {10^{-2}}g $
B) $ 28.3\times {10^{-3}}g $
C) $ 1.0\times {10^{-7}}g $
D) $ 1.0\times {10^{-4}}g $
Show Answer
Answer:
Correct Answer: A
Solution:
$ AgI{O_{3(s)}}\rightarrow A{g^{+}} _{(aq)}+I{O _{3(aq)}}^{-} $ Let the solubility of $ AgIO_3 $ be S $ K _{sp}=[A{g^{+}}][IO_3^{-}] $
$ K _{sp}=S\times S $ Or $ S=\sqrt{K _{sp}} $
$ S=\sqrt{1.0\times {10^{-8}}}=1.0\times {10^{-4}}mol/litre $
$ =1.0\times {10^{-4}}\times 283g/litre $
$ =\frac{1.0\times {10^{-4}}\times 283}{1000}\times 100g/100ml $
$ =2.83\times {10^{-3}}g/100ml=28.3\times {10^{-2}}g $
