Equilibrium Question 286

Question: If the solubility product of $ AgBrO_3 $ and $ Ag_2SO_4 $ are $ 5.5\times {10^{-5}} $ and $ 2\times {10^{-5}} $ respectively, the relationship between the solubilities of these can be correctly represented as [EAMCET 1985]

Options:

A) $ {S_{AgBrO_3}}>{S_{Ag_2SO_4}} $

B) $ {S_{AgBrO_3}}<{S_{Ag_2SO_4}} $

C) $ {S_{AgBrO_3}}={S_{Ag_2SO_4}} $

D) $ {S_{AgBrO_3}}\approx {S_{Ag_2SO_4}} $

Show Answer

Answer:

Correct Answer: B

Solution:

$ Ag_2SO_4 $ ⇌ $ \underset{4S^{2}}{\mathop{2A{g^{+}}}},+\underset{S}{\mathop{SO_4^{-,-}}}, $

$ K _{sp}=4S^{3};K _{sp}=2\times {10^{-5}} $

$ S=\sqrt[3]{\frac{2\times {10^{-5}}}{4}}=0.017,m/l $

$ =1.7\times {10^{-2}} $ Ag $ BrO_3 $ ⇌ $ \underset{S}{\mathop{A{g^{+}}}},+\underset{S}{\mathop{BrO_3^{-}}}, $

$ K _{sp}=S^{2};K _{sp}=5.5\times {10^{-5}} $

$ S=\sqrt{5.5\times {10^{-5}}}=7.4\times {10^{-3}},m/l. $



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