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BCECE Engineering BCECE Engineering Solved Paper-2006

  • question_answer
    Some chemists at ISRO wished to prepare a saturated solution of a silver compound and they wanted it to have the highest concentration of silver ion possible. Which of the following compounds, would they use? \[{{K}_{sp}}(AgCl)=1.8\times {{10}^{-10}},\] \[{{K}_{sp}}(AgBr)=5.0\times {{10}^{-13}},\] \[{{K}_{sp}}(A{{g}_{2}}Cr{{O}_{4}})=2.4\times {{10}^{-12}}\]

    A) \[AgCl\]               

    B)         \[AgBr\]

    C)  \[A{{g}_{2}}Cr{{O}_{4}}\]            

    D)         None of these

    Correct Answer: C

    Solution :

    For binary salts (like\[AgCl,AgBr\]), \[s=\sqrt{{{K}_{sp}}}\]                 \[\therefore \]Solubility of \[AgCl=\sqrt{1.8\times {{10}^{-10}}}\]                                                 \[=1.35\times {{10}^{-7}}\,mol/L\] Solubility of \[AgBr=\sqrt{5.0\times {{10}^{-13}}}\]                                 \[=7.1\times {{10}^{-7}}\,mol/L\] For, \[A{{g}_{2}}Cr{{O}_{4}},{{K}_{sp}}=4{{s}^{3}}\] \[\therefore \]Solubility of \[A{{g}_{2}}Cr{{O}_{4}}\]                                 \[=\sqrt[3]{\frac{{{K}_{sp}}}{4}}=\sqrt[3]{\frac{2.4\times {{10}^{-12}}}{4}}\]                                 \[=\sqrt[3]{600\times {{10}^{-15}}}\]                                 \[=8.44\times {{10}^{-5}}\,mol/L\] As \[\text{A}{{\text{g}}_{\text{2}}}\text{Cr}{{\text{O}}_{\text{4}}}\]has maximum solubility, it will give maximum \[\text{A}{{\text{g}}^{\text{+}}}\] ions in solution. Hence, it will be used.


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