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JEE Main & Advanced Sample Paper JEE Main Sample Paper-37

  • question_answer
    \[pH\] of a saturated solution of silver salt of monobasic acid HA is found to be 9. Find the \[{{K}_{sp}}\]of sparingly soluble salt \[Ag\] \[A\,(s)\]. Given \[{{K}_{a}}(HA)={{10}^{-10}}\].

    A)  \[1.1\times {{10}^{-9}}\]                    

    B)  \[1.1\times {{10}^{-10}}\]

    C)  \[1.1\times {{10}^{-11}}\]                   

    D)  \[{{10}^{-12}}\]

    Correct Answer: C

    Solution :

     \[\underset{x}{\mathop{Ag}}\,(l)+\underset{y}{\mathop{{{H}_{2}}O(\ell )}}\,\rightleftharpoons HA\underset{y}{\mathop{(aq)}}\,+O{{H}^{-}}(aq)\]\[{{K}_{sp}}=x(x-y)\] \[{{K}_{b}}=\frac{{{K}_{w}}}{{{K}_{a}}}=\frac{{{y}^{2}}}{(x-y)};\,\,\frac{{{10}^{-14}}}{{{10}^{-10}}}=\frac{{{({{10}^{-5}})}^{2}}}{(x-y)}\] \[x-y={{10}^{-6}}\] \[x={{10}^{-5}}+{{10}^{-6}}\] \[x=1.1\times {{10}^{-5}}\] \[{{K}_{sp}}=1.1\times {{10}^{-5}}\times {{10}^{-6}}\] \[{{K}_{sp}}=1.1\times {{10}^{-11}}\]


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