JEE Main & Advanced Sample Paper JEE Main Sample Paper-19

  • question_answer 10) Given, \[HF+{{H}_{2}}O\xrightarrow{{{K}_{a}}}{{H}_{3}}{{O}^{+}}+{{F}^{-}};\] \[{{F}^{-}}+{{H}_{2}}O\xrightarrow{{{K}_{b}}}HF+O{{H}^{-}}.\] Which relation is correct                             

    A)  \[{{K}_{b}}={{K}_{w}}\]       

    B)  \[{{K}_{b}}=\frac{1}{{{K}_{w}}}\]        

    C)  \[{{K}_{a}}\times {{K}_{b}}={{K}_{w}}\]       

    D)  \[\frac{{{K}_{a}}}{{{K}_{b}}}={{K}_{w}}\]

    Correct Answer: C

    Solution :

     \[{{K}_{a}}=\frac{[{{H}_{3}}{{O}^{+}}][{{F}^{-}}]}{[HF]\,[{{H}_{2}}O]}\] and \[{{K}_{b}}=\frac{[HF][O{{H}^{-}}]}{[{{F}^{-}}]\,[{{H}_{2}}O]}\] Therefore, \[{{K}_{a}}\times {{K}_{b}}=[{{H}_{3}}{{O}^{+}}][O{{H}^{-}}]={{K}_{w}}\].

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