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JEE Main & Advanced Chemistry Equilibrium / साम्यावस्था Question Bank Hydrogenion concentration pH scale and buffer solution

  • question_answer
    A certain buffer solution contains equal concentration of \[3.9\times {{10}^{-5}}\] and \[HX.\] The \[{{K}_{b}}\] for \[{{H}^{-}}\] is  \[{{10}^{-10}}.\] The \[pH\]of the buffer is [IIT 1984; RPMT 1997; CPMT 1996; DPMT 2004]

    A)                 4             

    B)                 7

    C)                 10          

    D)                 14

    Correct Answer: A

    Solution :

               \[{{X}^{-}}+{{H}_{2}}O\]⇌\[O{{H}^{-}}+HX\]                    \[{{K}_{b}}=\frac{[O{{H}^{-}}]\,\,[HX]}{[{{X}^{-}}]}\]                     HX ⇌ \[{{H}^{+}}+{{X}^{-}}\]                    \[{{K}_{a}}=\frac{[{{H}^{+}}]\,\,[{{X}^{-}}]}{[HX]}\]                    \[\therefore \,{{K}_{a}}\times {{K}_{b}}=[{{H}^{+}}]\,\,[O{{H}^{-}}]={{K}_{w}}={{10}^{-14}}\]                    Hence \[{{K}_{a}}={{10}^{-4}}\]                                 Now as \[[{{X}^{-}}]=[HX],\,\,pH=p{{K}_{a}}=4\].


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