JEE Main & Advanced Chemistry Equilibrium / साम्यावस्था Sample Paper Topic Test - Ionic Equilibrium

  • question_answer
    pH of an aqueous solution of HCl is 5. if 1 c.c. of this solution is diluted to 1000 times. The pH will become

    A) 8

    B) 5                 

    C) 6.9

    D)             None

    Correct Answer: C

    Solution :

    [c] pH of HCl solution = 5
    \[{{[{{H}^{+}}]}_{\text{initial}}}={{10}^{-5}}\]
    \[{{[{{H}^{+}}]}_{\text{initial}}}\times {{V}_{1}}={{[{{H}^{+}}]}_{\text{final}}}\times {{V}_{2}}\]
    \[{{[{{H}^{+}}]}_{\text{final}}}\times {{10}^{-8}}\]
    Let the \[{{H}^{+}}\] from water be x.
    \[{{H}_{2}}O\rightleftharpoons \underset{x+{{10}^{-8}}}{\mathop{{{H}^{+}}}}\,+\underset{x}{\mathop{O{{H}^{-}}}}\,\]
    \[x(x+{{10}^{-8}})={{10}^{-14}}\]
    \[{{x}^{2}}+{{10}^{-8}}-{{10}^{-14}}=0\]
    \[x=\frac{-{{10}^{-8}}\pm \sqrt{{{10}^{-16}}=4\times {{10}^{-14}}}}{2}\]
    \[\Rightarrow \]   \[x=\frac{-{{10}^{-8}}+{{10}^{-8}}\sqrt{401}}{2}=19\times {{10}^{-8}}=9.5\times {{10}^{-8}}\]
    \[{{[{{H}^{+}}]}_{\text{Total}}}={{[{{H}^{+}}]}_{\text{HCl}}}+{{[{{H}^{+}}]}_{\text{Water}}}\]
    \[={{10}^{-8}}+{{10}^{-8}}\times 9.5=10.5\times {{10}^{-8}}\]
    \[pH=8-\log \,10.5\]
    Slightly less then 7 Hence [c].


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