RAJASTHAN PMT Rajasthan - PMT Solved Paper-2011

  • question_answer
    The \[pH\] of an aqueous solution of a \[1\times {{10}^{-7}}M\] solution of \[HCl\] will be

    A)  7

    B)  slightly less than 7

    C)  slightly greater than 7

    D)  1

    Correct Answer: B

    Solution :

    \[[{{H}^{+}}]\] ions from \[HCl\] acid\[=1\times {{10}^{-7}}M\] Here, \[[{{H}^{+}}]\] ions from\[{{H}_{2}}O={{10}^{-7}}M\]cannot be neglected in comparison to \[{{10}^{-7}}M[{{H}^{+}}]\] ions from\[HCl\]. \[\therefore \]Total\[[{{H}^{+}}]={{10}^{-7}}+{{10}^{-7}}\]                         \[={{10}^{-7}}(1+1)\]                         \[=2\times {{10}^{-7}}M\]                 \[pH=-\log [{{H}^{+}}]\]                        \[=-\log [2\times {{10}^{-7}}]\]                                  \[=-[\log 2+\log {{10}^{-7}}]\]                        \[=-(0.3010-7)\]                        \[=6.6989\] \[\therefore \]\[pH\] of a solution of \[1\times {{10}^{-7}}M\] is slightly less than 7.


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