JEE Main & Advanced Sample Paper JEE Main Sample Paper-45

  • question_answer
    Percentage ionization of a weak acid  can be calculated by using the formula

    A)  \[100\sqrt{\frac{{{K}_{a}}}{C}}\]             

    B)  \[\frac{100}{1+{{10}^{(p{{K}_{a}}-pH)}}}\]

    C)  Both [a] and [b] are correct

    D)  None of these

    Correct Answer: C

    Solution :

                \[HA\xrightarrow{\,}\,{{H}^{+}}+{{A}^{-}}\] \[\therefore \]    \[x=\sqrt{\frac{{{K}_{a}}}{C}}\]    (we know) Also,                \[HA\xrightarrow{\,}\,{{H}^{+}}+{{A}^{-}}\] Intial conc.       C              0     0 Equil conc.       \[C-Cx\]   \[{{H}^{+}}\]   \[Cx\] \[\therefore \]    \[{{K}_{a}}=\frac{[{{H}^{+}}]\,[Cx]}{C(1-x)}=\frac{[{{H}^{+}}]x}{1-x}\] \[\therefore \]    \[\log \,{{K}_{a}}=\log \,[{{H}^{+}}]\,+\log \,\frac{x}{1-x}\] \[\therefore \]    \[p{{K}_{a}}=pH+\log \,\frac{1-x}{x}\] \[\Rightarrow \]            \[x=\frac{1}{1+{{10}^{(p{{K}_{a}}-pH)}}}\]

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