What is the $\mathrm{pH}$ of a $10^{-4} \mathrm{M} \mathrm{OH}^{-}$solution at $330 \mathrm{~K}$, if…

What is the $\mathrm{pH}$ of a $10^{-4} \mathrm{M} \mathrm{OH}^{-}$solution at $330 \mathrm{~K}$, if $\mathrm{K}_{\mathrm{w}}$ at $330 \mathrm{~K}$ is $10^{-13.6}$ ?
  1. 4
  2. $9.0$
  3. 10
  4. $9.6$

Solution

Given at $330 \mathrm{~K}$ $ \begin{aligned} \mathrm{K}_w & =10^{-13.6} \\ \text { i.e. } \quad \mathrm{pK}_w & =\mathrm{pH}+\mathrm{pOH} \\ \because \quad \mathrm{pOH}^2 & =-\log \left[\mathrm{OH}^{-}\right] \\ 13.6 & =\mathrm{pH}+\mathrm{pOH} \\ \mathrm{pOH} & =-\log 10^{-4} \\ 13.6 & =\mathrm{pH}+4 \\ \therefore \quad \mathrm{pH} & =13.6-4 \\ & =9.6 \end{aligned} $

Asked in: JEE Main 2013 (23 Apr Online)

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