Q10 / 180 · KCET 2009 · Chemistry

$10^{-6} \mathrm{M} \mathrm{NaOH}$ is diluted 100 times. The $\mathrm{pH}$ of the diluted base is

  • Correct answer
    A
    between 7 and 8
  • B
    between 5 and 6
  • C
    between 6 and 7
  • D
    between 10 and 11

Solution

$\left[\mathrm{OH}^{-}\right]$in the diluted base $=\frac{10^{-6}}{10^{2}}=10^{-8}$ Total $\left[\mathrm{OH}^{-}\right]=10^{-8}+\left[\mathrm{OH}^{-}\right]$of water $$ \begin{aligned} &=\left(10^{-8}+10^{-7}\right) \mathrm{M} \\ &=10^{-8}[1+10] \mathrm{M} \end{aligned} $$ $\begin{aligned} &=11 \times 10^{-8} \mathrm{M} \\ \mathrm{pOH} &=-\log 11 \times 10^{-8} \\ &=-\log 11+8 \log 10 \\ &=6.9586 \\ \mathrm{pH} &=14-6.9586 \\ &=7.0414 \end{aligned}$

Hence, the correct answer is option: 'A'.

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