Question

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

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

Answer 1

Answer: (C)

between 7 and 8

Answer 2

$\left[ OH ^{-}\right]$ in the diluted base $=\frac{10^{-6}}{10^{2}}=10^{-8}$

Total $\left[ OH ^{-}\right]=10^{-8}+\left[ OH ^{-}\right]$ of water

$=\left(10^{-8}+10^{-7}\right)\,M$
$=10^{-8}[1+10]\, M$
$=11 \times 10^{-8} M$
$pOH =-\log 11 \times 10^{-8}$
$=-\log 11+8 \log 10$
$=6.9586$
$pH =14-6.9586$
$=7.0414$