Question

An alcoholic drinks substance $pH=4.7$ then ${}^{-}OH$ ion concentration of this solution is:

• A. $3\times 10^{-10}$
• B. $5\times 10^{-10}$
• C. $1\times 10^{-10}$
• D. $5\times 10^{-2}$

Answer 1

Answer: (B)

$pH=-{\log }_{10}\left[H^{+}\right]$
or ${\log }_{10}\left[H^{+}\right]=-4.7$
$\left[H^{+}\right]=10^{-4.7}$
$=10^{-5}\times 10^{+0.3}$
$=10^{-5}\times$ anti $\log 0.3$
$=2\times 10^{-5}$
$K_w=\left[H^{+}\right]\left[O{H}^{-}\right]$
$\left[O{H}^{-}\right]=\frac{K_w}{\left[H^{+}\right]}=\frac{10^{-14}}{2\times 10^{-5}}$
$=0.5\times 10^{-9}=5\times 10^{-10}$