Question

Which of the following solution will have a pH exactly equal to 9 ?

• A. ${10}^{-9}MHCl\text{solution at}{25}^{0}C$
• B. $2\times {10}^{-3}MBa(OH{)}_2\text{solution at}{25}^{0}C$
• C. ${10}^{-9}MNaOH\text{solution at}{25}^{0}C$
• D. None of the above

Answer 1

The correct option is D None of the above

(a) ${10}^{-9}M$ $HCl$ is a very dilute solution where water dissociation needs to be considered to calculate the total $\left[H^{+}\right]$ ions present in the solution.
$\left[H^{+}\right]$ from $HCl$ = ${10}^{-9}M$
$\left[H^{+}\right]$ from $H_{2}O$ = ${10}^{-7}M$
$Total\left[H^{+}\right]=({10}^{-9}+{10}^{-7})=1.01\times {10}^{-7}M$
We know that $pH=-{\log }_{10}\left[H^{+}\right]$
$pH=-{\log }_{10}(1.01\times {10}^{-7})=6.99$.

(b) $Ba(OH{)}_2$ is a strong base and in 1 liter aqueous solution $1molBa(OH{)}_2$ dissociates to give $2molO{H}^{-}$ ions.
$\therefore \left[O{H}^{-}\right]=4\times {10}^{-3}M\Rightarrow \left[H^{+}\right]\left[O{H}^{-}\right]={10}^{-14}\Rightarrow \left[H^{+}\right]=2.5\times {10}^{-12}M\Rightarrow pH=-{\log }_{10}\left[H^{+}\right]=-{\log }_{10}(2.5\times {10}^{-12})=11.60$

(c)
$\left[O{H}^{-}\right]$ from $H_{2}O$ = ${10}^{-7}M$
$Total\left[O{H}^{-}\right]=({10}^{-9}+{10}^{-7})=1.01\times {10}^{-7}M$

We know that $pOH=-{\log }_{10}\left[O{H}^{-}\right]$
$pOH=-{\log }_{10}(1.01\times {10}^{-7})=6.99pH+pOH=14pH=14-6.99=7.01$

Therefore none of these options are correct.