The pH value of pure water below $25$ degree Celsius is greater than $7$. Does that mean water is basic in nature? Justify your answer.

Which of the following equations give ionic product of water?

(i) ${\mathrm{NH}}_{3\left(\mathrm{aq}\right)}+{\mathrm{H}}_2\mathrm{O}\leftrightarrows {\mathrm{NH}}_{4\left(\mathrm{aq}\right)}^{+}+{\mathrm{OH}}_{\left(\mathrm{aq}\right)}^{-}$

(ii) ${\mathrm{NH}}_{4\left(\mathrm{aq}\right)}^{+}+{\mathrm{H}}_2\mathrm{O}\leftrightarrows {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{NH}}_{3\left(\mathrm{aq}\right)}$

(iii) ${\mathrm{NH}}_{2\left(\mathrm{aq}\right)}^{-}+{\mathrm{H}}_2\mathrm{O}\leftrightarrows {\mathrm{NH}}_{3\left(\mathrm{aq}\right)}+{\mathrm{OH}}^{-}$

(iv) ${\mathrm{NH}}_{3\left(\mathrm{aq}\right)}+{\mathrm{OH}}_{\left(\mathrm{aq}\right)}^{-}\leftrightarrows {\mathrm{NH}}_{2\left(\mathrm{aq}\right)}^{-}+{\mathrm{H}}_2\mathrm{O}$

0.1 mole of ${\mathrm{CH}}_3·{\mathrm{NH}}_2\left({\mathrm{K}}_{\mathrm{b}}=5\times {10}^{-4}\right)$ is added to 0.08 moles of $\mathrm{HCl}$ and solution is diluted to one liter. The resulting $\left[{\mathrm{H}}^{+}\right]$ is:

What is the $\mathrm{pH}$ of a $1.0\times {10}^{-8} \mathrm{M}$ solution of $\mathrm{NaOH}$?

Answer correct up to two places of decimal.