Explanation:
As we are given pure water. This means that concentration of hydrogen and hydroxide ions will be the same as pure water is neutral in nature.
Also, value of [tex]K_{w}[/tex] = [tex]2.92 \times 10^{-14}[/tex].
Relation between [tex]K_{w}[/tex] and concentration of hydrogen and hydroxide ions is as follows.
[tex]K_{w} = [H^{+}][OH^{-}][/tex]
Since, [tex][H^{+}][/tex] = [tex][OH^{-}][/tex].
So, [tex]K_{w} = [H^{+}][OH^{-}][/tex] = [tex][H^{+}]^{2}[/tex]
[tex][H^{+}][/tex] = [tex]\sqrt{K_{w}}[/tex]
= [tex]\sqrt{2.92 \times 10^{-14}}[/tex]
= [tex]1.709 \times 10^{-7}[/tex]
As we know that pH = [tex]-log[H^{+}][/tex]
pH = [tex]-log(1.709 \times 10^{-7})[/tex]
= 6.676
Thus, we can conclude that pH of pure water under given conditions is 6.676.
