Answer :
Answer:
- [tex]\rm [H_3O^{+}] = 10^{-8.55}\;M\approx 2.82\times 10^{-9} \;M[/tex], and
- [tex]\rm [OH^{-}] = 10^{-5.45}\; M\approx 3.55\times 10^{-6}\;M[/tex]
This solution is likely to be basic.
Assumption: this solution is under room temperature, where [tex]K_w = 10^{-14}[/tex].
Explanation:
The concentration of hydronium ions [tex]\mathrm{H_3O^{+}}[/tex] in the solution can be found from the [tex]\mathrm{pH}[/tex] value. This relationship does not depends on temperature.
[tex]\mathrm{[H_3O^{+}]} = 10^{-\mathrm{pH}} = 10^{-8.55}[/tex].
The question states that for this solution, [tex]\rm [H_3O^{+}] = 8.55\;M[/tex]. Apply the relationship between [tex]\mathrm{[H_3O^{+}]}[/tex], [tex]\mathrm{[OH^{-}]}[/tex], and [tex]K_w[/tex]. Note that the value of [tex]K_w[/tex] is dependent on the temperature of the solution.
[tex]\displaystyle \rm [OH^{-}] = \frac{\mathnormal{K_w}}{[H_3O^{+}]} = \frac{10^{-14}}{10^{-8.55}} = 10^{-5.45}\; M[/tex].
In other words,
- [tex]\rm [H_3O^{+}] = 10^{-8.55}\;M\approx 2.82\times 10^{-9} \;M[/tex], and
- [tex]\rm [OH^{-}] = 10^{-5.45}\; M\approx 3.55\times 10^{-6}\;M[/tex] assuming that [tex]K_w = 10^{-14}[/tex].
[tex]\rm [H_3O^{+}] < [OH^{-}][/tex].
In other words, this solution is basic.