[H30+]=[OH-] ???

[Megan Verschuur 1C]

In textbook problem 6A.21 which reads:
The value of Kw for water at body temperature (37 degrees Celcius) is 2.1 * 10^-14.
(a) What is the molar concentration of H30+?
(b) What is the molar concentration of OH-?

The answer for both is 1.4 * 10 ^ -7. How do you get this? Do you square root the Kw value? Also, why are they both the same?

[Jay Solanki 3A]

Yes you have to square root the Kw value. This is because the water equilibrium involved a one-to-one ratio of hydronium to hydroxide ions, so the equilibrium will result in their equilibrium concentrations being the same. Note that they are only the same in distilled water, since there are no other acids or bases to drastically change the pH. Hope this helps!

[Anirudh Mahadev 1G]

Yes that is correct, you would square root the value. This makes sense because water should have a neutral pH of 7, which would happen as a result of hydroxide and hydronium concentrations being equal.

[OwenSumter_2F]

In addition, anything with both H₃O⁺ and OH^- will multiply to the K_W, just normally not the same number

[OwenSumter_2F]

In addition, anything with both H₃O⁺ and OH^- will multiply to the K_W, just normally not the same number

[Justin Lin 1B]

Yes you would square root the Kw value because water is neutral, so we know that [H3O+] and [OH-] have to be the same value.

[austin-3b]

Since it's neutral, you can assume these concentrations are equal. Therefore, you can assign the same variable (x). You do that, square root every side and you get 1 * 10^-7.

[Olivia Smith 2E]

It is only in neutral water too! That this applies. Any other reaction will not have this

[Malakai Espinosa 3E]

Because the two concentrations are the same, we can both define the values as x. Thus, Kw would be x^2. In order to find the concentration of either, we need to square root the Kw that is given.