Textbook Problem 6A.21

[Hasmik Dis 2F]

The value of K w for water at body temperature (37 °C) is 2 .1 × 10^-14 . (a) What is the molar concentration of H3O + ions at 37 °C? (b) What is the molar concentration of OH − in neutral water at 37 °C?

So for this problem, I know that Kw = [OH-][H30+]. At first, I thought of doing x^2 = Kw (which is 2.1x10^-14), but then I realized: how can they [OH-] and [H30+] be equal if Kw is not 10^-14? I know it's close to it but doesn't it have to be exact if we're going to assume that the two concentrations are equal?

[Kayla Law 2D]

The Kw is a constant. At 25°C the Kw = 1 x 10^-14, but at other temperatures the Kw will be different. The question tells us that the Kw is 2 .1 × 10^-14 at 37°C. So just like the [H3O+] and [OH-] are the same at 25°C for neutral water, and you would just take the square root of the Kw to find the concentrations of each, you would do the same for the Kw at 37°C in this question. Therefore, the concentrations of both [H3O+] and [OH-] are just the square root of 2.1 x 10^-14, or 1.4 x 10^-7 M. Hope this helps! :)

[annabelchen2a]

Kayla explained this really well! I just wanted to add that with these types of problems, to the extent of my knowledge, [H3O+][OH-] is always going to equal Kw. So if you're given Kw for a specific temperature and asked for the molar concentrations of H3O+ and OH-, then all you have to do is take the square root of Kw to get your answer.

[Natalie Do 3F]

Kw is H3O+ times OH- which is essentially x^2 since they are equal so you take the square root to solve for x