If Kw = 1 * 10^-13, what is the concentration of H+ at neutrality?

At neutrality, the concentration of hydrogen ions ([H^+]) is equal to the concentration of hydroxide ions ([OH^-]) in pure water. The ion product of water ((K_w)) is defined as the product of the concentrations of hydrogen ions and hydroxide ions:

[ K_w = [H^+][OH^-] ]

Given that (K_w = 1 \times 10^{-13}), at neutrality, the concentrations of hydrogen and hydroxide ions are equal, where ([H^+] = [OH^-]). Let's denote the concentration of hydrogen ions as (x). Thus, we can express (K_w) as:

[ K_w = x \times x = x^2 ]

Substituting the given value of (K_w):

[ x^2 = 1 \times 10^{-13} ]

To find (x), we take the square root of both sides:

[ x = \sqrt{1 \times 10^{-13}} = 1 \times 10^{-6.5} ]

Consequently, at neutrality, the concentration of hydrogen ions ([H^+]) is