To find the hydroxide ion concentration ([OH-]) of a solution with a pH of 12.40, we can use the relationship between pH and [OH-]:

pH = -log[H+]

and

[H+][OH-] = Kw

where Kw is the ion product constant for water (Kw = 1.0 x 10^-14 at 25°C).

First, we calculate the hydrogen ion concentration ([H+]) using the given pH:

[H+] = 10^(-pH)

[H+] = 10^(-12.40)

[H+] = 3.98 x 10^-13 M

Next, we use the relationship [H+][OH-] = Kw to calculate [OH-]:

[OH-] = Kw/[H+]

[OH-] = (1.0 x 10^-14)/(3.98 x 10^-13)

[OH-] = 2.51 x 10^-2 M

Therefore, the hydroxide ion concentration of the solution is 2.51 x 10^-2 M.