## Calculating Hydronium and Hydroxide Concentrations

The equation for the ionization constant of water can be used to calculate either the hydronium or hydroxide ion concentration if the other one is known.

As an example, let's calculate [OH-] given that [H3O+] = 4.5 x 10-5 M. Starting with the water constant equation [H3O+]·[OH-] = Kw, we can figure that [OH-] = Kw/[H3O+]. Then, substitute the known values for Kw and [H3O+] to get that [OH-] is equal to 1.0 x 10-14 divided by 4.5 x 10-5. That comes out to be 2.2 x 10-10 M for the concentration of hydroxide ion.
 Problem: Given that [H3O+] = 4.5 x 10-5 M, calculate [OH-]. [H3O+]·[OH-] = Kw, [OH-] = Kw/[H3O+]. [OH-] = (1.0 x 10-14) ÷ (4.5 x 10-5) [OH-] =  2.2 x 10-10 M

### Practice

Now you figure out the missing values in this table (also shown in exercise 24-c in your workbook). Check your answers below and then continue.
 [H3O+] [OH-] 4.5 x 10-5 M 2.2 x 10-10 M 3.3 x 10-2 M 1.4 x 10-10 M

The missing values are [H3O+] = 3.0 x 10-13 M and [OH-] = 7.1 x 10-5 M.
 [H3O+] [OH-] 4.5 x 10-5 M 2.2 x 10-10 M 3.0 x 10-13 M 3.3 x 10-2 M 1.4 x 10-10 M 7.1 x 10-5 M

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