Calculating H-OH Ion Concentrations
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Calulating Hydronium and Hydroxide Concentrations

The equation for the ionization constant of water can be used to calculate either the hydronium or hydroxide in 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 18c 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  

 

Answers

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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