### Calculate the Ksp of a Saturated Solution When Given the pH

Please be aware that this problem does not require a concentration to be given in the problem. We know the pH and we know the solution is saturated. This information will be sufficient.

Warning: you need to know about Ksp AND acid base ideas to do this problem type. If you lack one or the other of these skills, just be aware you just might struggle a little in your understanding of this problem type.

To solve the problem, we must first calculate the [OH¯]. To do this, we will use the pH and acid base concepts. Then, we will use the Ksp expression to calculate the Ksp

Final Note: Ksp are almost always given at 25.0 °C in reference sources. All problems in this tutorial are taken to be at 25.0 °C. If you were to see a problem where the specified temperature was different, it's probably just that the reference source gave a Ksp that, for whatever reason, was not at 25.0 °C.

Example #1: A saturated solution of Mg(OH)2 is prepared. The pH of the solution is 10.17. What is the Ksp for this compound?

Solution:

1) The chemical equation:

Mg(OH)2 ⇌ Mg2+ + 2OH¯

2) The Ksp expression:

Ksp = [Mg2+] [OH¯]2

3) Use the pH to get the pOH:

14.00 - 10.17 = 3.83

4) Use the pOH to get the [OH¯]:

[OH¯] = 10¯pOH = 10¯3.83 = 1.479 x 10¯4 M

5) From the chemical equation, we note that the [Mg2+] is half the value of the [OH¯], therefore:

[Mg2+] = 1.479 x 10¯4 M divided by 2 = 7.395 x 10¯5 M

6) We now have the necessary values to put into the Ksp expression:

Ksp = (7.395 x 10¯5) (1.479 x 10¯4)2

Ksp = 1.62 x 10¯12

Note: the book value for the Ksp of Mg(OH)2 is 5.61 x 10¯12. The reason for the difference is that teachers like to change the values slightly so as to not allow a student to simply look up the correct answer and claim they did all their work on the calculator.