### pOH and how to calculate it

Sörenson defined pH as the negative logarithm of the hydrogen ion concentration.

pH = −log [H+]

We can define the pOH in a similar way:

pOH = −log [OH¯]

In words, the pOH is the negative logarithm of the hydroxide ion concentration.

Example #1: The [OH¯] in a solution is measured to be 0.0010 M. What is the pOH?

Solution:

1) Plug the [OH¯] into the pOH definition:

pOH = −log 0.0010

2) An alternate way to write this is:

pOH = −log 10¯3

3) Since the log of 10¯3 is -3, we have:

pOH = −(−3)

pOH = 3.00

Example #2: Calculate the pOH of a solution in which the [OH¯] is 4.20 x 10¯4 M.

Solution:

pOH = −log 4.20 x 10¯4

This problem can be done very easily using your calculator. However, be warned about putting numbers into the calculator.

Enter 4.20 x 10¯4 into the calculator, press the "log" button (NOT "ln") and then the sign change button (usually labeled with a "+/-").

pOH = 3.377

I hope you took a look at the significant figures and pH discussion. If not, why don't you go ahead and do that right now. I can wait.

Comment regarding the examples below: keep in mind this equation:

pH + pOH = 14

The ChemTeam also keeps in mind that acidic pH is less than 7 and that a basic pH is greater than 7. So, if I have a pOH = 4, I know that the pH = 10 and that this is a basic solution. In a similar way, if I know the pOH is 11, then the pH is 3 and this is an acidic solution.

For the examples below, convert each hydroxide ion concentration into a pOH. Identify each as an acidic pOH or a basic pOH.

Example #3: 0.0045 M

pOH = −log 0.0045

pOH = −(−2.35)

2.35

This is a basic pOH.

Example #4: 5.0 x 10¯10 M

pOH = −log 5.0 x 10¯10

pOH = −(−9.30) = 9.30

This is an acidic pOH.

Example #5: 1.0 M

pOH = −log 1.0

pOH = −(−0.00)

pOH = 0.00

This is a basic pOH.

Note the value of zero. See the pH discussion for a comment.

Example #6: 3.27 x 10¯3 M

pOH = −log 3.27 x 10¯3 = −(−2.485) = 2.485

This is a basic pOH.

Example #7: 1.00 x 10¯12 M

pOH = −log 1.00 x 10¯12 = 12.000

This is an acidic pOH.

Example #8: 0.00010 M

pOH = −log 0.00010 = 4.0

This is a basic pOH.

Suppose you know the pOH and you want to get to the hydroxide ion concentration ([OH¯])?

Here is the equation for that:

[OH¯] = 10¯pOH

That's right, ten to the minus pOH gets you back to the [OH¯] (called the hydroxide ion concentration).

This is actually pretty easy to do with the calculator. Here's the sample problem: calculate the [OH¯] from a pOH of 3.45.

The calculator technique depends on which type of button you have. Let's assume you have the standard key. It's labed EITHER xy or yx.

1) Enter the number "10" into the calculator.
2) Press the xy (or the other, depending on what you have)
3) Enter 3.45 and make it negative.
4) Press the equals button and the calculator will do its thing.

Some people have a calculator with a key labeled "10x." In that case, enter the 3.45, make it negative, then press the "10x" key. An answer appears!! Just remember to round it to the proper number of significant figures and you're on your way.