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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.

So let's try a simple problem: The [OH¯] in a solution is measured to be 0.0010 M. What is the pOH?

The solution is pretty straightforward. Plug the [OH¯] into the pOH definition:

pOH = - log 0.0010

An alternate way to write this is:

pOH = - log 10¯3

Since the log of 10¯3 is -3, we have:

pOH = - (- 3)

Which, of course, is 3.

Let's discuss significant figures and pOH.

Another sample problem: Calculate the pOH of a solution in which the [OH¯] is 4.20 x 10¯4 M.

For the solution, we have:

pH = - 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.

So you 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 "+/-").

The answer, to the proper number of significant digits is: 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.)

Practice Problems

Convert each hydroxide ion concentration into a pOH. Identify each as an acidic pOH or a basic pOH.

1) 0.0045

2) 5.0 x 10¯10

3) 1.0

4) 3.27 x 10¯3

5) 1.00 x 10¯12

6) 0.00010

Go to the answers

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.

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