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Fifteen conversions between pH, pOH, [H_{3}O^{+}], and [OH¯]

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

Let's discuss significant figures and pOH.

**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 0.0045pOH = −(−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 1.0pOH = −(−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) = 2.485This is a basic pOH.

**Example #7:** 1.00 x 10¯^{12} M

pOH = −log 1.00 x 10¯^{12}= 12.000This is an acidic pOH.

**Example #8:** 0.00010 M

pOH = −log 0.00010 = 4.0This 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 x^{y} or y^{x}.

1) Enter the number "10" into the calculator.

2) Press the x^{y}(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 "10^{x}." In that case, enter the 3.45, make it negative, then press the "10^{x}" key. An answer appears!! Just remember to round it to the proper number of significant figures and you're on your way.

Go to a similar discussion about pH

Fifteen conversions between pH, pOH, [H_{3}O^{+}], and [OH¯]