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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.

Yes, a pOH of zero is possible, it is just uncommon. In fact, watch out for this teacher test trick. What's the pOH when [OH¯] = 2.0 M? That's right, NEGATIVE 0.30. It is possible to have a negative pOH, it is just uncommon to see them.

**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.

**Example #9:** Calculate the [OH¯] given a pOH of 2.45.

1) The calculator technique depends on which type of calculator button you have. The following instructions assume you have a key labeled EITHER x^{y} or y^{x}.

(a) Enter the number "10" into the calculator. (Do NOT then press the EXP or EE key.)

(b) Press the x^{y}(or the other, depending on what you have)

(c) Enter 2.45 and make it negative with the +/- key.

(d) Press the equals button and the calculator will do its thing.

2) The following instructions are for a calculator with a key labeled "10^{x}."

Enter the 2.45, 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.

3) One more comment about the way the answer appears on the calculator. The two most common ways for the answer to appear are:

3.548133892E-3 or 0.003548133892That E-3 means this:

x 10¯

^{3}<--- that x is a times signThe final answer (to the proper number of significant figures) is

[OH¯] = 3.5 x 10¯

^{3}M or 0.0035 MNotice the inclusion of the M for molarity.

Go to a similar discussion about pH

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