However, some people lack this enzyme, so their bodies cannot break down lactose. The lactose remains intact and undergoes a process known as bacterial fermentation, producing gases and causing nausea, abdominal cramps, and diarrhea. Lactase functions better at pH 6, so changing **pH** has a big effect on lactase activity.

What exactly is** pH** and how does it relate to **pOH**? Keep reading to find out!

- First, we will look at the difference between pH and pOH
- After, we will learn about the pOH scale and how it differs from the pH scale.
- Then, we will talk about the pH of strong acids and bases
- Lastly, we will dive into the calculations involving pH and pOH.

## Difference between pH and pOH

Before diving into the world of pH and pOH, we need to recall the definition of acids and bases. Acids and bases have different definitions, depending on who you ask!

Svante Arrhenius was the first chemist to classify acids and bases. **Arrhenius acids** are acids that dissociate in water and form H^{+} ions. **Arrhenius bases**, on the other hand, dissociate in water and form OH^{- }ions.

Other chemists who came up with acid and base definitions were Johannes Brønsted and Thomas Lowry. Together, they defined acids and bases by their ability to donate and accept protons (hydrogen ions). **Brønsted-Lowry acids** are proton (H^{+}) donors, whereas **Brønsted-Lowry bases** are proton (H^{+}) acceptors.

Now that we know a bit more about acids and bases, let's define what pH and pOH are!

**pH** is referred to as a logarithmic measure of the concentration of hydrogen ions (H^{+}) in a solution.

**pOH** is referred to as a logarithmic measure of the concentration of hydroxide ions (OH^{-}) in a solution.

pH is measured using a **pH scale** that ranges from 0 to 14. The smaller the pH, the more acidic a solution is, and the higher the concentration of H^{+} ions in the solution. So, acidic solutions have a very small concentration of OH^{-} ions compared to the high amount of H^{+} ions in the solution.

- Acidic solutions have a pH of smaller than 7
- Basic solutions have a pH of greater than 7
- Solutions containing pH 7 are considered neutral.

Think about an area in the world where the atmosphere is polluted with gases such as nitrogen dioxide and sulfur dioxide. When it rains, the gases can dissolve in rainwater, making rain more acidic. When this happens, we call it **acid rain**. Acid rain can also occur naturally near volcanic eruptions and plant decomposition.

Acid rain corrodes statues made of limestone, reduces the rate of photosynthesis, and raises the acidity of rivers and lakes, killing many animals.

## pOH scale

The sum of the pH and pOH of an aqueous solution equals 14. The relationship between pH and pOH is as follows:

$\mathrm{pH}+\mathrm{pOH}=14$

So, if you know either the pH or pOH, you can easily calculate the missing value! For example, if you have a pOH of 3, then the pH would be equal to 11, because 11 + 3 = 14. Remember:

- The lower the pH value, the more acidic a solution is, the higher the H
^{+}concentration and the lower the OH^{- }concentration. - The lower the pOH value, the more basic a solution is, the higher the OH
^{- }concentration and the lower the H^{+}^{ }concentration.

**If the pH of a solution is 4.6, calculate the pOH. **

We know that the sum of pH and pOH should be equal to 14. So, we can rearrange the equation above to solve for pOH.

$\mathrm{pOH}=14-\mathrm{pH}\phantom{\rule{0ex}{0ex}}\mathrm{pOH}=14-4.6\phantom{\rule{0ex}{0ex}}\mathrm{pOH}=9.4$

### pH and pOH Formula

The formula to calculate pH and pOH is:

$\mathrm{pH}=-{\mathrm{log}}_{10}\left[{\mathrm{H}}^{+}\right]\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{pOH}=-{\mathrm{log}}_{10}\left[{\mathrm{OH}}^{-}\right]$

Those formulas might look a bit confusing, but don't worry, we will put them to practice!

**Find the pH of a solution with an [H ^{+}] ion concentration of**$\mathbf{5}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{}\mathbf{M}$.

This is a simple question. We are given the value for [H^{+}], so all we need to do is plug it into the pH formula!

$\mathrm{pH}=-{\mathrm{log}}_{10}\left[{\mathrm{H}}^{+}\right]\phantom{\rule{0ex}{0ex}}\mathrm{pH}=-{\mathrm{log}}_{10}[5.5\times {10}^{-10}\mathrm{M}]\phantom{\rule{0ex}{0ex}}\mathrm{pH}=9.26\phantom{\rule{0ex}{0ex}}$

Now, let's look at an example involving pOH.

**Find the pOH of a solution containing an [H+] ion concentration of** $\mathbf{8}\mathbf{.}\mathbf{0}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{7}}\mathbf{}\mathbf{M}$.

First, we need to calculate the pH of the solution, and then use the formula pH + pOH = 14 to solve for pOH.

$\mathrm{pH}=-{\mathrm{log}}_{10}[8.0\times {10}^{-7}\mathrm{M}]\phantom{\rule{0ex}{0ex}}\mathrm{pH}=6.1\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{pH}+\mathrm{pOH}=14\phantom{\rule{0ex}{0ex}}\mathrm{pOH}=14-6.1\phantom{\rule{0ex}{0ex}}\mathrm{pOH}=7.9$

#### Using pH and pOH to calculate Ion Concentration

We can rearrange the pH and pOH formulas to find the concentrations of hydrogen and hydroxide ions!

$\left[{\mathrm{H}}^{+}\right]={10}^{-\mathrm{pH}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left[{\mathrm{OH}}^{-}\right]={10}^{-\mathrm{pOH}}$

Let's solve another example!

**Calculate the [OH ^{-}] ion concentration of a solution that has a pH of 3.3.**

Here, we need to put into action some of the formulas that we learned so far. ** **

Step 1: Find the value for pOH using pH.

$\mathrm{pOH}=14-3.3\phantom{\rule{0ex}{0ex}}\mathrm{pOH}=10.7$

Step 2: Find the [OH^{-}] ion concentration using pOH.

$\left[{\mathrm{OH}}^{-}\right]={10}^{-10.7}\phantom{\rule{0ex}{0ex}}\left[{\mathrm{OH}}^{-}\right]=1.99\times {10}^{-11}\mathrm{M}$

## pOH to pH

During your AP chemistry exam, you will most likely be asked to convert pOH to pH. This can be accomplished by using the different formulas that we learned so far. The simplest way is by using the formula **pH + pOH = 14.**

However, sometimes you will have to use more than one formula to find pH. Let's look at an example.

**Find the pH of a substance containing an [OH ^{-}] concentration of 3.2 x 10^{-7} M.**

Step 1: Use [OH^{-}] to calculate pOH.

$\mathrm{pOH}=-{\mathrm{log}}_{10}\left[{\mathrm{OH}}^{-}\right]\phantom{\rule{0ex}{0ex}}\mathrm{pOH}=-{\mathrm{log}}_{10}[3.2\times {10}^{-7}\mathrm{M}]\phantom{\rule{0ex}{0ex}}\mathrm{pOH}=6.5$

Step 2: Use the calculated pOH to solve for pH.

$\mathrm{pH}=14-\mathrm{pOH}\phantom{\rule{0ex}{0ex}}\mathrm{pH}=14-6.5\phantom{\rule{0ex}{0ex}}\mathrm{pH}=7.5$

## pH of Strong Acids

**Strong acids** are acids that completely dissociate in aqueous solutions to form positive hydrogen ions.

Strong acids have very** low pH**, mostly between 0 and 1.

Some common strong acids you should know include:

- HCl
- HBr
- HI
- HNO
_{3} - HClO
_{3} - HClO
_{4} - H
_{2}SO_{4}

Since strong acids completely dissociate in the solution, we can assume that the concentration of the strong acid will be equal to the concentration of the hydrogen ions in the solution!

**Calculate the pH of a solution of a 0.023 M HCl solution.**

$\mathrm{HCl}\stackrel{}{\to}{\mathrm{H}}_{\left(\mathrm{aq}\right)}^{+}+{\mathrm{Cl}}_{\left(\mathrm{aq}\right)}^{-}$

The question tells us the HCl solution has a 0.023 M concentration. So, we can assume that the [H^{+}] ion concentration will also be 0.023 M because HCl is a strong acid!

So, we can calculate the pH using the formula: $\mathrm{pH}=-{\mathrm{log}}_{10}\left[{\mathrm{H}}^{+}\right]$

$\mathrm{pH}=-{\mathrm{log}}_{10}[0.023\mathrm{M}]\phantom{\rule{0ex}{0ex}}\mathrm{pH}=1.64$

Can a solution ever have a negative pH? The answer is yes! For example, if an acid, such as HCl, has a very high concentration of H^{+} ions, let's say 10 M, then it will have a pH of **-1**.

Also, did you know that one of the strongest acids known by chemists is called fluoroantimonic acid and has a pH of -31.3? Another fluoroantimonic acid derivative is so strong of an acid it is (appropriately) called magic acid.

## pH of Strong Bases

**Strong bases** are bases that dissociate completely in aqueous solutions, forming OH^{-} ions. Contrary to strong acids, strong bases have very** high pH**,** **usually around 12-14

Some strong bases you need to be familiar with are:

- NaOH
- LiOH
- KOH
- RbOH
- CsOH
- Ca(OH)
_{2} - Mg(OH)
_{2} - Ba(OH)
_{2} - Sr(OH)
_{2}

The same principle applies to strong bases. Since strong bases also completely dissociate, we assume that the concentration of the strong base will be equal to the concentration of the hydroxide ions in the solution.

**Calculate the pH of a solution of a 0.023 M Ca(OH) _{2 }solution.**

**$\mathrm{Ca}\left({\mathrm{OH}}_{2}\right)\stackrel{}{\to}{\mathrm{Ca}}_{\left(\mathrm{aq}\right)}^{2+}+2{\mathrm{OH}}_{\left(\mathrm{aq}\right)}^{-}$**

First, notice the number 2 in front of the hydroxide ions in the chemical equation. This means that when calcium hydroxide dissociates, it forms 2 hydroxide ions.

So, we need to multiply the hydroxide ion concentration to account for this.

$\left[{\mathrm{OH}}^{-}\right]=2\times 0.023\mathrm{M}=0.046\mathrm{M}$

Now, we can use the [OH^{-}] ions concentration to calculate pOH, and subsequently convert it to pH.

$\mathrm{pOH}=-{\mathrm{log}}_{10}[0.046\mathrm{M}]\phantom{\rule{0ex}{0ex}}\mathrm{pOH}=1.34\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{pH}=14-\mathrm{pOH}\phantom{\rule{0ex}{0ex}}\mathrm{pH}=14-1.34\phantom{\rule{0ex}{0ex}}\mathrm{pH}=12.66$

Now, you should be familiar with pH and pOH and how to apply their formulas to different problems!

## pH and pOH - Key takeaways

**pH**is a measure of the concentration of hydrogen ions (H^{+}) in a solution.**pOH**is a measure of the concentration of hydroxide ions (OH^{-}) in a solution- The sum of the pH and pOH of a solution should always equal 14.
- Strong acids are acids that completely dissociate in aqueous solutions to form positive hydrogen ions.
- Strong bases are bases that dissociate completely in aqueous solutions, forming OH- ions.

_{References:}

_{Malone, L. J., Dolter, T. O., & Gentemann, S. (2013). Basic concepts of Chemistry (8th ed.). Hoboken, NJ: John Wiley & Sons.}

_{Swanson, J. W. (2020). Everything you need to Ace Chemistry in one big fat notebook. Workman Pub.}

_{Saunders, N. (2020). Supersimple Chemistry: The Ultimate Bitesize Study Guide. London: Dorling Kindersley.}

_{ }

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##### Frequently Asked Questions about pH and pOH

How to calculate the pH of a strong base?

To calculate the pH of a strong base, we can use the following formulas:

- pOH = -log [OH
^{-}] - pH + pOH = 14

For example, if you are given the [OH^{-}] ion concentration of a solution, you can use it to find pOH and then solve for pH.

How do pH and pOH relate to the strength of an acid or base?

The lower the pH value, the more acidic a solution is, the higher the H^{+} concentration and the lower the OH^{-} concentration.

The lower the pOH value, the more basic a solution is, the higher the OH^{-} concentration and the lower the H^{+} concentration.

What is the pH of a strong acid and strong base?

Strong acids have very low pH values, whereas strong bases have very high pH values.

How do you find the pOH of a strong acid?

To calculate the pH of a strong acid, we can use the following formulas:

- pH = -log [H
^{-}] - pH + pOH = 14

So, f you are given the [H^{-}] ion concentration of a solution, you can use it to find pH.

What is the pOH if the pH is 11?

In a solution, the sum of the pH and pOH values equals 14. So, a solution containing a pH value of 11 has a pOH of 3 because 14 - 11 = 3.

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