What is pH? The Mathematics of Hydrogen

You may have heard someone say, “Water has a pH of 7.” Or, you may have read that to keep your pet fish happy, you need to “closely monitor the pH of their water.” But what exactly is pH?

To understand what pH is, we must first understand the “H.”

Hydrogen, the first element in the periodic table of elements, is quite possibly the most abundant element in the universe.

Suggested Activity

While reading this article, you may want to pull out a Molecular Modeling Kit and follow along. You can construct water molecules, OH molecules, and set aside H molecules to see the relationship between acids and bases.

Hydrogen Highlighted in the Periodic Table of Elements

Hydrogen earned its place as the first element because it has an atomic number of 1. It has exactly one proton and, surprisingly, no neutrons in its nucleus. To be stable, hydrogen often has one proton and one electron, allowing it to make exactly one bond with another element.

Hydrogen Atom

You may have also learned that a water molecule is made up of 2 Hydrogen and 1 Oxygen atoms, or H2O. This is true…mostly. ?

Water Molecule
Hydrogen Atom

Pure Water

An OH- Molecule

Pure water is made up of a lot of water molecules. When these molecules bump up against each other, they react. Some of the H+ molecules combine to form H3O leaving an OH- molecule. These H3O molecules are represented as the “power” of hydrogen, and this is where we get the term “pH”. pH stands for how much hydrogen is present in, or removed from, a solution.

Mathematics of pH7

At the perfect ratio of 1 hydrogen ion to 1 OH molecule, we have a neutral pH. We say this is a pH of 7 because in a liter of water, there are 10-7 molecules of H+. This is where the math starts to get confusing.

1 to 1 Ratio to -7 exponent
10^-7 mol/L

Here’s what this value really means.

First, 10-7 is scientific notation for a really small fraction. One ten-millionth to be exact. This is how we calculate this fraction:

Second, we need to remember that this is one-ten-millionth mol (or molars, or molecules) PER LITER.

This means that for every Liter of pure water, we can find only one-ten-millionth of it to be hydrogen ions floating around as H3O, making some of it acidic. Since these molecules leave exactly one-ten-millionth mol of OH as well, the water is balanced.

Whew, that was a mouthful, right? Here’s a visual representation that might help.

2L bottle v 1L pitcher

You’ve probably seen 2 Liter bottles of soda in the grocery store. For our molar measurement, we’re talking about half of that amount of liquid: 1 Liter.

In this 1 liter of liquid, you will find that one-ten-millionth of it is the amount of hydrogen floating around.

Coincidently, it’s also the number of OH-molecules floating around.

Hydrogen molecules and OH molecules are opposite of each other. When a hydrogen molecule bumps up against an OH molecule, they essentially form a perfect little water molecule.

1 L Pitcher with Molcules

You can think of this as a ratio:

1:1 Ratio of H to OH-

Or, as a division problem:

Division of a One to One Ratio

In the world of pH, things start to get really interesting when you add or remove hydrogen ions to the liquid. We say something has a pH of 6 when it has 10-6 moles per liter of water. Essentially, it looks like this:

Pitcher of pH6

Do you see the single zero missing in the hydrogen ions? That affects our balance of ions like this:

You can think of this as a ratio:

This means that hydrogen is ten times more present than OH. When there is more hydrogen than OH, we say that our solution is “acidic.” A common substance that has a pH of 6 is the saliva in our mouth. This helps break down our food just a little bit before reaching our stomach.

Here are some other common acids and their relative pH scale. Notice that battery acid isn’t just “more acidic” than the water we drink, it’s 10 million times more acidic! Unbelievably our bodies hold an extremely acidic substance in our stomach to break down our food.

pH7 to pH0

So, what happens if we go in the other direction? At neutral we have the same number of hydrogen ions and OH molecules. But what happens if we remove hydrogen instead of adding it?

In this case, you can think of the ratio as this:

1 to 10 Ratio of H+

Did you Know?

Pools use chlorine (a strong base) to make the water clean, but if we only put chlorine into the water it would burn our skin. To balance the pH, we have to add an acid—hydrochloric acid to be exact. The same acid we have in our very own stomachs!

In other words, hydrogen is now one-tenth as powerful as OH ions. It is less powerful. When there is less hydrogen, we say the solution is alkaline and we often call it a base.

If you’re a teacher and you like this article, please feel free to contact me for the downloadable PDF. I use articles all the time and “copy/pasting” them for reproduction in the classroom is a pain! I’d love to share the fully edited version with you instead.

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