A Homeschool Science Lesson about pH, Concentration of the Hydronium Ion, and Logarithmic Scales.

A pH lesson may be my very favorite lessons. It has all the best things – math, science, and rainbows. This lesson was a two day process, but I’ve been subtly leading us here for a while, on the math side of things anyway. Last week we talked about probability and before that we were doing a little bit of permutations. See my blog: Ice Cream Flavor Permutations. We also reviewed exponents with an exercise talking about doubling with bacteria.

Why do we need all this math with probability and exponents? Let’s back up and talk about chemistry for a moment. When you have a glass of water, it’s mostly made up of water molecules – one oxygen and two hydrogen elements stuck together (bonded) by sharing electrons (covalent bonding.) Every once in a while, a hydrogen will pop off. Tricky those hydrogen molecules (very reactive because they have a single valence electron in the first energy shell which only holds two electrons, meaning they really want to share.) 

In this blog post, you’ll find:

IMPORTANT NOTE: 

If you decide to do something similar, DO NOT MIX YOUR VARIOUS HOUSEHOLD CHEMICALS!!! Kids so want to mix and play and see what happens, but a few of these that we tested do not play well together, ammonia and bleach in particular. The combination of these two produces a gas that is lethal. Also note that LYE (SODIUM HYDROXIDE) IS CAUSTIC and if the solution gets onto the skin can cause a chemical burn. 

What you can do safely to let them play is give them citric acid or vinegar with some baking soda and some cabbage juice for a pH indicator. These all play well together and are safe. It also makes for exciting bubbles and colors. If you want to ‘trap’ the bubbles, you can safely add a little dish detergent to the test tubes/vials/containers. Safety glasses are advised.

Ok, now we’ve gone over safety, let’s move on.

Water Molecules and the Hydronium

Water, because of the micky-mouse shape of the water molecule has a slight charge. This also has to do with valence electrons (outer most electrons) and orbitals (shapes of the electron cloud that an electron can be found in) of the oxygen atom. When a water molecule runs into the hydrogen, they stick ever so slightly together causing a special water molecule – a hydronium. That’s one oxygen, but now paired with 3 hydrogen. The pH scale measures how often we are likely to find this hydronium in the water.

Exponents in the pH Scale

This is where exponents and probability come in. Let’s start with exponents. The pH scale is a logarithm scale, meaning that 1 through 14 is talking about exponents, not counting numbers. So, what’s our base if the pH scale is the exponent? Ten. The numbers in the scale are telling us how many times we are multiplying 10 by itself. The one means 1 x 10, giving us 10. The 7, which is neutral on the pH scale means 10 x 10 x 10 x 10 x 10 x 10 x 10 or 10⁷ which is 10,000,000, because for base 10, the number of the exponent corresponds to the number of 0’s after the 1. A 14 on the pH scale is referring to 10¹⁴ or 100,000,000,000,000.

Concentration of the Hydronium in Water

Now let’s talk about the probability. The pH scale tells us the probability or concentration of a hydronium molecule to all the other water molecules. If we have a pH of 1, that means there is 1 to 10¹ chance of finding a hydronium in the water solution or the concentration is likely to be 1 hydronium for every 10 water molecules. When the pH is 7, there is a 1 in 10⁷ chance of finding a hydronium, and the ratio of hydronium to water is 1:10,000,000.

Acids and Bases

Let’s talk about Acids and Bases. Acids have a lot of hydrogen to give. Let’s look at a strong acid, hydrogen chloride. Hydrogen chloride has one hydrogen and one chlorine. The bond they share is a covalent bond, meaning the hydrogen and chlorine both share a pair of electrons. This fills both of their outer electron shells. However, the bond that they share is weak, and when hydrochloric acid is in water, the hydrogen and chlorine separate. This leaves a lot of extra hydrogen. You want to know what those hydrogen are doing? They are hooking up with the water molecules to form hydroniums. That means the changes of finding a hydronium are high. Like in hydrochloric acid’s case, 1 out of 10, giving it a pH of 1. 

On the flip side, bases do the opposite. They suck up hydrogen like nobody’s business. They bind it to form other molecules leaving no extra hydrogen. Let’s look at a strong base who loves to bind hydrogen – sodium hydroxide. Sodium hydroxide is made of a sodium atom and a hydroxide group which means it contains an oxygen and hydrogen pair. Unlike the hydrochloric acid bond, the bond for sodium hydroxide is an ionic bond. The sodium just gives it’s electron away. No one is sharing anything here. 

When sodium hydroxide hits water, the bonds break. Sidenote here: this breaking of bonds for sodium hydroxide specifically, releases a lot of energy (exothermic reaction: exo=outside, thermic=heat.) It also is a caustic mixture (will chemically burn skin if expose) and releases a toxic gas. Great guy, sodium hydroxide. But he does turn fat into soap, so there’s that. Anyway, now we have this hydroxyl group floating around in water (OH), and it’s just missing one hydrogen that it needs to be a water molecule. So you know what’s coming, right?! That oxygen-hydrogen combination finds every last free hydrogen in the water and binds to it. So now how many hydroniums do you think we have. Nada. Close to none. In sodium hydroxide’s case, we can only find 1 hydronium for every 10,000,000,000,000 molecules of water. That’s 1 in 10¹³ chance, giving it a pH of 13.

Rainbows and pH Indicators

The most fun part of pH is that there are several household items or chemicals that work as a pH indicator, meaning they change color towards one part of the color scale when you add acids and the other part of the pH scale when you add a base. For our lab, we used cabbage juice as the pH indicator. It’s super easy to make. Chop some red cabbage, place in a sauce pot, cover with water, and boil for a few minutes. Strain and you have the perfect pH indicator. Here is a pH scale to use for red cabbage. Neutral, pH of 7, is purple. The acids tend towards the pink and orange color scale depending on their strength, and the bases tend towards the blue and green end of the spectrum depending on their strength. 

Making the Rainbow

After working on our main lesson page going over the pH scale, we collected several different household items to test the pH. We are using the vials that I suggest from my Botany Guide for the root growth observation activity. These are so versatile, and we love them. I’m getting ready to buy more. I like them far more than test tubes; they have lids and flat bottoms. We added our cabbage juice solution to each one of our vials, noted the color by comparing it to a vial of pure cabbage juice, and used the pH scale to determine our pH. We then recorded our placement of this item on the pH scale into our main lesson books (notebook.) 

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