pH isn’t a scale between 0 and 14: Many diagrams are just incomplete!

pH (historically, power of hydrogen or potential of hydrogen) is often described as a scale that goes from 0 to 14. If we look at the formula that defines pH, we’ll see that it has no upper or lower bound.

pH = -log₁₀[H₃O⁺ (aq)]

pH is equal to the negative logarithm (base 10) of the concentration of hydronium ions (H₃O⁺) in water.

Sometimes H3O⁺ is written as H⁺, in the case with pH – it’s the same thing.

H⁺ is called a hydron, a proton, a hydrogen cation, or a hydrogen ion.

In the case of pH, since we’re looking at aqueous solutions, we assume the H⁺ is bound to a water molecule (H₂O).

H₂O plus a H⁺ is H₃O⁺.

If we look at this part of the formula: [H₃O⁺ (aq)]

The (aq) tells us it is aqueous – it is dissolved in water.

The square brackets tells us it is a concentration – a type called molarity or molar concentration. Molarity or molar concentration is the number of moles of solute (the thing dissolved) per liter.

Moles can be confusing, but one way to think of it is like a dozen.

A dozen = 12

A mole = 6.022×10²³ (6.022 times 10 to the power of 23)

You can have a dozen of something or a mole of something. A dozen hydronium ions is 12. A mole of hydronium ions is 602200000000000000000000.

Let’s say we have a solution of sugar in water with a molarity of 1.

That means if we measured out 1 liter of that sugar solution, it would contain 1 mole (6.022×10²³) of sugar molecules.

What is the pH of a solution with a 1.0×10⁻¹² (1 times 10 to the negative power of 12) hydronium ion molarity?
Or, in other words, what is the pH of a solution with 0.000000000001 moles of hydronium ions per liter?

pH = -log₁₀[10⁻¹²] = (-1)(-12) = 12

What is the pH of a solution with a 10⁻³ hydronium ion molarity?

pH = -log₁₀[10⁻³] = (-1)(-3) = 3

What about a hydronium ion molarity of 10⁻¹⁵?

pH = -log₁₀[10⁻¹⁵] = (-1)(-15) = 15

That’s above 14!

What about a hydronium ion molarity of just 10?

pH = -log₁₀ = (-1)(1) = -1That’s below 0!

We’re not likely to bump into things with a pH higher than 14 or below 0, that’s why diagrams often end there. But they do exist!

A 37% concentration of hydrochloric acid has a pH that’s around -1.

A saturated solution of sodium hydroxide has a pH of about 15.In California at the Richmond Mine of the Iron Mountain the pH of the water has been measured to be as low as -3.6!

While this may seem pedantic, I think it’s important to understand what we’re discussing and educating others about – especially in the beauty science community.

For example, did you know the way acid and bases are often described in the beauty community is only one of the theories?

It’s called the Arrhenius theory of acid and bases, but there’s also the Brønsted-Lowry theory and the Lewis theory!