Most people have a vague concept of pH in that it has something to do with acidity and alkalinity, but what exactly is pH and why is it written the way it is?

This post will answer those questions by focusing on the chemistry behind pH. Knowing the science behind this very important soil property will help you appreciate its importance all the more next week, when we’ll focus on the practical aspects of pH, and its relevance to soils and plants — and you!

The Danish chemist Søren Sørensen conceived the idea of a pH scale back in 1909 as a means of measuring acidity and its opposite, basicity (or alkalinity). He originally wrote it as p_H, with a subscript H!

pH is the measure of the concentration of hydrogen ions in a solution. This is where the H comes from, being the chemical symbol for hydrogen, and why it is always capitalised. The more hydrogen ions in solution, the more acidic that solution. The fewer hydrogen ions in solution, the more basic (alkaline) a solution. (Chemists use the word ‘base’ in preference to ‘alkaline’ but the two are interchangeable.)

But what about the ‘p’? There is some dispute as to its origins, but ‘power of’ or ‘potential’ are two common contenders. Thus ‘pH’ stands for ‘power of Hydrogen’ or ‘potential Hydrogen’. The ‘p’ is always written in lowercase.

What does ‘power of/potential hydrogen’ mean? Please bear with me as we get slightly chemical and mathematical — I’ll step you through all of this!

Don’t worry about where this came from, but the formula for calculating pH is:
pH = -log[H⁺]
In words: pH is the negative log of the concentration of hydrogen ions.

What a mouthful! Let’s break this down.

First the chemical part:

A hydrogen atom is written as H, and has one proton (one positive charge) and one electron (one negative charge), making it neutral in charge overall. But when in solution, it loses that electron and becomes a hydrogen ion with one positive charge overall. We write that as H⁺.

In chemistry when you see square brackets, read “concentration of the solution in the brackets”. Thus [H⁺] reads as the concentration of hydrogen ions. This is the ‘power/potential’ part — the higher the concentration of hydrogen ions, the more power or potential those ions have. (To create acidity, in this case.)

So far so good?

Now the mathematical part:

The ‘log’ part is short for ‘logarithm’. Think of ‘logarithm’ as ‘how many times must we multiply one number by itself to get another number?’

For example, log₁₀(100) asks: how many times must we multiply 10 by itself to get to 100?
The answer is 2, as 10 × 10 = 100.

Similarly, log₁₀(1000) is 3 and log₁₀(10000) is 4 — this is too easy!

The ‘₁₀’ part refers to ‘base 10’. You could have logs of other bases, like log₂(8) = 3 (2 × 2 × 2 = 8), or log₄(256) = 4 (4 × 4 × 4 × 4 = 256), and so on, but we really don’t need to worry about these here. The point is to recognise the pattern.

As base 10 is our regular everyday number system,  log₁₀ is very common in science (like, for calculating pH!). To save writing it all the time, people drop the ‘₁₀’ part altogether and write it as ‘log’. If you see ‘log’ by itself, know it to automatically mean log₁₀.

Thus we could equally write log(100) = 2 or log(1000) = 3.

Realising that
log(100) = 2
can be rearranged as
100 = 10 × 10 = 10²

let’s get back to our formula:

pH = -log[H⁺]

Let’s switch both sides of the equal sign around to make this easier to follow:

-log[H⁺] = pH

Just as log(100) = 2 can be rearranged as 100 = 10², so too can
-log[H⁺] = pH be rearranged as [H⁺] = 10^-pH

In chemistry, concentrations are expressed as units of molarity, or M, which means ‘moles per litre’. To explain this more fully is quite involved and not really relevant to this discussion, so just know that ‘M’ is a unit of concentration, and let’s continue:

From [H⁺] = 10^-pH,
if [H⁺] = 10^-5.7 M, then pH = 5.7
if [H⁺] = 10^-7.0 M, then pH = 7.0
if [H⁺] = 10^-8.2 M, then pH = 8.2

You’re probably already familiar with the concept that pH 7 is neutral, with a number less than 7 indicating an acid pH, and and a number greater than 7 indicating a basic (alkaline) pH.

This is because as numbers decrease from 7, the concentrations of hydrogen ions increase. For example, a pH 4 solution has a concentration of 10^-4 M. 10^-4 is 0.0001; this is a larger number than than 10^-7, or 0.000 000 1.

On the other hand, as numbers increase from 7, the concentrations of hydrogen ions decrease. For example, a pH 9 solution has a concentration of 10^-9 M. 10^-9 is 0.000 000 001; this is a smaller number than than 10^-7, or 0.000 000 1.

The following terms break specific pH ranges into more meaningful degrees of acidity or alkalinity:

Now that you have seen how pH is determined by the concentration of hydrogen ions, lets revisit our formula pH = -log[H⁺] and cover one last point.

As the ‘log’ part of the formula would suggest, the pH scale is logarithmic.

For pH, this means that for every increase of one pH unit, the degree of acidity decreases by an order of ten. Similarly, every decrease of one pH unit increases acidity ten-fold.

This means that a pH of 4 is ten times more acidic than a pH of 5 and one hundred times more acidic than pH 6. (pH 5 is still ten times more acidic than pH 6.)

Going in the opposite direction, a pH of 8 is one hundred times less acidic than a pH of 6.

It might be easier to see below that as pH increases from 0 to 14 (the typical range of a pH scale) the concentration decreases ten-fold:

pH = 0 is 10⁰ M, or 1.0 M (or one part H⁺ in one part solution)
pH = 1 is 10^-1 M, or 0.1 M (or one-tenth part H⁺ in one part solution)
pH = 2 is 10^-2 M, or 0.01 M (or one-hundredth part H⁺ in one part solution)
pH = 3 is 10^-3 M, or 0.001 M (or one-thousandth part H⁺ in one part solution)
pH = 4 is 10^-4 M, or 0.000 1 M (etc)
pH = 5 is 10^-5 M, or 0.000 01 M
pH = 6 is 10^-6 M, or 0.000 001 M
pH = 7 is 10^-7 M, or 0.000 000 1 M
pH = 8 is 10^-8 M, or 0.000 000 01 M
pH = 9 is 10^-9 M, or 0.000 000 001 M
pH = 10 is 10^-10 M, or 0.000 000 000 1 M
pH = 11 is 10^-11 M, or 0.000 000 0000 1 M
pH = 12 is 10^-12 M, or 0.000 000 000 001 M
pH = 13 is 10^-13 M, or 0.000 000 000 000 1 M
pH = 14 is 10^-14 M, or 0.000 000 000 000 01 M

Now — I do hope! — you know far more about pH than was ever hinted at in any gardening book! And that it is no longer some vague and mysterious concept. The three key points to remember are:

1. pH is determined by the concentration of hydrogen ions
2. Acidity and alkalinity are determined by the concentration of (or lack of) hydrogen ions present
3. pH increases or decreases ten-fold with every one unit decrease or increase respectively

With the chemistry behind pH now covered, next week we’ll discuss the practical importance of soil pH to plant health.