What is pH?

Curiosity is the hallmark of any science student. You likely remember your high school chemistry teacher introducing the pH scale as a ruler ranging from 0 to 14. But if you’ve ever looked at concentrated laboratory acids or industrial alkalis, you might have wondered: Can pH be negative? Can it go above 14?

The short answer is yes. While most common solutions fall within the 0–14 range, the scale is not actually limited by these numbers. Here is the scientific breakdown of why we use this range and when the "rules" of chemistry start to bend.

What is pH? The Mathematical Definition

To understand the limits of the scale, we first look at the formula. The pH of a solution is defined as the negative base-10 logarithm of the molar concentration of hydronium ions ( $H_3O^+$ ) in a solution:

pH = -\log_{10} [H^+]

In a standard pharmaceutical or laboratory setting, we rarely deal with solutions exceeding a 1 Molar (1M) concentration. This leads to the two extremes we see on the standard scale:

High Acidity: A 1M concentration of hydrogen ions results in a pH of $0$ ( $-\log[1] = 0$ ).
High Alkalinity: A 1M concentration of hydroxide ions ( $OH^-$ ) corresponds to a 1M concentration of $H^+$ at $10^{-14}$ (due to the water dissociation constant), resulting in a pH of $14$ .

Why the 0–14 Range is the "Standard"

The reason we usually stop at 0 and 14 is due to the self-ionization of water. Water naturally dissociates into hydrogen and hydroxide ions. This equilibrium is represented by the constant $K_w$ :

Because this constant is $10^{-14}$ , the sum of $pH$ and $pOH$ always equals 14 at room temperature. However, nature doesn't always follow the "under 1M" rule. Concentrated sulfuric acid or saturated sodium hydroxide can easily exceed 1M, resulting in negative pH values (e.g., -1.0) or values above 14 (e.g., 15.0).

The Role of Ion "Activity" vs. "Concentration"

For advanced chemistry students, there is a technical nuance: pH is actually a measure of the activity of hydrogen ions, not just their concentration.

In extremely concentrated solutions, ions are so crowded that they begin to interfere with one another. This makes "activity" difficult to measure experimentally. For 99% of applications, using the molar concentration formula is accurate enough, but it explains why the 0–14 scale is a practical convention rather than a universal physical law.

The "Villain" of the Experiment: Temperature

If there is one factor that disrupts the perfect 0–14 scale, it is temperature. Temperature affects the equilibrium and dissociation rates of water.

At Room Temperature (25°C): Pure water has a pH of 7.0 (neutral).
At Higher Temperatures: The $K_w$ of water changes. For instance, at boiling temperatures, the neutral point of water might shift to a pH of around 6.14.

This is why a pH meter must always be calibrated with temperature compensation. Without accounting for the temperature, your results will be "interfered with" by the thermal energy affecting ion dissociation.