pH Scale — Acids, Bases & How to Calculate pH

The pH scale tells you how acidic or basic an aqueous solution is. In introductory chemistry, it is commonly written as

$$\mathrm{pH} = -\log_{10}[H_3O^+]$$

where $[H_3O^+]$ is the hydronium concentration in moles per liter. Lower pH means more acidic. Higher pH means more basic.

The main idea that makes pH click is that it is not a linear scale. A change of 1 pH unit means a factor of 10 in $[H_3O^+]$. So pH 3 is much more acidic than pH 4, not just a little more.

What The pH Scale Measures

In water, acids increase hydronium concentration and bases reduce it. Because pH is the negative base-10 logarithm of $[H_3O^+]$, more hydronium gives a lower pH.

Many textbooks write $[H^+]$ as shorthand. In water, $[H_3O^+]$ is the more precise way to describe the acidic species.

For most school problems, you will see pH presented on a scale from 0 to 14:

• below 7: acidic
• about 7: neutral
• above 7: basic

That rule is a good classroom guide for dilute aqueous solutions near $25^\circ \mathrm{C}$. It is not a universal rule for every temperature or every concentration.

How To Calculate pH

If you know hydronium concentration, use the definition directly:

$$\mathrm{pH} = -\log_{10}[H_3O^+]$$

If you know hydroxide concentration first, you can find pOH:

$$\mathrm{pOH} = -\log_{10}[OH^-]$$

Then, for dilute aqueous solutions at about $25^\circ \mathrm{C}$, use

$$\mathrm{pH} + \mathrm{pOH} = 14$$

That last equation depends on temperature, so state the condition when you use it.

Worked Example: Find The pH Of A Solution With $[H_3O^+] = 1.0 \times 10^{-3}\,\mathrm{M}$

Start with the definition:

$$\mathrm{pH} = -\log_{10}[H_3O^+]$$

Substitute the concentration:

$$\mathrm{pH} = -\log_{10}(1.0 \times 10^{-3})$$

Since $\log_{10}(10^{-3}) = -3$,

$$\mathrm{pH} = 3$$

So the solution is acidic.

This example also shows the scale's logic. A solution with pH 3 has ten times the hydronium concentration of a solution with pH 4, and one hundred times the hydronium concentration of a solution with pH 5.

Why The Scale Feels Unintuitive At First

People often read pH values as if they were spaced evenly. They are not. The logarithm compresses large concentration changes into small number steps.

That is why a 2-unit change is a factor of $100$, and a 3-unit change is a factor of $1000$:

$$10^2 = 100,\qquad 10^3 = 1000$$

Once you keep that in mind, pH comparisons become much easier to interpret.

Common Mistakes

Treating pH As A Linear Scale

The difference between pH 2 and pH 3 is not the same kind of difference as between 20 cm and 21 cm. It represents a tenfold change in hydronium concentration.

Assuming Neutral Always Means pH 7

That is the standard classroom value for pure water around $25^\circ \mathrm{C}$. The exact neutral pH changes with temperature.

Mixing Up Acid Strength And pH

A strong acid ionizes more completely than a weak acid under the same conditions, but pH also depends on concentration. A dilute strong acid can have a higher pH than a more concentrated weak acid.

Using pH Equations Outside Their Stated Setting

The simple formulas above are most reliable in introductory aqueous chemistry. In more exact work, chemists use activity rather than simple concentration.

When The pH Scale Is Used

The pH scale is used whenever you want a quick measure of acidity or basicity in water-based systems. Common examples include acid-base titrations, water quality, soil chemistry, food chemistry, and biological fluids.

It is also useful because it connects chemistry ideas that students often learn separately: concentration, logarithms, acids and bases, and equilibrium in water.

Try Your Own Version

Calculate the pH for $[H_3O^+] = 10^{-2}\,\mathrm{M}$ and $[H_3O^+] = 10^{-6}\,\mathrm{M}$. Then compare the two solutions in words, not just numbers. That is the fastest way to make the logarithmic scale feel concrete.