A few water molecules split into H⁺ and OH⁻ ions at any moment. Add an acid and the H⁺ goes up; add a base and it goes down. Because the numbers involved are tiny and vary hugely, chemists count them with powers of ten, which you know from Whole-Number Exponents.
Key idea
pH measures how acidic a solution is: 7 is neutral, lower is acidic (more H⁺), higher is basic (fewer H⁺). Each step of 1 is a tenfold change in H⁺. Buffers soak up or release H⁺ to keep the pH of living things steady.
Why it works
The pH is the power of ten in the hydrogen ion concentration, with the sign dropped: a solution at pH 3 has $[\text{H}^+] = 10^{-3}$ mol/L, and at pH 5 it has $10^{-5}$ mol/L. So the lower pH has more H⁺, and two steps apart means $10^{2} = 100$ times as much.
Worked example: How many times more?
How many times more H⁺ does a solution at pH 4 have than one at pH 8?
- The difference in pH is $8 - 4 = 4$ steps.
- Each step is a factor of 10: $10^{4} = 10{,}000$.
- The lower pH (4) is the one with more H⁺.
Answer: $10{,}000$ times more
Worked example: From pH to concentration
What is the hydrogen ion concentration at pH 6?
- $[\text{H}^+] = 10^{-\text{pH}}$.
- So $[\text{H}^+] = 10^{-6}$ mol/L $= 0.000001$ mol/L.
Answer: $10^{-6}$ mol/L
Human blood stays between about pH 7.35 and 7.45. The main buffer is a pair, carbonic acid and bicarbonate: when acid is added, bicarbonate takes up the extra H⁺; when base is added, carbonic acid gives H⁺ back. Enzymes depend on this, as you will see in Temperature, pH and Enzymes.
Common mistake
Thinking pH 4 is "twice as acidic" as pH 8, or that a lower pH means fewer hydrogen ions. The scale is logarithmic: each whole step is ten times, so pH 4 has $10^{4} = 10{,}000$ times more H⁺ than pH 8. And lower pH means more H⁺. Check: lemon juice (pH 2) is sour because it is full of H⁺.