pH is one of the most familiar numbers in science, but it is fundamentally a statement about molarity — specifically, the molar concentration of hydrogen ions. Understanding that link turns pH from a memorised scale into something you can calculate and reason about.
pH is a concentration on a log scale
pH is defined as the negative base-ten logarithm of the hydrogen-ion concentration in mol/L:
The logarithm compresses an enormous range of concentrations into a tidy 0–14 scale. Each whole pH unit is a ten-fold change in hydrogen-ion molarity: pH 3 has ten times the H+ of pH 4 and a hundred times that of pH 5.
pOH and the water relationship
The hydroxide concentration has its own measure, pOH = −log[OH−]. In water at 25 °C the two are tied together because the product of the ion concentrations is fixed:
So if you know one, you know the other. A solution of pOH 2 has pH 12, strongly basic.
Calculating the pH of a strong acid
Strong acids dissociate completely, so the hydrogen-ion concentration equals the acid's molarity. For 0.01 M HCl, [H+] = 0.01 M and pH = −log(0.01) = 2. This direct equality is exactly why an accurate molarity matters: the pH follows immediately from it.
Calculating the pH of a strong base
For a strong base, find pOH from the hydroxide molarity, then subtract from 14. A 0.001 M NaOH solution has [OH−] = 0.001 M, pOH = 3, and therefore pH = 11. For bases that release more than one hydroxide per formula unit, such as Ca(OH)2, double the concentration first — the link to normality.
Weak acids and bases only partly dissociate, so [H⁺] is not equal to the molarity. Their pH needs the acid dissociation constant Ka and an equilibrium calculation, which is a separate topic from the strong-acid shortcuts here.
From pH back to molarity
Reverse the definition to recover the concentration: [H+] = 10−pH. A solution of pH 4.5 has a hydrogen-ion molarity of 10−4.5 = 3.2 × 10−5 M. Being fluent in both directions — concentration to pH and back — is the core skill, and it all rests on molarity.
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