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You learn pH = −log[H⁺] as a formula. Its inventor, Søren Sørensen, had a practical reason for it: he was measuring how fast enzymes broke down proteins and found that tiny amounts of acid mattered enormously. This post covers his life, what his 1909 paper actually said, worked numbers taken from it, common mistakes, and what you can learn from how he worked.
Who was Søren Sørensen?
According to the Dansk Biografisk Leksikon, S. P. L. Sørensen was born on 9 January 1868 at Havrebjerg near Slagelse, in a farming family, and died on 12 February 1939. A village schoolteacher noticed his ability. He began studying medicine in Copenhagen but switched to chemistry, and won the university's gold medal twice, first in 1889 for a prize essay on the history of chemical theory.
In 1901 he became head of the chemistry department of the Carlsberg Laboratory, which was funded by the brewery. The lexicon notes that he chose proteins as his new field because barley proteins matter in brewing. His study of how enzymes break proteins into amino acids led him straight to the question of acidity.
What did his 1909 paper say?
The paper, "Enzymstudien II" (Enzyme studies II), appeared in the Biochemische Zeitschrift, volume 21, received on 29 May 1909. Its subtitle, in our translation, is "On the measurement and the significance of the hydrogen ion concentration in enzymatic processes".
He wrote each hydrogen ion concentration as a negative power of 10. A 0.01 normal acid has 10⁻². Then he said, in our translation, that he uses "the name 'hydrogen ion exponent' and the symbol pH for the numerical value of the exponent of this power." His three examples gave pH 2, 12.14 and 7.07.
Why use a logarithm at all?
Sørensen gave two reasons in the same paper.
First, the absolute amounts are tiny. For sugar-splitting by the enzyme invertin at its best acidity, he calculated that all the hydrogen ions in 100 cc of solution were fewer than in one drop of 0.1 normal hydrochloric acid. One drop of alkali could turn the solution from weakly acidic to weakly alkaline and stop the enzyme.
Second, enzyme speed followed relative changes. In our translation: "a doubling or halving of the ion concentration causes a decrease or increase of the ion exponent by about 0.3." He concluded that it is convenient to calculate "not with the absolute values of the hydrogen ion concentrations, but with their logarithms".
Worked example: checking Sørensen's numbers
0.01 M hydrochloric acid. [H⁺] = 10⁻² mol/L, so pH = 2. Same as his first example.
0.01 M sodium hydroxide. At 25 °C, using Kw = 10⁻¹⁴ as in NCERT's Equilibrium chapter, [OH⁻] = 10⁻², [H⁺] = 10⁻¹², pH = 12. Sørensen got 12.14 and 7.07 for neutral water because the water ion product he used was 10⁻¹⁴·¹⁴ (twice 7.07). His measurements were not made at 25 °C, so neutral was not exactly 7.
Doubling. His series runs 4.6, 4.9, 5.2: each step of 0.3 halves [H⁺].
The one-drop test (sample numbers). Take 100 mL of a solution at pH 4.6. [H⁺] = 10⁻⁴·⁶ = 2.5 × 10⁻⁵ mol/L, so the beaker holds 2.5 × 10⁻⁶ mol of H⁺. One drop of about 0.05 mL of 0.1 M acid holds 0.1 × 0.05 × 10⁻³ = 5 × 10⁻⁶ mol, twice as much. That is why one drop of acid or alkali can swamp an unbuffered solution.
Sørensen's answer to step 4 was buffers. The lexicon notes that his paper gave recipes for solutions that hold their pH steady, and chemicals were later sold labelled "after Sørensen". Our post on pH and buffers shows how they work.
What mistakes do students make with pH?
Treating pH as linear. pH 3 is ten times more acidic than pH 4, not "a bit" more.
Assuming neutral is always 7. Neutral is pH 7 only at 25 °C, where Kw = 10⁻¹⁴. Sørensen's own 7.07 shows this.
Dropping the minus sign. pH = −log[H⁺]. A positive pH comes from a negative logarithm.
Forgetting dilution of strong bases. Find [OH⁻] first, then pOH, then pH = 14 − pOH at 25 °C.
If logarithms are the stumbling block rather than the chemistry, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing.
What else did he do?
The lexicon records that he measured the molecular mass of egg albumin as about 34,000, joined the Royal Danish Academy of Sciences in 1906 and became its president in 1938. He also introduced the formol titration method for amino acids in 1907.
What can you take from how he worked?
Measure the thing that matters. He saw that "acidity" was too vague and replaced it with a number.
Choose the scale that fits the data. A logarithm made small, relative changes easy to compare.
Solve the practical problem too. Having shown that pH must be controlled, he gave recipes to control it.
Next step: work out the pH of 0.001 M HCl and of the same solution diluted tenfold, and check that each step adds exactly 1.
