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Today it seems obvious that common salt dissolved in water exists as Na⁺ and Cl⁻ ions. In 1884, when a 25-year-old Swedish student put a version of that idea in his doctoral thesis, many chemists found it hard to believe. Svante Arrhenius went on to win the Nobel Prize for it. This post covers what he proposed, why it met resistance, how to use his idea to find a degree of dissociation, where his name turns up again in chemical kinetics, and what a student can learn from him.
Who was Svante Arrhenius?
His Nobel Prize facts page gives his birth as 19 February 1859 at Vik in Sweden and his death as 2 October 1927 in Stockholm. His Nobel biography says he entered the University of Uppsala in 1876 to study mathematics, chemistry and physics, and in 1881 moved to Stockholm to work under Professor E. Edlund at the Academy of Sciences. There he measured how well solutions conduct electricity, which led to his 1884 thesis on the "galvanic conductivity of electrolytes".
He won the 1903 Nobel Prize in Chemistry "in recognition of the extraordinary services he has rendered to the advancement of chemistry by his electrolytic theory of dissociation".
What did his thesis claim?
The Nobel biography summarises his conclusion: electrolytes dissolved in water become, to varying degrees, split into electrically opposite positive and negative ions, and the degree of splitting depends on the substance and its concentration, being greater the more dilute the solution.
The Science History Institute biography explains why this was a bold claim. Michael Faraday and others held that ions form only when an electric current starts to flow. Arrhenius said they are there already. Many chemists also found it hard to accept because a salt solution shows none of the properties of sodium metal or chlorine gas.
The thesis was received coolly at Uppsala. The Nobel biography says its value "was not well understood by the science faculty". Arrhenius had sent copies to chemists abroad, and Wilhelm Ostwald travelled to Uppsala to meet him. Between 1886 and 1888 he worked with Ostwald, Friedrich Kohlrausch, Ludwig Boltzmann and Jacobus van 't Hoff, and showed how dissociation explains the extra lowering of freezing point and osmotic pressure in salt solutions.
That definition and its limits are in NCERT's equilibrium unit.
Worked example: how much of a weak acid splits into ions?
Arrhenius's idea gives a way to measure dissociation from conductivity. In NCERT Class 12 Electrochemistry, the degree of dissociation of a weak electrolyte is α = Λm / Λm°, where Λm is the molar conductivity at concentration c and Λm° the limiting value at infinite dilution. NCERT works out Λm° for acetic acid as 390.5 S cm² mol⁻¹ using Kohlrausch's law.
Suppose 0.010 mol L⁻¹ acetic acid has a measured Λm of 16.3 S cm² mol⁻¹.
α = 16.3 / 390.5 = 0.0417. Only about 4% of the molecules are ionised.
For HA ⇌ H⁺ + A⁻, Ka = cα² / (1 − α).
Ka = 0.010 × (0.0417)² / (1 − 0.0417) = 0.010 × 0.001739 / 0.9583 ≈ 1.8 × 10⁻⁵.
That matches the familiar value for acetic acid. Dilute the solution and α rises, just as Arrhenius said.
Common mistakes:
Using α = Λm / Λm° for a strong electrolyte. Strong electrolytes are almost fully dissociated; the change in their Λm with dilution has a different cause.
Dropping the (1 − α). Leaving it out is only an approximation, fine when α is very small.
Unit slips. When you calculate Λm from conductivity κ, use Λm = κ × 1000 / c with κ in S cm⁻¹ and c in mol L⁻¹.
Where else does his name appear?
In chemical kinetics. NCERT Class 12 gives the Arrhenius equation, k = Ae^(−Ea/RT), and notes that it was first proposed by van 't Hoff, while Arrhenius "provided its physical justification and interpretation". His 1889 paper on the rate at which acids invert cane sugar belongs to this part of his work. For a full treatment, see our guide to the Arrhenius equation and activation energy.
He also worked well beyond chemistry. In 1896 he published On the influence of carbonic acid in the air upon the temperature of the ground, an early calculation of how carbon dioxide affects Earth's temperature. The Science History Institute notes that he thought warming would benefit Sweden's chilly climate.
What can a student take from how Arrhenius worked?
Trust careful measurements over first reactions. His conductivity data pointed to ions before others were ready to accept them.
Send your work to people who can judge it. Copies to Ostwald and van 't Hoff turned a poorly received thesis into a new field, physical chemistry.
Look for one idea that explains several facts. Dissociation explained conductivity, freezing points and osmotic pressure together.
For more on conductivity, read our guide to conductance and Kohlrausch's law. If a step in a calculation like the one above keeps tripping you up, the Fermi Problem Library has a step-by-step solver that explains the reasoning, not just the answer.
Try this now: repeat the worked example for 0.0010 mol L⁻¹ acetic acid with Λm = 49.5 S cm² mol⁻¹, and check that α has gone up.
