Svante Arrhenius

Chapter 1 · A Fourth Class

The thesis that nearly ended a career

1859 – 1884 · Vik · Uppsala · Stockholm

Svante August Arrhenius was born near Uppsala in February 1859, the son of an estate steward and later a university surveyor. He taught himself arithmetic at three by watching his father do the accounts, and was a prodigy at school.

He studied at Uppsala, found the physics teaching poor, and moved to Stockholm to work under Erik Edlund at the Academy of Sciences on the conductivity of solutions — while remaining registered at Uppsala, which had to examine him.

His thesis, submitted in 1884, was on the electrical conductivity of electrolytes, and it made a claim his examiners found close to absurd.

The accepted view came from Faraday: a solution of a salt contains intact molecules, and the *current* passing through it tears them apart into ions, which then migrate to the electrodes.

Arrhenius argued that the ions are *already there*. A salt dissolving in water spontaneously comes apart into charged particles, which move about independently of one another, and the current merely directs their motion. That is why a solution begins conducting the *instant* the electrodes are dipped in — with no interval for anything to be torn apart.

He supported it with dilution series showing exactly how conductivity varies with concentration, and argued that at greater dilution a larger proportion of the substance is dissociated.

The objection was serious. Sodium metal reacts violently with water and chlorine is a poisonous gas — and Arrhenius was saying that dissolving common salt fills the water with sodium and chlorine as separate particles. The answer, that a charged sodium ion is a wholly different thing from a sodium atom, requires understanding the electron.

The Uppsala faculty awarded the thesis a *fourth class* — the lowest grade compatible with passing — and a corresponding grade for the defence. It disqualified him from a lectureship.

“I shall call this the hydrogen-ion exponent.”

— Attributed within the tradition Arrhenius's dissociation theory made possible

Why this matters

Arrhenius's claim looked absurd because nobody yet had the electron, and a charged sodium ion is entirely unlike a sodium atom.

You have the thesis and the fourth class. What would you ask him?

Ask Arrhenius

• “Why should the ions be there before the current?”
• “How can salt water contain sodium and not explode?”
• “What did the fourth class do to you?”
• “Why does a solution conduct the instant you dip the electrodes?”
• “Were your examiners being unreasonable?”

Chapter 2 · Ostwald Comes to Sweden

The Ionists, and a subject invented

1884 – 1903 · Uppsala · Riga · Leipzig · Amsterdam

Arrhenius sent the thesis to a number of European scientists. Most did not reply.

Wilhelm Ostwald, at Riga, read it, recognised what it was, and *travelled to Sweden* to meet the author — arriving, by the account, on the day Arrhenius's father died. He offered him a position.

The offer alone changed matters at Uppsala, where the faculty rather hurriedly found Arrhenius a lectureship after all.

Ostwald, Arrhenius and Jacobus van 't Hoff became the core of a group their opponents nicknamed the *Ionists* — and out of them came *physical chemistry* as a discipline: the application of thermodynamics and physical measurement to chemical problems, rather than preparation and analysis.

Van 't Hoff had shown that osmotic pressure in a dilute solution behaves like gas pressure, and that a dissolved substance behaves as though it were a gas occupying the volume of the solution. But *electrolytes* gave osmotic pressures — and freezing-point depressions, and boiling-point elevations — that were too large by a factor of roughly two, or three, depending on the salt.

Arrhenius's dissociation explains it exactly. If sodium chloride comes apart into two particles, it produces twice the effect of an undissociated substance at the same concentration. Calcium chloride gives three particles and three times the effect.

So one hypothesis reconciles conductivity data, freezing-point data, osmotic pressure data and boiling-point data across every electrolyte, quantitatively.

That is what won it. Within a decade dissociation was accepted, and in 1903 Arrhenius received the Nobel Prize in Chemistry — for the thesis Uppsala had nearly failed.

Why this matters

Dissociation was accepted because one hypothesis reconciled conductivity, freezing-point, boiling-point and osmotic data across every electrolyte at once.

You have Ostwald on the doorstep and the Ionists. What is your question?

Ask Arrhenius

• “What did Ostwald see that your examiners did not?”
• “Why is salt water's freezing point depressed twice as much as expected?”
• “What was physical chemistry before you three?”
• “Why were you called the Ionists as an insult?”
• “How did Uppsala behave once Ostwald had called?”

Chapter 3 · What an Acid Is

Hydrogen ions, hydroxide ions, and one number for neutralisation

1887 · Stockholm

From dissociation Arrhenius drew the definitions that every chemistry student still meets first.

An *acid* is a substance that produces hydrogen ions in aqueous solution. A *base* or alkali is one that produces hydroxide ions. And *neutralisation* is those two combining to form water.

Before this, an acid was defined by a list of properties: sour taste, turns litmus red, reacts with metals to give hydrogen, reacts with carbonates to give carbon dioxide. That is a description of behaviour, not an account of what an acid *is*.

Arrhenius's definition says what all acids have in *common*, and it immediately explains why they share those properties: they all put the same particle into solution.

And it explains something that had been a genuine puzzle. When almost any strong acid is neutralised by almost any strong alkali, the heat given out per mole of water formed is *almost exactly the same* — around 57 kilojoules — whatever the acid and whatever the alkali. Hydrochloric with sodium hydroxide, nitric with potassium hydroxide, sulphuric with lithium hydroxide: essentially the same number.

On the old view this is inexplicable. Different acids and different alkalis are different substances, so why should they release identical heat?

On Arrhenius's view it is obvious. All these substances are already fully dissociated. The sodium and chloride ions are spectators and do nothing. The *only* reaction taking place, in every case, is a hydrogen ion combining with a hydroxide ion to form water. Same reaction, same heat.

That is the argument, and it is very hard to answer.

The definition has limits. It only works in water, and it cannot handle ammonia, which is a base and contains no hydroxide. Brønsted and Lowry generalised it in 1923.

Why this matters

The near-identical heat of neutralisation for every strong acid and alkali is inexplicable unless the same single reaction is happening in every case.

You have the definition and the constant heat. What would you ask?

Ask Arrhenius

• “Why is the heat of neutralisation always the same?”
• “What is a spectator ion?”
• “Why is a list of properties not a definition?”
• “How would you handle ammonia?”
• “Does your definition work outside water?”

Chapter 4 · Why Heating Speeds a Reaction

The activation energy, 1889

1889 · Stockholm

In 1889 Arrhenius addressed a different problem: why does raising the temperature speed up a reaction so dramatically?

A rough rule was known — around ten degrees roughly doubles many reaction rates. But heating a gas by ten degrees from room temperature increases the average molecular speed by only about two per cent, and the collision frequency by a similar amount. A two per cent increase in collisions cannot double a rate.

So collisions alone are not the answer. Something else is temperature-sensitive to a far greater degree.

Arrhenius's proposal: not every collision produces a reaction. Only the collisions in which the colliding particles have at least a certain minimum energy — the *activation energy* — result in a change. The reactants must first be raised into an intermediate high-energy state before they can become products.

And the *proportion* of molecules possessing at least that energy rises very steeply with temperature, because the distribution of molecular energies has a long tail. Heating by ten degrees barely changes the average, but it substantially increases the number in the tail — which is where the reacting molecules are.

He expressed this in the equation that carries his name, in which the rate constant depends exponentially on the negative of the activation energy divided by temperature.

The consequences are wide. It explains why a *catalyst* works: it does not push the molecules harder, it provides an alternative route with a *lower* activation energy, so a far larger fraction of collisions succeeds. It explains why food keeps longer in a refrigerator. And it is the basis of every calculation of reaction rate in chemical engineering.

He took the idea partly from van 't Hoff and gave the physical interpretation.

Why this matters

Heating barely changes the average molecular energy, so the reason reactions speed up is the steep rise in the number of molecules in the high-energy tail.

You have the activation energy and the tail of the distribution. What is your question?

Ask Arrhenius

• “Why can't more collisions explain the speed-up?”
• “What is an activation energy?”
• “How does a catalyst actually work, on your account?”
• “Why does a refrigerator keep food longer?”
• “What is the high-energy tail, and why does it matter?”

Chapter 5 · Carbonic Acid and the Temperature of the Ground

1896, and a calculation done by hand

1896 – 1927 · Stockholm

In 1896 Arrhenius published *On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground*.

The question that started it was the ice ages: why had the Earth been much colder in the past? A colleague, Arvid Högbom, had been working on the carbon cycle and on the quantities of carbon dioxide released by volcanoes and by industry.

Arrhenius took Samuel Langley's measurements of infrared radiation from the Moon, worked out how much is absorbed by water vapour and carbon dioxide in the atmosphere, and calculated what would happen to surface temperature if the concentration of carbon dioxide changed.

The calculation was done by hand. He worked through it for something like a year, by his own account making tens of thousands of individual computations, dividing the Earth into latitude zones and seasons.

His conclusion: halving atmospheric carbon dioxide would cool the Earth by around four to five degrees, and doubling it would warm it by around five to six degrees.

Modern estimates of climate sensitivity put the warming from doubling at roughly two and a half to four degrees. His figure is high, and it was reached in 1896 with hand arithmetic and incomplete data. It is a remarkable piece of work.

He also estimated, with Högbom, how long industrial coal burning would take to double the concentration, and got something like three thousand years — because he had 1890s emission rates and no way to anticipate their growth. Emissions have risen by orders of magnitude since.

And he thought it would be *good*. Writing from Sweden, he expected a warmer climate to improve agriculture and prevent another ice age, and said so.

He also promoted eugenics, serving on the board of the Swedish State Institute for Racial Biology — which is part of the record and not a footnote.

He died at Stockholm in October 1927, aged sixty-eight.

Why this matters

Arrhenius calculated the warming from doubled carbon dioxide by hand in 1896 and got a figure in the right range, while entirely misjudging how fast emissions would grow.

You have the calculation and the conclusion he drew from it. What would you ask?

Ask Arrhenius

• “How do you calculate the temperature of a planet by hand?”
• “Why did you think warming would be a good thing?”
• “Why was your estimate of three thousand years so far out?”
• “What were you actually trying to explain?”
• “How do you answer the charge about your eugenics work?”

What Arrhenius changed

Electrolytic dissociation is now taught as though it were obvious, which is the fate of a good idea. Arrhenius's definition of an acid — a substance producing hydrogen ions in water — is the first one a student meets, his equation relating rate to temperature underlies all reaction kinetics, and his 1896 calculation of carbon dioxide's warming effect reads today as the beginning of climate science.

A debate that continues

Arrhenius expected a warmer world to be beneficial and badly underestimated the growth of emissions; and his involvement with the Swedish State Institute for Racial Biology, on whose board he sat, is a serious part of his record.

Keep exploring — ask Arrhenius

• “What would you say to a chemist using your acid definition today?”
• “How do you tell a good idea from an absurd one?”
• “What would you calculate again with a computer?”

Related lives

• Søren Sørensen — Who Gave Acidity A Number
• Carl Remigius Fresenius — Who Put the Tests in Order
• Dmitri Mendeleev — Author of the Periodic Table
• Rachel Carson — Author of Silent Spring

Related themes

Acids, bases and ions · Rates of reaction · The greenhouse effect