Archive for the ‘physics’ Category

Anthony Carlisle (left) and William Nicholson, London, May 1800

Anthony Carlisle (left) and William Nicholson, London, May 1800

The rise of physical chemistry in the 19th century has at its root two closely connected events which took place in the final year of the 18th century. In 1800, Alessandro Volta in Lombardy invented what we now call the Voltaic pile, which Messrs. Carlisle and Nicholson in England promptly employed to discover electrolysis.

Carlisle and Nicholson’s discovery that electricity can decompose water into hydrogen and oxygen caused as big a stir as any scientific discovery ever made. It demonstrated the existence of a relationship between electricity and the chemical elements, to which Michael Faraday would give quantitative expression in his two laws of electrolysis in 1834. Faraday also introduced the term ‘ion’, a little word for a big idea that Arrhenius, Ostwald and van ‘t Hoff would later use to create the foundations of modern physical chemistry in the 1880s.

About this post

The story of Carlisle and Nicholson’s discovery properly begins with a letter that Volta wrote on March 20th, 1800 to the President of the Royal Society in London, Sir Joseph Banks. The leaking of that letter (which contained confidential details of the construction of the Voltaic pile) to among others Anthony Carlisle, forms the narrative of my previous post “The curious case of Volta’s leaked letter”.

This post is concerned with the construction details themselves, which have their own story to tell, and the experimental activities of Messrs. Carlisle and Nicholson after they had seen the letter, which were reported in July 1800 by Nicholson in The Journal of Natural Philosophy, Chemistry & the Arts – a publication that Nicholson himself owned.

The Voltaic pile

“The apparatus to which I allude, and which will no doubt astonish you, is only the assemblage of a number of good conductors of different kinds arranged in a certain manner.”
Alessandro Volta’s letter to Joseph Banks, introducing the Voltaic pile

Volta’s arrangement comprised a pair of different metals in contact (Z = Zinc, A = Silver), followed by a piece of cloth or other material soaked in a conducting liquid; this ‘module’ could be repeated an arbitrary number of times to build a pile in the manner illustrated below.

cn02

The Voltaic Pile: Volta’s own illustration enclosed with the letter to Banks

Volta believed the electrical current was excited by the mere contact of two different metals, and that the liquid-soaked material simply conducted the electricity from one metal pair to the next. This explains why Volta’s illustration shows the metals always in pairs – note the silver disc below the zinc at the bottom of the pile and a zinc disc above the silver at the top.

It was later shown that these terminal discs are unnecessary: the actual electromotive unit is zinc-electrolyte-silver. Volta’s arrangement can therefore be seen as a happy accident, in that his mistaken belief regarding the generation of electromotive force led him to the correct arrangement of repeated electrochemical cells, in which the terminal discs act merely as connectors for the external circuit wires.

Volta’s pile thus contained one less generating unit than he thought; it also caused the association of the two metals with the positive and negative poles of the battery to be reversed.

– – – –

Enter Mr. Carlisle

cn03

London’s Soho Square in the early 19th century. Animals were often driven to market through the square.

The president of the Royal Society, Sir Joseph Banks, lived in a house at No.32 Soho Square. Here he entertained all the leading members of the scientific establishment, and it was here in April 1800 that he yielded to temptation and disclosed the contents of Signor Volta’s confidential letter to certain chosen acquaintances. Among them was another resident of Soho Square, the fashionable surgeon Anthony Carlisle, who had just moved in at No.12.

Volta’s announcement of his invention made an instant impression on Carlisle, who immediately arranged for his friend the chemist William Nicholson to look over the letter with him, after which Carlisle set about constructing the apparatus according to the instructions in Volta’s letter.

Nicholson records in his paper that by 30th April 1800, Carlisle had completed the construction of a pile “consisting of 17 half crowns, with a like number of pieces of zinc, and of pasteboard, soaked in salt water”. Using coinage for the silver discs was smart thinking by Carlisle – with a diameter of 1.3 inches (3.3 cm), the half crown was an ideal size for the purpose, and was made of solid silver.

cn04

Silver half crown, diameter 1.3 inches

From Nicholson’s account, it seems likely that Carlisle obtained a pound (approx. ½ kilo) of zinc from a metal dealer called John Tappenden who traded from premises just opposite the church of Saint Vedast Foster Lane, off Cheapside in the City of London. A pound of zinc was enough to make 20 discs of the diameter of a half crown.

Having constructed the pile exactly according to Volta’s illustration above, Carlisle and Nicholson were ready to begin their experiments. But before describing their work, it is pertinent to draw attention to the way in which they approached their program of research, which was quite unlike that of Volta.

– – – –

Differences in approach

Alessandro Volta’s letter to Joseph Banks, apart from briefly detailing the construction of the pile, comprises a lengthy account of electric shocks administered to various parts of the human anatomy and the nature of the resulting sensations.

Volta does first prove with a charging condenser that the pile generates electricity, but having ascertained this fact, he makes no further observations on the pile, other than asserting that the device has “an inexhaustible charge, a perpetual action” and later commenting: “This endless circulation of the electric fluid (this perpetual motion) may appear paradoxical and even inexplicable, but it is no less true and real;”

cn05

One of Volta’s arrangements, using electrodes dipped in bowls of water for delivering electric shocks to the hands. If Volta had just put both electrodes in one bowl, he would have discovered electrolysis.

Volta appears not to have observed that the zinc discs quickly oxidise during operation; perhaps it was because he enclosed the pile in wax to prevent it from drying out. But nonetheless it seems strange that Volta did not discover during the course of his many experiments that the zinc discs do not have an unlimited lifetime.

William Nicholson also found it strange, commenting in his paper, “I cannot here look back without some surprise and observe that … the rapid oxidation of the zinc should constitute no part of his [Volta’s] numerous observations.”

Reading Volta’s communication to Banks, one is struck by the brevity of the text pertaining to his fabulous invention, and contrarily, the abundant descriptions of the shocks he administered with it. Volta is demonstrably more occupied with how humans experience the shocks that the pile delivers, than with the pile itself.

With Carlisle and Nicholson, the situation is very much the reverse. Having given themselves an obligatory shock with their newly-built machine, the attention immediately shifts to the pile itself. Their experiments and attendant reasoning show an approach that is more analytical in character.

– – – –

The path to discovery

On May 1st, 1800, Carlisle and Nicholson set up their pile – most likely in Carlisle’s house at 12 Soho Square – and began by forming a circuit with a wire and passing a current through it. To assist contact with the wire, a drop of river water was placed on the uppermost disc. As soon as this was done, Nicholson records

“Mr. Carlisle observed a disengagement of gas round the touching wire. This gas, though very minute in quantity, evidently seemed to me to have the smell afforded by hydrogen”

It is amazing that Nicholson was able to identify hydrogen from such a minute sample. But even more amazing was the thought that occurred to him next

“This [release of hydrogen gas], with some other facts, led me to propose to break the circuit by the substitution of a tube of water between two wires.”

Nicholson does not say what those other facts are, but he does record that on the first appearance of hydrogen gas, both he and Carlisle suspected that the gas stemmed from the decomposition of water by the electric current. Following that wonderfully intuitive piece of reasoning, Nicholson’s suggestion can be seen as a natural next step in their investigation.

cn06

William Nicholson (1753-1815)

On 2nd May, Carlisle and Nicholson began their experiment using brass wires in a tube filled with river water. A fine stream of bubbles, identifiable as hydrogen, immediately arose from the wire attached to the zinc disc, while the wire attached to the silver disc became tarnished and blackened by oxidation.

This was an unexpected result. Why was the oxygen, presumably formed at the same place as the hydrogen, not evolved at the same wire? Why and how does the oxygen apparently burrow through the water to the other wire where it produces oxidation of the metal? This finding, which according to Nicholson “seems to point at some general law of the agency of electricity in chemical operations” was to occupy physical chemists for the next 100 years…

Meanwhile, Carlisle and Nicholson responded to their new experimental finding with another wonderfully intuitive piece of reasoning. What would be the effect, they asked, of using electrodes made from a metal that resisted oxidation, such as platinum?

Immediately they set about finding the answer. With electrodes fashioned from platinum wire they observed a plentiful stream of bubbles from the wire attached to the zinc disc and a less plentiful stream from the wire attached to the silver disc. No tarnishing of the latter wire was seen. Nicholson wrote

“It was natural to conjecture, that the larger stream was hydrogen, and the smaller oxygen.”

The conjecture was correct. On a table top in Soho Square, Nicholson and Carlisle had successfully decomposed water into its constituent gases by the use of the Voltaic pile, and had thereby discovered electrolysis – a technique which was to prove of immeasurable importance to industry.

vol04

Anthony Carlisle (1768-1840)

– – – –

Quantitative analysis

Carlisle and Nicholson realised that the decomposition of water using platinum wires “offered a means of obtaining the gases separate from each other”. This not only provided a new way of producing these gases, but also opened up a new avenue of analysis. By measuring the relative volumes of hydrogen and oxygen evolved from the wires, they could compare their result with known data for water. [It should be noted that Carlisle and Nicholson did not have the benefit of Avogadro’s law, which was not formulated until 1811].

Carlisle and Nicholson subjected water to electrolysis for 13 hours, after which they determined the weight of water displaced by each gas in the respective tubes. The weights were in the proportion 142:72 in respect of hydrogen and oxygen; this is very close to the whole number ratio of 2:1 which was known to be the proportions in which these gases combine to produce water. Here then was quantitative evidence that the hydrogen and oxygen observed in Carlisle and Nicholson’s electrolytic cell originated from the decomposition of water.

– – – –

The experimental observations – explained

It was that drop of water placed on the uppermost disc to assist contact with the metal wire that opened the path to discovery. The fact that gas was formed “round the touching wire” indicates that the contact was intermittent: when the wire was in contact with the water drop but not the uppermost disc, a miniature electrolytic cell was formed and hydrogen gas was evolved.

Illustrating this graphically requires some qualifying explanation, since as already mentioned the terminal discs of the Voltaic pile assembled according to Volta’s instructions were unnecessary, and acted merely as conductors. Electrochemically, the uppermost disc of Carlisle and Nicholson’s Voltaic pile was a silver cathode, connected to the water drop via a zinc disc; the lowest disc in the pile was a zinc anode, which via an interposed silver disc was connected to the water drop via an unspecified metal wire. The electrochemical processes can be illustrated as follows

cn07

Carlisle and Nicholson’s first experiment, May 1st, 1800

The drop of water shown in blue acted as an electrolytic cell supplied by a zinc anode (the uppermost disc) and an unspecified metal cathode (the wire). When current was passed through this cell at moments when the wire lost contact with the zinc disc, reduction of hydrogen ions produced bubbles of hydrogen at the cathode, i.e. around the wire, as Carlisle observed. At the anode, the oxygen formed would have immediately oxidised the zinc with no visible evolution of gas.

The hydrogen released at the silver discs in the Voltaic pile would not have been visible since it was evolved at the inner surface in contact with the moistened pasteboard.

– – – –

And so to the experimental set-up with which Carlisle and Nicholson successfully decomposed water into its constituent gases by the use of the Voltaic pile, and thereby discovered electrolysis. Electrochemically, the uppermost disc in the pile was a silver cathode, which via an interposed zinc disc was connected to the water in the tube via a platinum electrode; the lowest disc in the pile was a zinc anode, which via an interposed silver disc was connected to the water in the tube via a platinum electrode. The electrochemical processes can be illustrated as follows

cn08

Carlisle and Nicholson’s electrolysis of water, May 1800

The tube of water shown in blue acted as an electrolytic cell supplied by a platinum anode and cathode. When current was passed through this cell, reduction of hydrogen ions produced bubbles of hydrogen at the cathode, while the oxidation of water produced hydrogen ions and bubbles of oxygen at the anode.

As before, the hydrogen released at the silver discs in the Voltaic pile would not have been visible since it was evolved at the inner surface in contact with the moistened pasteboard.

– – – –

Mouse-over links to original papers mentioned in this post

Volta’s letter to Banks (begins on page 289)

Nicholson’s paper (begins on page 179)

– – – –

ventus001

У меня имеется цифровая метеостанция с беспроводным датчиком, расположенным вне помещения. На фотографии: в верхнем правом квадранте отображается температура и относительная влажность вне помещения (6,2°C/94%) и в помещении (21,6°C/55%).

Я считаю, что эта разница (в помещении и вне) очень важна для определенных целей. Давайте посмотрим на цифры. Когда я смотрю на показания, то всегда задаюсь вопросом о том, различается ли количество водяного пара в воздухе внутри и вне помещения? Простой вопрос, а ответ потребует некоторых рассуждений. За основание возьмем уравнение идеального газа; для вычисления абсолютной влажности по температуре и относительной влажности необходим еще специальный алгоритм расчета давления насыщенного пара как функции от температуры. А это не очень простая вещь.

Формула для вычисления абсолютной влажности

В формуле ниже, температура (Т) измерена в градусах Цельсия, относительная влажность (rh) — в %, а е — это основание натурального логарифма 2,71828 [возведенное в степень, указанную в скобках]:

Абсолютная влажность (г/м3) =
6,112 x e^[(17,67 x T)/(T+243,5)] x rh x 18,02
(273,15+T) x 100 x 0,08314

что упрощается до

Абсолютная влажность (г/м3) =
6,112 x e^[(17,67 x T)/(T+243,5)] x rh x 2,1674
(273,15+T)

Точность этой формулы в пределах 0,1% на диапазоне температур от –30°C до +35°C

– – – –

формат gif

ah3a

формат jpg

ah1a

– – – –

Дополнительные примечания для студентов

Стратегия вычисления абсолютной влажности, определяемой как плотность водяного пара (г/м3) по температуре (Т) и относительной влажности (rh):

1. Водяной пар — это газ, поведение которого при обычной температуре атмосферы приближено к поведению идеального газа.

2. Применимо уравнение идеального газа PV = nRT. Газовая постоянная R и переменные T и V в этом случае известны (Т измерена, V = 1 m3). Для вычисления n необходимо рассчитать Р.

3. Чтобы получить значение Р можно применить следующий вариант формулы [см. eq.10] Магнуса-Тетенса, которая дает давление насыщенного пара Psat (гектопаскали) как функцию от температуры Т (в градусах Цельсия):

Psat = 6,112 x e^[(17,67 x T)/(T+243,5)]

4. Psat — это давление при относительной влажности 100%. Для вычисления давления P при любом значении относительной влажности, выраженном в %, мы умножаем выражение для Psat на коэффициент (rh/100):

P = 6,112 x e^[(17,67 x T)/(T+243,5)] x (rh/100)

5. Теперь мы знаем P, V, R, T и можем вычислить n, а это и есть количество водяного пара в молях. Значение затем умножается на 18,02 — это молекулярный вес воды. Ответ получается в граммах.

6. Обобщение:
Формула абсолютной влажности получена из уравнения идеального газа. Она выражает n всего через две переменные: температуру (Т) и относительную влажность (rh). Давление вычисляется как функция от обеих этих переменных; объем указан (1 m3), а газовая постоянная R известна.

– – – –

ОБНОВЛЕНИЯ

– – – –

Комментарий автора: Производителям метеостанции следует рассмотреть возможность использования дисплея с переключением RH/AH

ventus2

Январь 2017: Понятие относительной влажности (RH) хорошо знакомо тем, кто имеет образование в науках об атмосфере, а вот обычный человек у которого тоже может быть термометр-гигрометр с секциями вне/внутри помещений при работе с RH легко может ошибиться.

Рассмотрим данные на рисунке. Я не удивлюсь, если кто-то решит, что вне помещения в воздухе пара больше, поскольку внешняя RH (58%) в два с половиной раза больше, чем внутренняя RH (21%).

Данные коварны. Подставьте числа в мою формулу, которая вычисляет абсолютную влажность (AH) как плотность водяного пара г/м3. Вы увидите, что AH внутри помещения в два раза выше, чем AH снаружи. Можно ли было предсказать такой результат глядя только на значения T и RH? И я бы не смог.

Поэтому я и думаю, что добавление отображения AH могло бы быть отличной идеей для производителей этих приборов. Люди хорошо понимают концепцию «масса на объем» гораздо лучше, чем проценты от максимального значения переменной, зависимой от температуры.

Для производителя вывести AH на экран труда не составит. Моя формула вычисляет AH прямо от Т и RH, поэтому можно просто переключаться между отображением RH и AH. Возможно, что посетители блога, работающие в проектах с микропроцессорами, могли бы собрать прототип?

– – – –

Игорь пользуется моей формулой, чтобы поддерживать ячейку погреба сухой.

igor01

Октябрь 2016: Я впечатлился системой управления влажностью основания здания, разработанной Игорем, и даже опубликовал отчет на форуме Amperka.ru.

Внутри короткой трубки установлен вентилятор с круговым уплотнением, распечатанным на 3D-принтере. Вентилятор замещает воздух, находящийся в основании, на воздух снаружи. Он включается, если абсолютная влажность в ячейке выше, чем на улице на 0,5 г/м3. Предполагается, что температура снаружи ниже. Это как раз и гарантирует, что вода в ячейке превращается в пар и вытягивается, а обратный процесс не может произойти.

igor02

Полное описание с набором отличных фотографий → здесь

– – – –

Формула позволяет измерять AH по данным от высокоточного датчика RH и T

sht75

Датчик SHT75 RH и T от SENSIRION

Апрель 2016: Проф. Антониетта Франи (Prof. Antonietta Frani) на основе моей формулы создала миниатюрный прибор для измерения абсолютной влажности. Миниатюрный микроконтроллер Arduino Uno оборудован датчиком SHT75 RH и T и подключается к компьютеру по кабелю USB. Системный интегратор Роберто Валголио (Roberto Valgolio) разработал интерфейс для передачи данных в листы Excel и отображения графиков.

– – – –

Формула позволила создать калькулятор RH←→AH

reckoner

Март 2016: Немецкий веб-сайт rechneronline.de использует мою формулу для своего онлайн-калькулятора RH/AH

– – – –

Формулу процитировали в академической исследовательской публикации

ahcitat

Январь 2016: Исследовательская публикация в Landscape Ecology (октябрь 2015) посвящена микроклиматическим образцам в городской среде США. Там для вычисления абсолютной влажности по температуре и относительной влажности использована моя формула.

– – – –

Формула нашла применение и в блоках управления влажностью

Август 2015: ПО с открытым исходным кодом (проект Arduino) также использует в микроконтроллере управления влажностью основания здания мою формулу для расчета абсолютной влажности:

arduino

«Вся идея состоит в том чтобы измерить температуру и относительную влажность в подвале и на улице, на основании температуры и относительной влажности рассчитать абсолютную влажность и принять решение о включении вытяжного вентилятора в подвале. Теория для расчета изложена здесь – carnotcycle.wordpress.com/2012/08/04/how-to-convert-relative-humidity-to-absolute-humidity/.»

Дополнительные фотографии по ссылке http://arduino.ru/forum/proekty/kontrol-vlazhnosti-podvala-arduino-pro-mini

– – – –

Процедура вычисления AH применена в калибровке спутника погоды Американского Национального Космического Агентства (NASA)

Июнь 2015: Моя общая процедура расчета AH по RH и T применена для абсолютной калибровки Глобальной Спутниковой Системы Навигации Циклона (CYGNSS), причем именно в отношении данных RH, предоставленных Системой Непрерывного Анализа и Прогноза Климата (CFSR). Единственное изменение в моей формуле Psat состоит в том, что используется выражение Августа-Роше-Мангуса, а не Болтона.

Система CYGNSS имеет сеть из восьми спутников. Она предназначена для улучшенного прогноза силы ураганов. Запущена 15 декабря 2016 г.

Ссылка http://ddchen.net/publications (Технический отчет “An Antenna Temperature Model for CYGNSS”, июнь 2015)

– – – –

vol05

Sir Joseph Banks, President of the Royal Society in London, sat in the splendour of his office in Somerset House. It was an April morning in the year 1800. The clatter of horse-drawn carriages in the Strand rose to his window, but he did not notice; his attention was elsewhere. Staring into space, he clutched a letter that had been delivered to him that very morning. Dated March 20th and written in French, it had been sent from Como in Lombardy by an Italian professor of experimental physics named Alessandro Volta.

Professor Volta’s letter was clearly attended by some haste, since he had dispatched the first four pages in advance of the remainder, which was to follow. The subject matter was experiments on electricity, and the first pages of Volta’s letter to Banks described the invention of an apparatus “which will no doubt astonish you”.

vol02

Alessandro Volta (1745-1827) and his amazing invention

On that April morning in London, Banks read the letter and was duly astonished. Volta’s apparatus, consisting of a series of discs of two different metals in contact separated by brine-soaked pasteboard, was capable of generating a continuous current of electricity. This was a world apart from the static electricity of the celebrated Leyden jar and indeed a most astonishing discovery; no wonder Volta was so anxious to communicate it without delay to Banks and thereby to the Royal Society – of which Volta was also a fellow.

Still clutching the letter, Joseph Banks regained his composure and collected his thoughts. He must of course arrange for the letter to be read to the Society, after which it would duly appear in print in the Society’s Philosophical Transactions.

In the meantime, Banks was naturally obliged to keep Volta’s discovery confidential. But then again, with a such an astonishing discovery as this, it was sorely tempting to show Signor Volta’s letter – in the strictest confidence of course – to certain individuals in his large circle of scientific acquaintances, who would surely be fascinated by its contents. What could be the harm in that?

– – – –

Yielding to temptation

The state of mind into which Sir Joseph Banks was propelled by Professor Volta’s letter was pertinently observed (albeit almost a century later) by Oscar Wilde in his play Lady Windermere’s Fan, in which Lord Darlington famously quips “I can resist everything but temptation.”

vol03

32 Soho Square (right), the London home of Sir Joseph Banks

The London home of Joseph Banks, in Soho Square, was the centre of bustling scientific activity and attracted all the leading members of the scientific establishment. Within a month of receiving Volta’s letter, Banks had yielded to temptation and shown it to a number of acquaintances.

Among them was Anthony Carlisle, a fashionable London surgeon who was shortly to display remarkable abilities in the realm of physical chemistry. Having perused the letter, Carlisle immediately arranged for his friend the chemist William Nicholson to look over the pages with him, after which Carlisle set about constructing the apparatus according to Volta’s instructions – the fabled instrument we now call the Voltaic Pile.

vol04

Sir Anthony Carlisle (1768-1840), painted by Henry Bone in 1827

So within a month of Volta’s hastened communication to Banks, the details of the construction of the Voltaic Pile had been leaked to, among others, Carlisle and Nicholson, enabling the latter to begin experiments with Volta’s apparatus that would lead to their privileged discovery of electrolysis, before Volta’s letter had even been read to – let alone published by – the Royal Society.

– – – –

The chronology of the case

1800

March 20th
Volta sends a letter (in French) from Como, Lombardy, to Sir Joseph Banks at the Royal Society in London, announcing his invention of the Voltaic pile.

April
Banks leaks the contents of Volta’s letter to several acquaintances, including Anthony Carlisle, who arranges for William Nicholson to view the letter.

May
Carlisle and Nicholson construct a Voltaic Pile according to Volta’s instructions. With this apparatus they discover the electrolysis of water into hydrogen and oxygen.

June 26th
Volta’s letter is read to the Royal Society.

July
William Nicholson publishes a paper in The Journal of Natural Philosophy, Chemistry & the Arts, announcing the discovery of electrolysis by Anthony Carlisle and himself, using the Voltaic Pile.

September
Volta’s letter announcing his invention of the Voltaic pile is published in French in the Philosophical Transactions of the Royal Society, and in English in The Philosophical Magazine.

– – – –

Mouse-over links to original papers mentioned in this post

Volta’s letter to Banks (begins on page 289)

Nicholson’s paper (begins on page 179)

– – – –

lc01

8 octobre 1850 – 17 septembre 1936

History

Le Châtelier’s principle is unusual in that it was conceived as a generalization of a principle first stated by someone else.

In 1884, the Dutch theoretician JH van ‘t Hoff published a work entitled Etudes de Dynamique Chimique [Studies in Chemical Dynamics]. In it, he stated a principle drawn from observations of different forms of equilibrium:

“Lowering the temperature displaces the equilibrium between two different conditions of matter (systems) towards the system whose formation produces heat.”

The converse statement was also implied, leading van ‘t Hoff to the realization that application of the principle made it possible “to predict the direction in which any given chemical equilibrium will be displaced at higher or lower temperatures.”

A few months after the publication of the Etudes, the following note appeared on page 786 of volume 99 of Comptes-rendus de l’Academie des Sciences:

lc02

The note covers two pages, but the crucial paragraph is the one shown immediately above, in which Le Châtelier extends van ‘t Hoff’s recently published principle to include pressure and (in modern terms) chemical potential. Rendered in English, the paragraph reads

“Any system in stable chemical equilibrium, subjected to the influence of an external cause which tends to change either its temperature or its condensation (pressure, concentration, number of molecules in unit volume), either as a whole or in some of its parts, can only undergo such internal modifications as would, if produced alone, bring about a change of temperature or of condensation of opposite sign to that resulting from the external cause.”

Just as van ‘t Hoff used inductive reasoning to relate temperature change to displacement of equilibrium, so Le Châtelier adopts the same technique to extend the principle to changes of pressure and potential.

Having arrived at a generalized principle – that systems in stable equilibrium tend to counteract changes imposed on them – Le Châtelier then sought to deduce this result mathematically from equations describing systems in equilibrium. During this quest, he discovered that the American physicist Josiah Willard Gibbs had done a good part of the groundwork in his milestone monograph On The Equilibrium of Heterogeneous Substances (1876-1878). In 1899, Le Châtelier translated this hugely difficult treatise into French, thereby helping many scientists in France and beyond to access Gibbs’ powerful ideas.

– – – –

Early misunderstandings

Le Châtelier’s principle, first stated in 1884 and extended as the Le Châtelier-Braun principle in 1887, has stood the test of time. Today we view it as a very useful law, but that was not how it was viewed by some of the academic establishment in the early 20th century. Critics including the illustrious Paul Ehrenfest and Lord Rayleigh regarded the principle as vaguely worded and impossible to apply without ambiguity. As late as 1937, Paul Epstein in his Textbook of Thermodynamics wrote that this criticism “has been generally accepted since”.

This was news to me; when I was taught Le Châtelier’s principle at school, the wording was the same as in Epstein’s day but we had no issues with vagueness or ambiguity. I wondered what this criticism was all about, so I delved into the online archive of ancient journals. And came up with this:

lc05

From J Chem Soc, 1917; vol 111. CarnotCycle hopes that the misspelling of Braun in the title was a genuine typo, and not the deliberate use of irony to mock the authors of the principle.

It is clear from the first paragraph that the charge of ambiguity by Ehrenfest and Rayleigh arose from a failure to distinguish between cause and effect. Perturbations of systems in stable chemical equilibrium are caused by changes in generalized forces which, as Le Châtelier documents, are intensive variables. The ‘response of the system’, or generalized displacements, are the extensive conjugates. This answers Rayleigh’s question as to why we are to choose the one (pressure) rather than the other (volume) as the independent variable.

What surprised me was that this misunderstanding persisted for three decades. It just goes to show that in thermodynamics, even the most perspicacious individuals can have enduring blind spots.

– – – –

The Principle behind the Principle

lc06

In the Etudes of 1884, van ‘t Hoff stated his principle on the basis of different observations of equilibrium displacement with temperature. But while reaching his conclusion inductively, he still managed to give a precise mathematical expression of the principle. In modern notation it reads:

lc07

This famous equation, sometimes called the van ‘t Hoff isochore, was stated without proof in the 1884 edition, but in the second edition of 1896 a proof was provided which is based – as with many proofs of that era – on a reversible cycle of operations involving heat and work.

Although thermodynamically exact, the equation provides little insight into why a system in stable equilibrium tends to resist actions which alter that state. Not that this would have bothered van ‘t Hoff, who was much more interested in practicality than philosophical pondering.

But in the early 1900s, physical chemists began to look for an explanation. In A Textbook of Thermodynamics with special reference to Chemistry (1913), J.R. Partington remarked that Le Châtelier’s principle is an expression of “a very general theorem … called the Principle of Least Action. We can state it in the form that, if the system is in stable equilibrium, and if anything is done so as to alter this state, then something occurs in the system itself which tends to resist the change, by partially annulling the action imposed on the system.”

Partington was hinting at a more general notion underlying Le Châtelier’s original description. That notion was more concisely expressed in another volume entitled A Textbook of Thermodynamics, written by Frank Ernest Hoare in 1931, in which he stated “every system in equilibrium is conservative”.

– – – –

Interlude : Mapping chemical reactions

lc08

It is one the conditions of stable equilibrium in thermodynamic systems that for a given temperature and pressure, the Gibbs free energy is a minimum. In the context of a chemical reaction, it means that the Gibbs free energy of the reaction mixture will decrease in the manner shown above, where the difference between P (pure products) and R (pure reactants) is the standard free energy of reaction and E is the equilibrium point at the minimum point of the curve.

If the reactants are initially present in stoichiometric proportions, the x-axis represents the mole fraction of products in the reaction mixture. In 1920, a Belgian mathematician and physicist called Théophile de Donder proposed another name for this dimensionless extensive variable. He called it “the degree of advancement of a chemical reaction”, and represented it by the Greek letter ξ (xi).

– – – –

Defining conservative behavior

In 1937, Professor Mark Zemansky – at the time an associate professor of physics at what was then called the College of the City of New York – published a textbook entitled Heat and Thermodynamics.

In the last section of the last chapter of the book, Zemansky turns his attention to Le Châtelier’s principle. He considers a heterogeneous chemical reaction which is in phase equilibrium but not chemical equilibrium; under these circumstances the Gibbs free energy G is a function of temperature T, pressure P and degree of advancement ξ.

lc09

When the chemical reaction reaches stable equilibrium at temperature T and pressure P, it follows that ∂G/∂ξ = 0. Zemansky then considers a neighboring equilibrium state at temperature T+dT and pressure P+dP. The new degree of reaction will be ξ+dξ, but the change in the slope of the curve during this process is zero. Therefore

lc10

Zemansky thus arrives at a mathematical definition of conservative behavior for a thermodynamic system consisting of a reaction mixture in stable equilibrium with respect to the reaction to which ξ refers.

The next task is to use the operations of calculus to find expressions for the derivatives ∂ξ/∂T and ∂ξ/∂P in terms of ΔS (=ΔH/T) and ΔV respectively. The first step is to write out fully the condition on dT, dP and dξ required to maintain conservative behavior:

lc11

Zemansky then employs a neat device to introduce S and V into the calculation. The order of differentiation of a state function is immaterial, so he reverses the order of differentiation in the first two terms

lc12

Since (∂G/∂T)P,ξ = –S and (∂G/∂P)T,ξ = V,

lc13

For the sake of brevity, I will introduce at this point a shortcut that Zemansky did not use, but which does not in any way alter the results of his reasoning.

For any extensive property X which varies according to the degree of advancement of a chemical reaction ξ at constant temperature and pressure, the slope of the curve has the following property

lc14

Applying this fact to the above equation, we find that in order to maintain the equilibrium condition ∂G/∂ξ=0, dT, dP and dξ must be such that

lc15

Setting dP=0 yields the result

lc16

When ΔG=0, the denominator is positive. At equilibrium therefore, (∂ξ/∂T)P and ΔH have the same sign. So for an endothermic reaction (positive ΔH) the degree of reaction advancement at equilibrium increases as the temperature increases. This accords with Le Châtelier’s principle.

Setting dT=0 yields the result

lc17

When ΔG=0, the denominator is positive. At equilibrium therefore, (∂ξ/∂P)T and ΔV have opposite signs. For a reaction resulting in a reduction of volume, the degree of reaction advancement at equilibrium increases as the pressure increases. This accords with Le Châtelier’s principle.

Zemansky thus demonstrates that deductions from a mathematical definition of conservative behavior for a thermodynamic system consisting of a reaction mixture in stable equilibrium result in equations which “express in a rigorous form that part of Le Châtelier’s principle which concerns chemical reaction in heterogeneous systems”.

Le Châtelier never got to see this deduction of his principle. He died in 1936, just a year before Zemansky’s book was published.

– – – –

rb01a

The Honorable Robert Boyle FRS (1627-1691)

The fourteenth child of the immensely wealthy Richard Boyle, 1st Earl of Cork, Robert Boyle inherited land and property in England and Ireland which yielded a substantial income. He never had to work for a living, and following three years of travel and study as a teenager in Europe, Boyle decided at the age of 17 to devote his life to scientific research and the cultivation of what was called the “new philosophy”.

In Britain, Boyle was the leading figure in a move away from the Aristotelian view that knowledge was best obtained by the use of reason and logic. Boyle rejected this argument, and insisted that the path to knowledge was through empiricism and experiment. He won over many to his view, notably Isaac Newton, and in 1660 Boyle was a founding member of a society which believed that knowledge should be based first on experiment; we know it today as the Royal Society.

Boyle carried out a wealth of experiments in many areas of physics and chemistry, yet he seems to have been content with obtaining experimental results and generally stopped short of formulating theories to explain them.

Leibniz expressed astonishment that Boyle “who has so many fine experiments, had not come to some theory of chemistry after meditating so long on them”.

But what about Boyle’s law? you ask.

Well, it may surprise you to know that Robert Boyle did not originate the pressure-volume law commonly called Boyle’s law. A description of the reciprocal relation between the volume of air and its pressure does first appear in a book written by Boyle, but he refers to it as “Mr Towneley’s hypothesis”, for reasons we shall see.

– – – –

Torricelli leads the way

rb02

Torricelli using a lot more mercury than necessary to demonstrate the barometer.

It was Evangelista Torricelli (1608-1647) in Italy who started it all in the summer of 1644 with the invention of the mercury barometer. It was an impressive device, made all the more impressive by the insight that came with it. For one thing, Torricelli had no problem accepting the space above the mercury as a vacuum, in contrast to the vacuum-denying views of Aristotle and Descartes. For another, he was the first to appreciate the fact that air had weight, and to understand that the column of mercury was supported by the pressure of the atmosphere. As he put it: “We live submerged at the bottom of an ocean of air, which by unquestioned experiments is known to have weight.”

This led Torricelli to surmise that atmospheric pressure should be less in elevated places like mountains, an idea which was put to the test in France by Blaise Pascal, or more precisely by Pascal’s brother-in-law Florin Périer, who happened to live in Clermont-Ferrand, which has Puy de Dôme nearby.

rb03

Puy de Dôme in south-central France, close to Clermont-Ferrand.

On Saturday, September 19, 1648, Florin Périer and some friends performed the Torricelli experiment on the top of Puy de Dôme in south-central France. The height of the mercury column was substantially less – 85 mm less – than the control instrument stationed at the base of the mountain 1,400 metres below.

The Puy de Dôme experiment provided Pascal with convincing evidence that it was the weight of air, and thus atmospheric pressure, that balanced the weight of the mercury column. Torricelli’s instrument provided a convenient means of measuring this pressure. It was a barometer. The news quickly spread to England.

– – – –

Reaching new heights

The Torricellian experiment was demonstrated and discussed at the scientific centres of learning in London, Oxford and Cambridge from 1648 onwards. At Cambridge, there was an enthusiastic experimental scientist by the name of Henry Power, who was studying for a degree in medicine at Christ’s College. Power’s home was at Halifax in Yorkshire, and this gave him the opportunity to verify the Puy de Dôme experiment because unlike London, Oxford and Cambridge, the land around Halifax rises to significant heights.

rb04

The hills around Halifax in northern England

On Tuesday, May 6, 1653, Henry Power carried the Torricellian experiment to the summit of Halifax Hill, to the east of the town, where he was able to verify Pascal’s observation. In further experiments, he began to investigate the elasticity of air – i.e. its expansion and compression characteristics. And it was this change of focus that was to characterise England’s contribution to the scientific study of air.

The pioneering work in Italy and France had been concerned with the physical properties of the atmosphere. In England, attention was turning to the physical properties of air itself.

– – – –

The Spring of the Air

In 1654, the year after Henry Power’s excursion on Halifax Hill, Robert Boyle arrived in Oxford where he rented rooms to pursue his scientific studies. With the assistance of Robert Hooke, he constructed an air pump in 1659 and began a series of experiments on the properties of air. An account of this work was published in 1660 under the title “New Experiments Physico-Mechanicall, Touching The Spring of the Air, and its Effects”.

rb05

Boyle’s book was a landmark work, in which were reported the first controlled experiments on the effects of reduced air pressure. The experiments are divided into seven groups, the first of which concern “the spring of the air” i.e. the pressure exerted by the air when its volume is changed. It is clear that Boyle had an interest not only in demonstrating the elastic nature of air, but also in finding a quantitative expression of its elasticity. Due to inefficiencies in the air pump and the inherent difficulties of the experiment, Boyle failed in his first attempt. But it was not for want of trying.

– – – –

Enter Mr Towneley

Richard Towneley, whose home was near Burnley in Lancashire, northern England, was curiously similar to Robert Boyle in that the Towneley family estate also generated an income which meant that Richard did not have to work for a living. And just like Boyle, Towneley devoted his time to scientific studies.

Richard Towneley’s home, Towneley Hall in northern England, painted by JMW Turner in 1799

Now it just so happened that the previously-mentioned Henry Power of Halifax was the Towneley family’s physician. This gave Richard and Henry regular opportunities to share their enthusiasm for scientific experiments and discuss the latest scientific news.

In 1660 they both read Robert Boyle’s New Experiments Physico-Mechanicall, and this prompted further interest in the study of air pressure which Power had conducted on Halifax Hill seven years earlier. Not far to the north of Towneley Hall is Pendle Hill, whose summit is 1,827 feet (557 meters) above sea level, and it was here that Power and Towneley conducted an experiment that made history.

rb08

Pendle Hill, photographed by Lee Pilkington

On Wednesday 27th April 1661, they introduced a quantity of air above the mercury in a Torricellian tube. They measured its volume, and then using the tube as a barometer, they measured the air pressure. They then ascended Pendle Hill and at the summit repeated the measurements of volume and air pressure. As expected, there was an increase in volume and a decrease in pressure.

Although their measurements were only roughly accurate and doubtless affected by temperature differences between the base and summit of the hill, the numerical data was sufficient to give them the intuitive realization of a reciprocal relationship between the pressure and volume of air

rb09

On a high hill in northern England, nature revealed one of its secrets to Henry Power and Richard Towneley. Now they needed to communicate their finding.

– – – –

Boyle reports the news

It was not until two years after the Pendle Hill experiment that Henry Power eventually got around to publishing the results in Experimental Philosophy (1663). This delay explains why history has never associated the names of Power and Towneley with the gas law they discovered, because the news from Pendle Hill was first given to, and first reported by, Robert Boyle.

rb10

The second edition of 1662

In the appendix to the second edition of his New Experiments Physico-Mechanical published in 1662, Boyle reports Power and Towneley’s experimental activities, which in error he ascribes solely to Richard Towneley. It was on the basis of this second edition of Boyle’s book that the reciprocal relationship between the volume of air and its pressure became known as “Mr. Towneley’s hypothesis” by contemporary authors such as Robert Hooke and Isaac Newton.

A complication was added by the fact that Power and Towneley’s experiment led Boyle to the idea of compressing air in a J-shaped tube by pouring mercury into the long arm and measuring the volume and applied pressure.

rb211

From this experiment, conducted in September 1661, Boyle discovered that the volume of air was halved when the pressure was doubled. Curiously, he translated this finding into the hypothesis that there was a direct proportionality between the density of air and the applied pressure.

It didn’t occur to Boyle that the direct relation between density and pressure was the same thing as the reciprocal relation between volume and pressure discovered earlier by Power and Towneley. Boyle seems to have thought that compression was somehow different to expansion, and that his experiment broke new ground.

For this reason Boyle believed he had discovered something new, and since his name was far better known in scientific circles than that of Henry Power and Richard Towneley, it was inevitable that Boyle’s name would be associated with the newly-published hypothesis, which in time became Boyle’s law.

– – – –

Postscript : La loi de Mariotte

The pressure-volume law discovered by Power and Towneley, and confirmed by Boyle, is known as Boyle’s law only in Britain, America, Australia, the West Indies and other parts of what was once called the British Empire. Elsewhere it is called Mariotte’s law, after the French physicist Edme Mariotte.

rb12

Mariotte stated the pressure-volume relationship in his book De la nature de l’air, published in 1679, some 17 years after the second edition of Boyle’s New Experiments Physico-Mechanical. Mariotte made no claim of originality, nor did he make any reference to Boyle. But he was an effective publicist for the law, with the result that his name became widely associated with it.

Some might argue that the attribution is not quite deserved. However, Edme Mariotte stated something immensely important that Robert Boyle neglected to mention. He pointed out that temperature must be held constant for the pressure-volume relationship to hold:

rb11

In the view of CarnotCycle, the pressure-volume law so stated can with justification be called Mariotte’s law.

– – – –