Graham’s Law

Chemistry

Graham’s Law

Mr.Chemistry Formulas,

Graham’s Law

According to Graham’s law, the rate of diffusion of various gases is inversely proportional to the square root of their densities, at constant temperature and pressure.

r œ 1/ (d)1/2

Where, r = rate of diffusion
d = density of gas

Graham's law of effusion (also called Graham's law of diffusion) was formulated by Scottish physical chemist Thomas Graham in 1848. Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the molar mass of its particles. This formula can be written as:

${\displaystyle {{\mbox{Rate}}_{1} \over {\mbox{Rate}}_{2}}={\sqrt {M_{2} \over M_{1}}}}$,

where:

Rate₁ is the rate of effusion for the first gas. (volume or number of moles per unit time).

Rate₂ is the rate of effusion for the second gas.

M₁ is the molar mass of gas 1

M₂ is the molar mass of gas 2.

Graham's law states that the rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight. Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other (heavier gases diffuse more slowly). A complete theoretical explanation of Graham's law was provided years later by the kinetic theory of gases. Graham's law provides a basis for separating isotopes by diffusion—a method that came to play a crucial role in the development of the atomic bomb.

Graham's law is most accurate for molecular effusion which involves the movement of one gas at a time through a hole. It is only approximate for diffusion of one gas in another or in air, as these processes involve the movement of more than one gas.

In the same conditions of temperature and pressure, the molar mass is proportional to the mass density. Therefore, the rates of diffusion of different gases are inversely proportional to the square roots of their mass densities.

${\displaystyle {\mbox{r}}\propto {{\mbox{1}} \over {\sqrt {d}}}}$

ExamplesEdit

First Example: Let gas 1 be H₂ and gas 2 be O₂. (This example is solving for the ratio between the rates of the two gases)

${\displaystyle {{\mbox{Rate H}}_{2} \over {\mbox{Rate O}}_{2}}={\sqrt {M(O_{2}) \over M(H_{2})}}={{\sqrt {32}} \over {\sqrt {2}}}={\sqrt {16}}=4}$

Therefore, hydrogen molecules effuse four times faster than those of oxygen.^[1]

Graham's Law can also be used to find the approximate molecular weight of a gas if one gas is a known species, and if there is a specific ratio between the rates of two gases (such as in the previous example). The equation can be solved for the unknown molecular weight.

${\displaystyle {M_{2}}={M_{1}{\mbox{Rate}}_{1}^{2} \over {\mbox{Rate}}_{2}^{2}}}$

Graham's law was the basis for separating uranium-235 from uranium-238 found in natural uraninite (uranium ore) during the Manhattan Project to build the first atomic bomb. The United States government built a gaseous diffusion plant at the Clinton Engineer Works in Oak Ridge, Tennessee, at the cost of $479 million (equivalent to $5.57 billion in 2020). In this plant, uranium from uranium ore was first converted to uranium hexafluoride and then forced repeatedly to diffuse through porous barriers, each time becoming a little more enriched in the slightly lighter uranium-235 isotope.

Second Example: An unknown gas diffuses 0.25 times as fast as He. What is the molar mass of the unknown gas?

Using the formula of gaseous diffusion, we can set up this equation.

${\displaystyle {\frac {\mathrm {Rate} _{\mathrm {unknown} }}{\mathrm {Rate} _{\mathrm {He} }}}={\frac {\sqrt {4}}{\sqrt {M_{2}}}}}$

Which is the same as the following because the problem states that the rate of diffusion of the unknown gas relative to the helium gas is 0.25.

${\displaystyle 0.25={\frac {\sqrt {4}}{\sqrt {M_{2}}}}}$

Rearranging the equation results in

${\displaystyle M=({\frac {\sqrt {4}}{0.25}})^{2}={\frac {\mathrm {64g} }{\mathrm {mol} }}}$

History

Graham's research on the diffusion of gases was triggered by his reading about the observation of German chemist Johann Döbereiner that hydrogen gas diffused out of a small crack in a glass bottle faster than the surrounding air diffused in to replace it. Graham measured the rate of diffusion of gases through plaster plugs, through very fine tubes, and through small orifices. In this way he slowed down the process so that it could be studied quantitatively. He first stated in 1831 that the rate of effusion of a gas is inversely proportional to the square root of its density, and later in 1848 showed that this rate is inversely proportional to the square root of the molar mass.^[1] Graham went on to study the diffusion of substances in solution and in the process made the discovery that some apparent solutions actually are suspensions of particles too large to pass through a parchment filter. He termed these materials colloids, a term that has come to denote an important class of finely divided materials.

Around the time Graham did his work, the concept of molecular weight was being established largely through the measurements of gases. Daniel Bernoulli suggested in 1738 in his book Hydrodynamica that heat increases in proportion to the velocity, and thus kinetic energy, of gas particles. Italian physicist Amedeo Avogadro also suggested in 1811 that equal volumes of different gases contain equal numbers of molecules. Thus, the relative molecular weights of two gases are equal to the ratio of weights of equal volumes of the gases. Avogadro's insight together with other studies of gas behaviour provided a basis for later theoretical work by Scottish physicist James Clerk Maxwell to explain the properties of gases as collections of small particles moving through largely empty space.

Perhaps the greatest success of the kinetic theory of gases, as it came to be called, was the discovery that for gases, the temperature as measured on the Kelvin (absolute) temperature scale is directly proportional to the average kinetic energy of the gas molecules. Graham's law for diffusion could thus be understood as a consequence of the molecular kinetic energies being equal at the same temperature.

The rationale of the above can be summed up as follows:

Kinetic energy of each type of particle (in this example, Hydrogen and Oxygen, as above) within the system is equal, as defined by thermodynamic temperature:

${\displaystyle {\frac {1}{2}}m_{\rm {H_{2}}}v_{\rm {H_{2}}}^{2}={\frac {1}{2}}m_{\rm {O_{2}}}v_{\rm {O_{2}}}^{2}}$

Which can be simplified and rearranged to:

${\displaystyle {\frac {v_{\rm {H_{2}}}^{2}}{v_{\rm {O_{2}}}^{2}}}={\frac {m_{\rm {O_{2}}}}{m_{\rm {H_{2}}}}}}$

or:

${\displaystyle {\frac {v_{\rm {H_{2}}}}{v_{\rm {O_{2}}}}}={\sqrt {\frac {m_{\rm {O_{2}}}}{m_{\rm {H_{2}}}}}}}$

Ergo, when constraining the system to the passage of particles through an area, Graham's Law appears as written at the start of this article.

Gay Lussac’s Law

Chemistry

Joseph-Louis Gay-Lussac

Gay Lussac’s Law

Mr.Chemistry Formulas,

According to Gay Lussac’s law, the pressure of a gas of definite quantity at constant volume is directly proportional to absolute temperature.

P œ T
P = KT
P/T =K

P1/T1 = P2/T2
P1/P2 = T1/T2

A definite quantity of gas having volume (V1) at temperature (T1) and pressure (P1) changes to volume (V2), and the reaction is represented as below

P1V1T1 → P2VxT2 → P2V2T2

According to Boyle’s law
P1V1 = P2Vx
Vx = P1V1/ P2 ………………………………….(1)

According to Charle’s law
VxT1 = V2T2
Vx = V2T2/T1 ……………………………………(2)

V1/V2 = T1/T2

If we combine both the law, then as per equation (1) and (2)
P1 V1/ P2 = V2T2/T1
P1 V1/ T1 = P2V2/T2

PV/T = K
PV = KT
PV = nRT

Where, K = changes if quantity of gas changes = nR
n = quantity of gas in mole
R = gas constant

Joseph-Louis Gay-Lussac

Joseph-Louis Gay-Lussac, (born December 6, 1778, Saint-Léonard-de-Noblat, France—died May 9, 1850, Paris), French chemist and physicist who pioneered investigations into the behaviour of gases, established new techniques for analysis, and made notable advances in applied chemistry.

Born: December 6, 1778 France

Died: May 9, 1850 (aged 71) Paris France

Subjects Of Study: 

Charles’s law Gay-Lussac’s law of combining volumes atmosphere cyanogen potassium

Early career :

Gay-Lussac was the eldest son of a provincial lawyer and royal official who lost his position with the French Revolution of 1789. His father sent him to a boarding school in Paris to prepare him to study law. Early in his schooling, Gay-Lussac acquired an interest in science, and his mathematical ability enabled him to pass the entrance examination for the newly founded École Polytechnique, where students’ expenses were paid by the state. Although the school was designed primarily to train engineers, chemistry formed an important part of the curriculum. Gay-Lussac proved to be an exemplary student during his studies there from 1797 to 1800. Upon graduation, he entered the prestigious École Nationale des Ponts et Chaussées (School of Bridges and Highways). He withdrew from this school in 1801 to become chemist Claude-Louis Berthollet’s research assistant. Berthollet, who had recently set up a laboratory in his country house at Arcueil, just outside of Paris, became the focus of a small but very influential private scientific society. The society’s first volume of memoirs, published in 1807, included contributions from Gay-Lussac.

Searching for laws of nature

At Arcueil, Berthollet was joined by the eminent mathematician Pierre-Simon Laplace, who engaged Gay-Lussac in experiments on capillarity in order to study short-range forces. Gay-Lussac’s first publication (1802), however, was on the thermal expansion of gases. To ensure more accurate experimental results, he used dry gases and pure mercury. He concluded from his experiments that all gases expand equally over the temperature range 0–100 °C (32–212 °F). This law, usually (and mistakenly) attributed to French physicist J.-A.-C. Charles as “Charles’s law,” was the first of several regularities in the behaviour of matter that Gay-Lussac established. He later wrote, “If one were not animated with the desire to discover laws, they would often escape the most enlightened attention.” Of the laws Gay-Lussac discovered, he remains best known for his law of the combining volumes of gases (1808). He had previously (1805) established that hydrogen and oxygen combine by volume in the ratio 2:1 to form water. Later experiments with boron trifluoride and ammonia produced spectacularly dense fumes and led him to investigate similar reactions, such as that between hydrogen chloride and ammonia, which combine in equal volumes to form ammonium chloride. Further study enabled him to generalize about the behaviour of all gases. Gay-Lussac’s approach to the study of matter was consistently volumetric rather than gravimetric, in contrast to that of his English contemporary John Dalton.

Another example of Gay-Lussac’s fondness for volumetric ratios appeared in an 1810 investigation into the composition of vegetable substances performed with his friend Louis-Jacques Thenard. Together they identified a class of substances (later called carbohydrates) including sugar and starch that contained hydrogen and oxygen in the ratio of 2:1. They announced their results in the form of three laws, according to the proportion of hydrogen and oxygen contained in the substances.

Other researches

As a young man, Gay-Lussac participated in dangerous exploits for scientific purposes. In 1804 he ascended in a hydrogen balloon with Jean-Baptiste Biot in order to investigate the Earth’s magnetic field at high altitudes and to study the composition of the atmosphere. They reached an altitude of 4,000 metres (about 13,000 feet). In a following solo flight, Gay-Lussac reached 7,016 metres (more than 23,000 feet), thereby setting a record for the highest balloon flight that remained unbroken for a half-century. In 1805–06, amid the Napoleonic wars, Gay-Lussac embarked upon a European tour with another Arcueil colleague, the Prussian explorer Alexander von Humboldt.

Gay-Lussac’s research together with the patronage of Berthollet and the Arcueil group helped him to gain membership in the prestigious First Class of the National Institute (later the Academy of Sciences) at an early stage in his career (1806). Although no vacancy in the chemistry section existed, his credentials in physics were sufficiently strong to enable him to enter that section. In 1807 he published an important study of the heating and cooling produced by the compression and expansion of gases. This was later to have significance for the law of conservation of energy. Three years previously Gay-Lussac had been appointed to the junior post of répétiteur at the École Polytechnique where, in 1810, he received a professorship in chemistry that included a substantial salary. He was also granted a professorship in physics at the Faculty of Science in Paris upon its founding in 1808. In that same year he married Geneviève Rojot; the couple eventually had five children.

Rivalry with Davy

Gay-Lussac’s appointment to the faculty of the École Polytechnique in 1804 provided him with laboratory facilities in the centre of Paris. These accommodations eased his collaborations with Thenard on a series of experimental investigations. When they heard of the English chemist Humphry Davy’s isolation of the newly discovered reactive metals sodium and potassium by electrolysis in 1807, they worked to produce even larger quantities of the metals by chemical means and tested their reactivity in various experiments. Notably they isolated the new element boron. They also studied the effect of light on reactions between hydrogen and chlorine, though it was Davy who demonstrated that the latter gas was an element. Rivalry between Gay-Lussac and Davy reached a climax over the iodine experiments Davy carried out during an extraordinary visit to Paris in November 1813, at a time when France was at war with Britain. Both chemists claimed priority over discovering iodine’s elemental nature. Although Davy is typically given credit for this discovery, most of his work was hurried and incomplete. Gay-Lussac presented a much more complete study of iodine in a long memoir presented to the National Institute on August 1, 1814, and subsequently published in the Annales de chimie. In 1815 Gay-Lussac experimentally demonstrated that prussic acid was simply hydrocyanic acid, a compound of carbon, hydrogen, and nitrogen, and he also isolated the compound cyanogen [(CN)2 or C2N2]. His analyses of prussic acid and hydriodic acid (HI) necessitated a modification of Antoine Lavoisier’s theory that oxygen was present in all acids.

Applied science

Beginning in 1816, Gay-Lussac served as the joint editor of the Annales de chimie et de physique, a position he shared with his former Arcueil colleague François Arago. This was an influential position and a further source of income. As was customary, he continued to hold several teaching posts simultaneously; however, his major income during his later years was derived from a series of governmental and industrial consultancies. In 1818 he became a member of the government gunpowder commission. Even more lucrative was his 1829 appointment as director of the assay department at the Paris Mint, for which he developed a precise and accurate method for the assaying of silver. Gay-Lussac also performed experiments to determine the strength of alcoholic liquors. In his final years he served as a consultant for the glass factory at Saint-Gobain. Such a wide array of appointments attests to the value his contemporaries placed upon applying chemistry toward solving social and economic concerns. Still, Gay-Lussac did not escape criticism from colleagues for turning away from the path of “pure” science and toward the path of financial gain.

from the path of “pure” science and toward the path of financial gain.

Gay-Lussac was a key figure in the development of the new science of volumetric analysis. Previously a few crude trials had been carried out to estimate the strength of chlorine solutions in bleaching, but Gay-Lussac introduced a scientific rigour to chemical quantification and devised important modifications to apparatuses. In a paper on commercial soda (sodium carbonate, 1820), he identified the weight of a sample required to neutralize a given amount of sulfuric acid, using litmus as an indicator. He went on to estimate the strength of bleaching powder (1824), using a solution of indigo to signify when the reaction was complete. In his publications are found the first use of the chemical terms burette, pipette, and titrate. The principles of volumetric analysis could be established only through Gay-Lussac’s theoretical and practical genius but, once established, the analysis itself could be carried out by a junior assistant with brief training. Gay-Lussac published an entire series of Instructions on subjects ranging from the estimation of potash (1818) to the construction of lightning conductors. Among the most influential Instructions was his estimation of silver in solution (1832), which he titrated with a solution of sodium chloride of known strength. This method was later employed at the Royal Mint. In 1831 Gay-Lussac was elected to the Chamber of Deputies and in 1839 received a peerage.

In 1848 (the year of revolutions) Gay-Lussac resigned from his various appointments in Paris, and he retired to a country house in the neighbourhood of his youth that was stocked with his library and a private laboratory. In the spring of 1850, realizing that he was dying, he asked his son to burn a treatise he had begun called “Philosophie chimique.” In a eulogy delivered after his death at the Academy of Sciences, his friend, the physicist Arago, summed up Gay-Lussac’s scientific work as that of “an ingenious physicist and an outstanding chemist.”

Charle’s Law

Chemistry

Charle’s Law

According to Charle’s Law, the volume (V) of a definite quantity of gas is directly proportional to its absolute temperature (T), at constant pressure (P).

V œ T (Pressure constant)
V = KT K = Constant
V/T = K
Similarly
V1/T1 = V2/T2

Here we have temperature in a Kelvin temperature or absolute temperature. The temperature at which the volume of hypothetical gas will be zero is called as Kelvin temperature or absolute temperature. Kelvin has discovered this and the temperature is -273°C. The relation between Kelvin temperature (T) and Celsius temperature (t) is shown below.

T = t + 273

Dalton’s Law

Chemistry

Dalton’s Law

Dalton’s law is based on partial pressure of gas. Partial pressure is a sum of individual pressure of each gas in the gaseous mixture.

Consider one example:

A vessel contains a mixture of gas A and B having pressure of PA and PB respectively. According to Dalton’s law, the partial pressure of gaseous mixture is the sum of individual pressure of each gas.
P = PA + PB

Boyle’s Law

Chemistry

Robert Boyle

Boyle’s Law

Boyle’s Law

The volume of gas depends on its temperature and pressure. According to Boyle’s law, the volume (V) of a definite quantity of gas is inversely proportional to its pressure (P), at constant temperature (T).

V œ 1/P (Temperature constant)
V = K/P K = constant
PV = K

Let we consider the initial pressure of gas = P1

Initial volume of gas = V1
Final pressure of gas = P2
Final volume of gas = V2

P1V1 = P2V2

Robert Boyle

Born : 25 January 1627

Lismore, County Waterford, Ireland

Died : 30 December 1691

London, England

Summary :

Robert Boyle was an Irish-born scientist who was a founding fellow of the Royal Society. His work in chemistry was aimed at establishing it as a mathematical science based on a mechanistic theory of matter.

Biography :

Robert Boyle was born into a Protestant family. His father was Richard Boyle, Earl of Cork, who had left England in 1588 at the age of 22 and gone to Ireland. Appointed clerk of the council of Munster by Elizabeth I in 1600, he bought Sir Walter Raleigh's estates in the counties of Cork, Waterford, and Tipperary two years later. Robert's mother, Catherine Fenton, was Richard Boyle's second wife, his first having died within a year of the birth of their first child. Robert was the seventh son (and fourteenth child) of his parents fifteen children (twelve of the fifteen survived childhood). Richard Boyle was in his 60s and Catherine Boyle in her 40s when Robert was born. Of his father Robert would later write He, by God's blessing on his prosperous industry, from very inconsiderable beginnings, built so plentiful and so eminent a fortune, that his prosperity has found many admirers, but few parallels.

Indeed, Robert was fortunate to have the richest man in Great Britain for a father although, one would have to say, the Earl of Cork had acquired his fortune by somewhat dubious means. He was imprisoned in England on charges of embezzlement at one stage and later was fined heavily for possessing defective titles to some of his estates.

The Earl of Cork and his wife believed that the best upbringing for young children, up to the time they began their education, could be provided away from their parents. Robert was sent away to be brought up in the country while his father continued to aim for higher and higher political success. The Earl of Cork lived for four years in his town house in Dublin. He was appointed a lord high justice in 1629 and lord high treasurer in 1631. However, during this time in Dublin Robert's mother died and some time after this Robert returned from his stay with his country nurse to rejoin his family.

Robert was sent, together with one of his brothers, to study at Eton College in England in 1635. At this time the school was becoming fashionable as a place where important people sent their sons. The headmaster was John Harrison and the two young Boyle brothers lived in the headmaster's house 

Besides the strictly classical course of study then in vogue, the boys had private tutors in French, dancing, and music, for whom they paid extra fees.

Boyle paid tribute to Harrison in  where he writes that Harrison gave him a:-

... strong passion to acquire knowledge ...

At this stage of his time at Eton, Boyle's education was clearly going well. He was popular with both his headmaster and his fellow pupils. However, perhaps he had been given too much special attention by Harrison for, when Harrison retired, Boyle seemed unable to fit in with the educational discipline the new headmaster brought to the school. Realising that neither of his sons were progressing well at school under the new headmaster, the Earl of Cork took his sons away from the Eton in November 1638. After this Boyle was tutored privately by one of his father's chaplains.

At the age of 12 Boyle was sent by his father, with one of his brothers, on a European tour. From Dieppe they travelled to Paris, then on to Lyon before reaching Geneva. In Geneva Boyle studied with a private tutor French, Latin, rhetoric and religion. He also spent time in the afternoons playing tennis and fencing. Perhaps most importantly of all he began to study mathematics and soon 

... he grew very well acquainted with the most useful part of arithmetic, geometry, with its subordinates, the doctrine of the sphere, that of the globe, and fortification.

In 1641 Boyle learnt Italian in preparation for visiting there. In September of that year Boyle and his tutor were in Venice, then by the beginning of 1642 they were in Florence. Galileo died in his villa in Arcetri, near Florence, while Boyle was living in the city. He was much influenced by this event and he carefully studied Galileo's works. If any one event shaped Boyle's life and directed him towards science, then it was this. Of course his Protestant background, with an ingrained fear of Jesuits, contributed to his sympathy for Galileo and his treatment by the Roman Catholic Church. Boyle became a strong supporter of Galileo's philosophy and believed strongly from this time in the new approach to studying the world through mathematics and mechanics.

By May 1642 Boyle and his tutor were in Marseilles waiting for money from Boyle's father so that he could complete the journey home. This did not arrive, merely a letter from his father explaining that a rebellion in Munster was fully occupying his time and money. He did send £250 to pay for Boyle's return, but the money never reached him. Boyle returned to Geneva where he seems to have lived mainly on his tutor's earnings, while his father continued to fight the Irish at Lismore Castle. King Charles I negotiated a cease-fire with the Catholic rebels fighting the Earl of Cork so that he might bring his troops back to England to help him in the civil war which had broken out. The Earl of Cork never got over Charles treating the Irish as equals and he died shortly after in September 1643. Robert Boyle was still living in Geneva when his father died. In the summer of 1644 he sold some jewellery and used the money that he was paid to finance his return trip to England.

Back in England, Boyle lived for a while with his sister Katherine. She was thirteen years older than him and was a lady of some importance, married to Viscount Ranelagh. England was in a chaotic state, the civil war which had began in 1642 was being fought between King Charles and the parliament. Charles had moved to Oxford while the parliament had formed a treaty with the Scots. In return for Scots military support they were promised the establishment of a Presbyterian church. Several battles in 1644 left both King and parliament somewhat in disarray. Boyle had property in England, the manor of Stalbridge, left to him by his father but the situation in the country made things difficult. He wrote in a letter (see for example 

got safe into England towards the middle of the year 1644, where we found things in such a confusion, that although the manor of Stalbridge were by my father's decease descended unto me, yet it was near four months before I could get thither.

In fact although Boyle inspected his new home after four months, it was much longer before he was able to move in. This happened in March 1646 after he had spent more time with his sister and made a return trip to France to repay his debts to his tutor who continued to live there. Although Boyle did not intend to spend long at Stalbridge, he remained there for around six years. He probably studied harder than he admits in a letter sent to his old tutor in France in October 1646 (see for example 

As for my studies, I have had the opportunity to prosecute them but by fits and snatches, as my leisure and my occasions would give me leave. Divers little essays, both in verse and prose, I have taken pains to scribble upon several subjects. ... The other humane studies I apply myself to, are natural philosophy, the mechanics and husbandry, according to the principles of our new philosophical college ...

This "new philosophical college" is also called by Boyle the "Invisible College" later in the letter. It is the society which would soon became the "Royal Society of London" and it provided Boyle's only contact with the world of science while he lived a somewhat lonely life at Stalbridge. He would look forward to his visits to London where members of the College [3]:-

.. do now and then honour me with their company.

It was discussions in the Invisible College which led to Boyle reading Oughtred's Clavis Mathematica as well as the works of Mersenne and Gassendi. Boyle had from the time of his visit to Italy favoured the ideas of Copernicus and he now held these views deeply, together with a deep belief in the atomic theory of matter. In the Invisible College these views were considered to be those of the new natural philosophy.

This period was a difficult one for Boyle for he tried hard not to be forced to take sides in the civil war. His loyalties were somewhat divided, his father having been a staunch Royalist, his sister Katherine a staunch Parliamentarian. Basically he had little sympathy with either side, but the final outcome of the civil war turned out to his advantage. Charles I was defeated and executed but, in 1650, Charles II landed in Scotland and tried to regain power. Cromwell, leading the parliamentary forces, defeated the Scots in 1650, again in 1651, and the Irish were also defeated by Cromwell in 1652. Boyle went to Ireland in 1652 to look after his estates there. He ended up a very rich man when Cromwell apportioned Irish lands to the English colonists. From that time on he was able to devote himself entirely to science without the need to earn money. It should be noted, however, that Boyle was a very generous man with his money, and many around him benefited from this generosity.

Boyle met John Wilkins, the leader of the Invisible College, in London when he visited there in 1653. At this time Wilkins had just been appointed as Warden of Wadham College in Oxford and he was planning to run the Invisible College from there. He strongly encouraged Boyle to join them in Oxford and invited him to live in the College. Boyle decided to go to Oxford but preferred not to accept Wilkins' offer of accommodation, choosing instead to arrange his own rooms where he could carry out his scientific experiments. At Oxford he joined a group of forward looking scientists, including John Wilkins, John Wallis who was the Savilian Professor of Geometry, Seth Ward who was the Savilian Professor of Astronomy, and Christopher Wren who would succeed Ward as Savilian Professor of Astronomy in 1661. From 1654 Boyle lived in Oxford, although he never held any university post.

He made important contributions to physics and chemistry and is best known for Boyle's law (sometimes called Mariotte's Law) describing an ideal gas. Boyle's law appears in an appendix written in 1662 to his work New Experiments Physio-Mechanicall, Touching the Spring of the Air and its Effects (1660). The 1660 text was the result of three years of experimenting with an air pump with the help of Hooke whom he employed as his assistant. The apparatus had been designed by Hooke and using it Boyle had discovered a whole series of important facts. He had shown, among other things, that sound did not travel in a vacuum, he had proved that flame required air as did life, and he investigated the elastic properties of air.

The 1662 appendix did not only contain Boyle's law which relates volume and pressure in a gas, but it also contained a defence of Boyle's work on the vacuum which appeared in the main text. Many scientists, particularly Hobbes, had argued that a vacuum could not exist and claimed that Boyle's results obtained with the vacuum pump must be the result of some as yet undiscovered force. Another book by Boyle in 1666 was called Hydrostatic paradoxes. It is 

... both a penetrating critique of Pascal's work on hydrostatics, full of acute observations upon Pascal's experimental method, and a presentation of a series of important and ingenious experiments on fluid pressure.

In The Sceptical Chemist (1661) Boyle argued against Aristotle's view of the four elements of earth, air, fire and water. He argued that matter was composed of corpuscles which themselves were differently built up of different configurations of primary particles. Although many ideas in this work were taken over from Descartes, in one respect he fundamentally disagreed with him. Boyle's ideas that the primary particles move freely in fluids, less freely in solids, followed Descartes. However, Descartes did not believe in a vacuum, rather he believed in an all pervading ether. Boyle had conducted many experiments which led him to believe in a vacuum and, having found no experimental evidence of the ether, to reject that idea. He did follow Descartes in his overall belief that the world was basically a complex system governed by a small number of simple mathematical laws.

In considering optics, in particular colour, Boyle was not so successful. He published Experiments and considerations touching colours in 1664 but was quite prepared to acknowledge that Hooke's work of 1665 was superior and he completely acknowledged that Newton's ideas, published in 1672, should replace his own.

Boyle was a founding fellow of the Royal Society. He published his results on the physical properties of air through this Society. His work in chemistry was aimed at establishing it as a mathematical science based on a mechanistic theory of matter. It is for this reason that we have decided to include Boyle into this archive of mathematicians for, although he did not develop any mathematical ideas himself, he was one of the first to argue that all science should be developed as an application of mathematics. Although others before him had applied mathematics to physics, Boyle was one of the first to extend the application of mathematics to chemistry which he tried to develop as a science whose complex appearance was merely the result on simple mathematical laws applied to simple fundamental particles.

In 1668 Boyle left Oxford and went to live with his sister Lady Ranelagh in London. There he became a neighbour of Barrow but seemed to have more common scientific interests with another neighbour Thomas Sydenham, a physician. In 1669 his sister's husband died. Some however, were keen to find Boyle a wife. Wallis found someone whom he considered particularly suitable to be Boyle's wife and wrote to him saying:-

If I might be the happy instrument in making two so excellent persons happy in each other ... I do not know in what else I could more approve myself.

Boyle seemed to have successfully avoided such attempts to marry him off. In June 1670 he had a stroke which left him paralysed but slowly he recovered his health. He continued to work and to entertain at his London home. Visitors were so frequent that he had to restrict visits so that he had time to continue with his scientific researches, which he did with the help of many excellent assistants.

In 1680 he declined the offer that he serve as President of the Royal Society. He explained his reasons were religious in that he could not swear to necessary oaths. The religious side of Boyle is one which we have not mentioned in this biography, yet it was an important force in his life. Perhaps the reason it has not been necessary to mention his strong Christian faith earlier is that to Boyle there was no conflict with religion and a mechanistic world [1]:-

... for him a God who could create a mechanical universe - who could create matter in motion, obeying certain laws out of which the universe as we know it could come into being in an orderly fashion - was far more to be admired and worshipped than a God who created a universe without scientific law.