Alright. So one of the gas laws you'll see in class is going to be Gay Lussac's law. And Gay Lussac actually explained the relationship between pressure and temperature when the volume remains constant. Let's actually look at this ourselves.
So we have a container here and it's a five litre container of and has, inside has gas particles. Okay it's at room temperature and the gas particles are heating in some sort of pressure, that's fine. Let's say we heat it up. So we're increasing the, increasing the temperature and the kinetic energy of the particles within the, within the five litre container, it's increasing as well. And they're heating the gas at the sides of the container at high speeds. And so what's going to happen, as long as the temperature, sorry. As long as the volume remains constant which it is, the pressure inside the container is going to increase dramatically depending on how much the temperature is increasing. So let's talk about this relationship. We know it's a direct relationship. As temperature increases, so does pressure. And conversely, as temperature decreases, so does pressure. So temperature and pressure have a good relationship as long as the volume remains constant.
Okay. So let's put this in mathematical formula. Pressure one over temperature one equals to pressure two over temperature two. Because this is direct relationship, they are divided by each other. The temperature we're going to make sure it's in kelvin and the reason we make sure it's in kelvin is because we want to make sure that there's no negative numbers on the denominator and kelvin's the only temperature scale that actually only has positive numbers. So we're going to make sure this is in kelvin and this is our, this is Gay Lussac's law mathematically.
Graphically we can put the temperature on the x axis and pressure on the y axis. We know that as we increase temperature, we also increase pressure creating a positive slope.
Okay. Let's actually look at this in demonstration. So what I have right here, I'm going to put my goggles on. Make sure we're safe. Safety comes first. We have what I'm having on this hot plate is a coke can as you can see. And I'm heating it up. Let's say the gas particles inside the container are heating up also and they're heating the pressure of the soda can at high speed. But it actually it's open so it has a place to escape so the pressure inside the container is equal to the pressure outside here and so everything is all good. What I'm going to do is I'm going to flipping the can over into this ice water bath sealing the container. And what's that, what's going to happen is the temperature is going to drop and the pressure inside the container is also going to drop. And but the pressure outside is going to remain the same. so what is going to happen? Let's see.
So, as you can see it actually didn't take much at all. What happened was the pressure outside was so much greater than the pressure inside because we had dropped the temperature so dramatically that it actually pushed on the can and crashed it as you can see. Completely crashed it.
Okay. Don't try that home. Alright. Let's turn this off and let's go solve a problem together. Okay. So the pressure in a car tyre is 1.88 atmospheres. That's our first pressure at 25 degrees celsius, there's our first temperature. What will be the pressure if the temperature warms up to 37 degrees celsius? Okay. So first I want to make sure these temperatures are in kelvin not in celsius. I'm going to change them. 25 degrees celsius plus 273 is equal to 298 kelvin. 37 degrees celsius, it should be degrees celsius plus 273 is equal to 310 kelvin. Okay, so my first pressure when I woke up, I put the tyre pressure at 1.88 atmospheres. And the temperature outside was 298 kelvin. We don't know pressure at the end of the day when it's 37 degrees celsius. We don't know it. So we're going to say x over 310 kelvin. We cross multiply 1.88 times 310 divided by 298 and it's going to give me 1.96 atmospheres.
The pressure inside the tyre is actually going to increase as expected because temperature also increased. So this is an example of Gay Lussac's law in an everyday application.
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.
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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.
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.
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.
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.”Maurice P. Crosland