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When I started learning about Laws related to "constant proportions" and other hypothesis like "all matter is composed of smallest indivisible particles", I didn't notice it was not so obvious for people earlier to even think about it like we do, so I dug up a little bit and then started asking all sorts of question that how did people in those times even proceed with such propositions, Here, I write a Quick recap/Summary while also giving detailed explanations about some "Significant" points, I am answering This to share what I have found From original sources and my understandings, That I gathered in My notes

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A summary according to timeline for pre-Daltonian chemistry related to Atomism

  1. Democritus (460-370 BCE):He was an ancient Greek philosopher, whose mentor was "Leucippus", Democritus was central figure in development of philosophical atomism, he reasoned that if the stone were to be continually cut into smaller and smaller pieces then; at some point, there would be a piece which would be so small as to be indivisible. He called these small pieces of matter "Atomos," the Greek word for indivisible. Democritus, theorized that atoms were specific to the material which they composed, less known, An Indian Philosopher named "Kanad" also Proposed an atomist view of matter, and taught so in his school of thoughts.

  2. Aristotle and Plato: One of the best ancient Greek philosophers were against the idea that everything was made up of atoms, they believed that everything is infinitely cuttable, meaning Materials are eternal and can be cut any number of times, he (Aristotle) also believed that Four core elements can be transformed into one another, namely earth, water, air and fire.

  3. The atomist theory got its noticeable revival in $17^{th}$ century when In 1643, Evangelista Torricelli, an Italian mathematician and pupil of Galileo, showed that air had weight and was capable of pushing down on a column of liquid mercury (thus inventing the barometer), Daniel Bernoulli (Swiss) proposed that gases could be composed of particles too small to be seen by eyes, loosely packed in empty space..

  4. Joseph Priestley, who in 1770s started experimenting with red calx. Specifically, mercury calx, a red colored stone. When he heated the stone(using magnifying glass and sun rays), it not only converted to silver liquid metal, But also formed a strange gas, He conducted The famous experiment of Mouse under jar, in which he placed a mouse under a jar and observed the time required for its death, and then collected the strange gas, and placed the mouse in container with this strange gas, and found that it lived longer, also when flames were burnt in this gas, It burned with vigorous flame, He called the gas "dephlogisticated air".

  5. Antoine Lavoisier: He belonged to a wealthy family in France, He was a firm believer in Accurate calculations and its importance, he is well known for the shift from qualitative to quantitative analysis in Chemistry, He performed a series of experiments on This "dephlogisticated air", and found that it changed some substances acidic, also during that period it was known that acids react with metal to form a highly inflammable gas, called phlogiston, He mixed these two gases "phlogiston" and "dephlogisticated air" in a container and slide a match, The gases immediately burnt and he saw some water droplets in container, He then did these type of experiments with lots of other gases and demonstrated that new substances can be formed by combining gases, Phlogiston was named "hydrogène", French word for "hydrogen", One of his most famous experiments was the combustion of mercury in a closed vessel. He showed that the weight of the mercury and the vessel increased after the reaction, and that the same amount of air was used up. This result contradicted the phlogiston theory, which predicted that the weight of the mercury and the vessel would decrease after the reaction

  6. Jeremias Benjamin Richter: In 1972, German chemist Richter had a firm belief that reaction followed a specific mathematics which can be explained with accurate quantitative measurements, Evidence for the existence of atoms was the law of definite proportions proposed by Jeremias Benjamin Richter in 1792. Richter found that the ratio by weight of the compounds consumed in a chemical reaction was always the same. He coined the term "Stoichiometry", From Greek words "Stoikheion" for element and "Metron" for measurement

  7. Proust: Joseph louis Proust was a French chemist, Proust studied iron sulfides, tin oxides and other substances like copper carbonates, he even made artificial copper carbonate and compared it with Natural one, and showed that each had same proportions of $(Cu ,O,C)$,Through different experiments like Adding a little more of One Element , And still found that, The extra weight remained unreacted, Leading to conclusion that no intermediate compound other than these proportions was possible, He Then gave his Famous "Law of definite proportions", Scholars who have reviewed the writings of Proust found that he had enough data to have discovered the law of multiple proportions himself, but somehow he did not

"Now here are Significant interesting parts"

Dalton: John Dalton was an English chemist and Physicist, here is how he contributed to Atomist Philosophy.

In his paper, He mentioned that there are three kinds of matter present, namely , Solid, liquid and Elastic fluids, He then further stated, That everything is made up of indivisible particles, and they are attracted to each other with forces with power more or less according to condition, This almost explains well the states ,The force is called attraction of cohesion

One important and Interesting question That Dalton had in his mind was as follows

If atomic theory was In fact true, Then do all such atoms(particles) of water have same shape and figure and weight?

Here is how he responded to this query in his paper:

If it was case, if really some particles of water were heavier than other, then, hypothetically, if one parcel of liquid water was made of those heavier water, it will and should affect specific gravity of water, Which is clearly not the case"

Although now, we know isotopes exist

He further proposed that gases are of two types

(1) Pure gases(Which cannot be made of combination of other gases)

(2) Mixed gases(Which can be made by combination of other gases)

And Further for explaining chemical reactions, he used rule of greatest simplicity, that particles of two chemicals form a binary molecule of 1:1 correspondence, example

Hydrogen gas+ Oxygen gas gives water, Note that they did not knew what were the molecular formulas for these gases like our modern days, for them , These gases were elements

After Taking the values of Lavoisier's rough measurement of weights of reactants, He used the rough Lavoisier measurement that 2.7 gram of Hydrogen gas react with 15.3 grams of oxygen gas to give 18g of water, Which led him to find relative atomic masses, These were the first attempts to compare masses of fundamental particles of two different elements(their definition of element applies), Hence, due to Dalton's assumption

He believed that 1 fundamental particle of Hydrogen gas react with One fundamental particle of oxygen gas to form one fundamental particle of water, Hence relative masses of can simply be found by simply taking ratios of weight in which they react, hence he then gave Mass of Oxygen's fundamental particle as $\frac {15.3}{2.7}=5.5$ times the mass of Hydrogen's fundamental particle, If Lavoisier calculation would have been accurate, he would have found the relative mass of Oxygen's fundamental particles as 8 times the mass of hydrogen's fundamental particles

using this Binary assumption, He carried out many more such reaction and Gave his table of Atomic weights where he put atomic weight of Hydrogen element as "1 unit", Note this was the first time relative atomic weight was being measured, so he really had the choice to set the weight of Hydrogen element to "1 relative measuring unit"

As the time progressed, Dalton Found the law of Multiple proportions, Which led him to revise his theory about binary 1:1 fundamental particles combination, He then revised it and stated that as long as 1:1 ratio compounds exist(with lowest weight), He made some rules that $2^{nd}$ lowest weight compound will combine as 1:2 then 1:3 etc.

In modern terms, example can be given as as long as nitrous gas(nitrous oxide) exist, there can exist nitrogen dioxide etc..

Quick fact: This revised theory caused a lot of debate in future as Dalton refused to believe that water can be $H_2O$ without existence of compound like $HO$ as Avogadro proposed later

Important Point to note is that Dalton thought that all pure gases/elastic fluids are monoatomic in nature, He then observed that when equal volumes of azotic gas(Modern day Nitrogen gas) and oxygen gas is taken, It instantly forms twice the volume of "Nitrous gas"

Hence Dalton first reached to a conclusion "that equal volumes of oxygen and nitrogen gas contain equal number of molecules as they react completely to form Nitrous gas", But at that time, it was assumed that nitrogen and oxygen are monoatomic and result in 1:1 binary molecule, But above conclusion was quickly rejected by Dalton himself as if two gases had equal number of particles, then as per this conclusion, The nitrous gas formed must have twice the amount of particles as that of either nitrogen or oxygen as twice the volume of nitrous gas was formed, But this cannot be the case if Nitrogen and oxygen reacted in 1:1 particle combination, at most, have same number of molecules as that of either oxygen or nitrogen, it cannot form twice the number of particle of nitrous gas out of nothing, Hence Dalton rejected the conclusion that equal volumes of gases had equal number of particles, The KEY point to note here is that Dalton had no idea that a Gas can Be Diatomic, If Dalton had known that A gas could be diatomic, He might have explained this observation properly

Now, Gay Lussac later found experimentally that volumes of gases too, react in multiple simple whole number proportion, Example just for explanation(Don't know if he actually used this reaction)

1 volume of azotic gas react with 1 volume of oxygen gas to form 2 volume of nitrous gas,

2 volumes of nitrogen gas react with 1 volume of oxygen gas to form 2 volume of modern day ($N_2O$)

1 volume of nitrogen gas react with 2 volumes of oxygen gas to form 2 volume of modern day ($NO_2$)

Now, Dalton replied to New observations of gay Lussac and tried to convince that somehow, Gay Lussac's observations are similar to his observation and lead to conclusion similar to that of Dalton's earlier conclusion mention above, If The conclusion that equal volumes, equal particles conclusion was true, This would lead to definite proportion law in volumes of gases, similar to Dalton's Definite proportion law, But the only difference would be that Dalton's Law would be applicable everywhere while , This law would only be valid for Elastic fluid, Dalton further Tries to highlight that this irregular conclusion might just be due to the limitations of the measurement instruments of that period, and further in time, It would get better

Now , "Lorenzo Romano Amedeo Carlo Avogadro", who was an Italian scientist, Wrote a paper named "essay on a manner of determining the relative masses of the elementary molecules of bodies, and the proportions in which they enter into these compounds" after Release of Interesting paper by Gay Lussac named "Memoir on the Combination of Gaseous Substances with Each Other", In which Avogadro states that If Dalton atomic theory is true, and indeed Gay Lussac experiments are hereby of less errors, There must exist a relation between volume and number of particles in gas, the simplest of all such relations would be that equal volumes of all gases contain equal number of elementary particles, But if relations were different for different For different for different gases, though Quantized by volumes, It would be scarcely possible that law regulating distances between these particle(that has direct impact on volume) could give in all cases, relation so simple as conclusion as according to Gay Lussac

A simple explanation of what Avogadro meant to say is as follows

Explanation: We already know by Gay Lussac multiple proportion volume experiment that number of atoms/elementary particles must be quantized to a particular volume at same external conditions

Now there can be these two cases

Case 1) The quantization might be same for all gases i.e $\frac {V}{n}=k$, $k$ is a natural number, and $k$ is same for all gases, which in turn means, All Gases have same number of particles in equal volumes

Case 2) The value of k Is different for different gases, meaning particles are still quantized with volume, but the quantization is different for different gases

Now considering case 2, Let us take an example of reaction of two gases $G_1$ AND $G_2$

Suppose

$G_1$ has $n_1$ particles per volume '$V$'

$G_2$ has $n_2$ particles per volume '$V$'

Now SUPPOSE $V$ volumes of gas $G_1$ react with $xV$ volume of gas $G_2$ completely, $x$ is a natural number

$$V(G_1)+xV(G_2)$$ react completely

Hence, $n_1$ particles of $(G_1)$ react completely with $xn_2$ particles of $(G_2)$

meaning,

$xn_2=k'n_1$ where $k'$ is an integer,

The relation states that exactly $xn_2$ particles of $G_1$ gas forms integral volume $(k'V)$ of $G_1$

As Avogadro said the relation is so simple taking into account the laws governing distances between particles, affecting volume

This simple relation for case 2 might exist in reality, but will be rare for all gases and scarcely plausible that integral volumes of other gas $G_2$ are formed by number of particles of $G_2$ exactly Integral multiple of number of particles Of $G_1$

This might be very rare relation to to true for all gas pairs, hence Avogadro assumed that case 1 is more plausible and hence hypothesised it

note: The theoretical proof backing up the hypothesis that equal volume of gases have equal number of particles was later given using KTG, also experimental evidence of hypothesis was found by studying effusion and diffusion of gases

After Considering Avogadro hypothesis to be true, Following deduction can be quickly made

1)The ratio of densities of Two gases will give ratio of their respective atomic masses,

because $\frac{\rho_1}{\rho_2}=\frac{\frac{M_1N_1}{V_1}}{\frac{M_2N_2}{V_2}}$

As

$\frac{N_1}{V_1}=\frac{N_2}{V_2}$ according to hypothesis, it follows

$\frac{\rho_1}{\rho_2}=\frac{M_1}{M_2}$

2)Experimentally ,The following data was available to Avogadro

$\rho_{oxygen}=1.10359$ $\rho_{hydrogen}=0.07321$

Hence

$\frac{\rho_{oxygen}}{\rho_{hydrogen}}=\frac{M_{oxygen}}{M_{hydrogen}}=\frac{1.10359}{0.07321}=15.074$

Hence Avogadro found that $M_{Oxygen}=15 \cdot M_{Hydrogen}$

similarly

$\frac{\rho_{nitrogen}}{\rho_{hydrogen}}=\frac{M_{nitrogen}}{M_{hydrogen}}=\frac{0.96913}{0.07321}=13.2381$

3)Now observing carefully, When a gas combines with two or more times volume of another gas, completely, It is now expected that resulting compound must form volume equal to that of first of these gases, as it is limiting factor for number of particles, example, when $V$ volume of $G_1$ gas react with $3V$ volume of $G_2$ gas, completely, Each particle of $G_1$ gas must combine with 3 particles of $G_2$, But experimental observations showed that it was not always true, example

2 volumes of Hydrogen gas react completely with 1 volume of oxygen gas to form 2 volume of water, Here it was expected that only 1 volume of water would be formed

But, Still being persistent About the Hypothesis to be true, It is almost natural to conclude that instead of hydrogen gas and oxygen gas being made of single elementary particle, they might be made up of two or more elementary particles forming one elementary entity, Which then further redivide into Elementary particles during reaction

Example If we consider Hydrogen to be made of two Hydrogen elementary particle formed 1 elementary entity "$H_2$" And similar for oxygen As "$O_2$", This consideration will now perfectly align with experimental results

That are

2V volume of Hydrogen gas react with V volume of Oxygen completely , Meaning,

2n entities of Hydrogen gas react completely with n entities of Oxygen ,Meaning

4n elementary particle particles of Hydrogen react completely with 2n elementary particles of oxygen

Notice there is a difference in how I used Elementary "Particles" and Elementary "Entities", In modern day definition ,Particles refer to Atoms, while Entities refer to molecules, There was a huge confusion in Amedeo Avogadro's original text regarding How he used terms like "Molecule"

As experimentally 2V volume of water is formed, It follows that 2n entities of water is formed, Giving a result that each 2 of Hydrogen Gas particles reacted with Each one of Oxygen gas particles to form 2n entities of water, Meaning every entity of water has composition $H_2O$

Notice, We would have supposed that elementary entity of Hydrogen gas would consist of 4 hydrogen particles and Elementary entity of Oxygen consist of 4 elementary particles of Oxygen, This would also have followed the experimental result

But according to Occam's razor, simplest theory of all theories, explaining all experimental results must be adopted, $H_2O$ composition is simpler that $H_4O_2$, Hence it must be adopted

Using modern techniques, like X-ray Crystallography and others, we have evidence that Composition of water is Indeed $H_2O$

This Hypothesis led Jean Perrin To calculate Avogadro Constant using Brownian motion, Which Was a significant step in Quantitative physical chemistry

References

Link to original paper: https://iiif.wellcomecollection.org/pdf/b24855169

Other sources: Wikipedia.org, britannica.com, https://web.lemoyne.edu/~giunta/

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