Experiment A9

Combining Ratios & Atoms

evidence of the former required the latter as explanation

nearing completion


With few exceptions, the new chemistry of Antoine Lavoisier (b1743, d1794) of Paris, was adopted by chemists everywhere.  With the nature of the airs, metals, and earths understood, chemists turned their attention to determining the composition of compounds, and the nature of what holds them together.  European chemists rapidly collected data based on the new definition of element.  They found that typically each substance was combined in only a single set ratio of component mass or volume (when constrained to constant temperature and pressure).  As we might expect in retrospect, there was some confusion caused by several complicating factors. 


Joseph Louis Proust (b1754, d1826; portrait at right→), teaching at Madrid in 1799 showed that the composition of copper carbonate is fixed, no matter where it is obtained or how it is synthesized.  Over the next 9 years he purified, analyzed and collecting data for numerous other compounds.  He suggested a new law of nature, the Law of Constant Proportions, which stated we must recognize an invisible hand which holds the balance in the formation of compounds.  A compound is a substance to which Nature assigns fixed ratios.  Proust proposed that the metals are permitted only two degrees of oxidation, a minimum and a maximum.  (Read Proust's paper on Copper compounds at Carmen Giunta's Classic Chemistry.)

BertholletClaude Louis Berthollet (←shown at left; b1748, d1822), a collaborator with Lavoisier on the new nomenclature, approached chemical composition in his books Recherches sur les lois de l'affinite (1801) and Essai de statique chimique chimique (1803) as a matter of chemical affinities similar to gravity.  Berthollet thought that compounds are always formed in very variable proportions, unless they are determined by special causes, such as crystallization, insolubility, or elasticity.  Believing that there is no difference between solutions and compounds, he argued that Proust's law of constant proportions was an accidental effect of saturated solutions.


John Dalton (b1766, d1844, portrait at right→) of Manchester, as part of a life-long series of weather observations and research on gases, speculated upon the nature and constitution of the atmosphere.  Fellow Englishman, Issac Newton, earlier developing the physics of a gas, treated it as an elastic fluid composed of small particles (or atoms) repelled by an inverse square force much as Newton had considered gravity as an attractive inverse square force.  It occurred to Dalton to contemplate the effect of the difference of size of the particles in such a fluid under different pressures and temperatures.  He tried to determine the relative sizes and weights of atoms from the numbers of atoms in a given volume.  This led to consideration of combinations of gases and the numbers of atoms in such combinations.

In 1801 Dalton applied the atomic concept to account for a mixture of gases exerting a pressure equal to the sum of their partial pressures.  (I.e., each gas exerts its own pressure independent of other gases.)  In 1803 he announced that the amount of gas dissolved in water from a mixture of gases is proportional to the partial pressure of that gas.

By 1808 Proust's Law of Constant Proportions had been accepted by most chemists.  But missing was any theoretical explanation for that empirical finding.

In studying two gases made of only Carbon and Hydrogen, olefiant gas and carburetted hydrogen, Dalton had found the latter had exactly twice as much Hydrogen in relation to equal amounts of Carbon.  After successfully applying his procedure to carbonic oxide, ammonia, and water, Dalton felt that he had sufficient insight to propose an explanation for Proust's Constant Proportions.  So in 1808 Dalton published New System of Chemical Philosophy claiming that if substances were assumed to be composed of small, indivisible particles called atoms, the experimental evidence of constant compound proportions could be explained.  Dalton suggested that compounds between two elements form so that one atom of one element unites with one, two, three, or more atoms of the other.  It logically followed from Dalton's atomic theory that compounds must therefore be formed in constant proportions.  Other chemists agreed and Dalton's atomic theory rapidly become the accepted as their working hypothesis.  (You may want to read an excerpt from A New System of Chemical Philosophy by Dalton, 1808.)

Dalton's Atomic Theory

In short, Dalton combined the Atomic Theory with Lavoisier's new definition of element, two ideas previous considered contradictory, to explain the Law of Constant Proportions.

Dalton listed the atomic weights of each element compared to the lightest element, Hydrogen.  In determining relative weights, Dalton relied on the results of quantitative analysis of compounds, and the assumed formulas for the compounds.  Dalton presumed the simplest of formulas:  thus water was composed of one atom Hydrogen to one atom of Oxygen, something which would soon be disputed based on volume ratios, but not established for another half century.

Dalton's atomic weights (1808)


















Gay-LussacJoseph Louis Gay-Lussac (b1778, d1850, shown at right→) in 1808 read before the Philomathic Society a claim that when held to constant temperature and pressure, the compounds of gaseous substances with each other are always formed in very simple ratios, so that representing one of the terms by unity, the other is 1, or 2, or at most 3. These ratios by volume are not observed with solid or liquid substances, nor when we consider weights. While Gay-Lussac pointed out that such simple ratios don't apply to solids or liquids, he and most chemists viewed these gas volume ratios as additional evidence generally supporting Dalton's atom theory.

Also in 1808 Scottish Thomas Thomson (b1773, d1852) and his English friend, William Hyde Wollaston (b1766, d1828) presented confirmation of the Law of Multiple Proportions:  they showed that when oxalic acid combines with potash and strontia to form two sets of salts, one of the salts has twice as much base as the other.  The Atomic Theory not only explained Proust's Law of Constant Composition, but also predicted the Law of Multiple Proportions:  when two compounds are formed from the same two elements, the weights of one element from each compound are in a simple ratio to each other when combining with a fixed weight of the other element.

The second and third volumes of Dalton's New System of Chemical Philosophy were published in 1810 and 1827.

The new definition of element by Lavoisier and the new application by Dalton of the ancient atom concept provided
Such major paradigm shifts are rare in science.  They involve turmoil where the future is largely uncertain.  Some people miss the value of potential changes and cling to the old ideas and methods.  They may be left behind.  Others find most exciting the exchange of new data, strange thoughts and even stranger implications.  There are often many new paths to follow, not all of which will turn out to be productive.  New vocabulary springs into use and other terms change meaning.  New leaders often emerge as others fall by the wayside.


To experimentally obtain the necessary chemical reagents, equipment, and facilities to personally perform all of the following chemical reactions and measurements would require a sizable financial investment and considerable time.  While that in itself would be of much value, what may be of more importance is to gain an understanding of how the revolutionary period spanning a lifetime from the last quarter of the 18th Century through the middle of the 19th Century provided the framework for our current understanding of our material world.  It might be much easier, less expensive, and less time consuming to accept observation and measurements such as they obtained and then do the thinking and analysis necessary for us to build our own understanding.

So you will find below carefully selected observations and data, free from the risks of corrosive chemicals, poisonous gases, explosions, incomplete reactions, and messes to properly dispose.  But to provide just a glimmer of what joy and excitement we will be missing, consider a brief description from the childhood of Ira Remsen:

While reading a textbook of chemistry I came upon the statement, nitric acid acts upon Copper.  I was getting tired of reading such absurd stuff and I was determined to see what this meant.  Copper was more or less familiar to me, for Copper cents (coins) were then in use.  I had seen a bottle marked nitric acid on a table in the doctor's office where I was then doing time.  I did not know its peculiarities, but the spirit of adventure was upon me.  Having nitric acid and Copper, I had only to learn what the words acted upon meant.  The statement nitric acid acts upon Copper would be something more than mere words.  All was still.  In the interest of knowledge I was even willing to sacrifice one of the few Copper cents then in my possession.  I put one of them on the table, opened the bottle marked nitric acid, poured some of the liquid on the copper and prepared to make an observation.  But what was this wonderful thing which I beheld?  The cent was already changed and it was no small change either.  A green-blue liquid formed and fumed over the cent and over the table.  The air in the neighborhood of the performance became colored dark red.  A great colored cloud arose.  This was disagreeable and suffocating.  How should I stop this?  I tried to get rid of the objectionable mess by picking it up and throwing it out of the window.  I learned another fact.  Nitric acid not only acts upon Copper, but it acts upon fingers.  The pain led to another unpremeditated experiment.  I drew my fingers across my trousers and another fact was discovered.  Nitric acid acts upon trousers.  Taking everything into consideration, that was the most impressive experiment and relatively probably the most costly experiment I have ever performed.  .  .  .  It was a revelation to me.  It resulted in a desire on my part to learn more about that remarkable kind of action.  Plainly, the only way to learn about it was to see its results, to experiment, to work in the laboratory.

The experiment we wish to accomplish is to determine the atomic weights of some of the elements for ourselves, using only typical data available to Dalton and the other chemists of their time.  We are NOT going to actually weigh atoms!  That wasn't possible in their time, and is rather challenging to do now (unless we use a trick like using electricity and our knowledge about electrons to count atoms).  What we hope to accomplish is to get a clear understanding of how Dalton and his peers produced atomic weights without actually weighing individual atoms.


Consider the following measurements, much of it provided in Gay-Lussac's 1808 paper:
  1. John Dalton suggested based on combining weights he measured, Hydrogen atoms are the lightest.  Below are measurements for forming water.  If more Oxygen is used, the excess Oxygen will remain.  Or if less oxygen is used, some of the Hydrogen will remain unreacted.  The excess can be identified by inserting a glowing splint.  Excess Hydrogen will produce a brief but loud bang, while excess Oxygen will result in the splint either glowing brighter or bursting back into flame with a weak pop.  The same ratio of combination can also be obtained by decomposing water be electrolysis and measuring the amounts of Hydrogen and Oxygen produced.  The volume ratios reported by Gay-Lussac are also listed.
    Composition of Water
    data from M. Humboldt, & Gay-Lussac Dalton
    water volume Hydrogen volume Oxygen weight Hydrogen weight Oxygen
    200 100 1.0 g 8.0 g
    1. First we need a formula for water.  Either accept Dalton's proposal of 1:1, or use the volume ratio to guess your own formula.

    2. Next adjust the weights so we have equal numbers of each kind of atom.  If you used Daltons formula of HO (one atom of Hydrogen for each atom of Oxygen) then the weights Dalton measured already have equal numbers of atoms.  But if you decided on a formula such as H2O (two atoms of Hydrogen for each atom of Oxygen) then we will need to double the the amount of Oxygen and the measured weight of Oxygen to calculate the weight of Oxygen which would have the same number of atoms as the Hydrogen.

    3. Scale both weights so the Hydrogen weight equals exactly ONE.  This set won't be needed unless you reduced the hydrogen weight (say to 1/2) to match the number of Oxygen atoms in the previous step.

    4. Take the weights of equal amounts of Hydrogen (set to 1) and Oxygen and start your list of atomic weights.

  2. Composition of Ammonia
    data from M. Amédée Berthollet Dalton
    ammonia volume Hydrogen volume Nitrogen weight Hydrogen weight Nitrogen
    300 100 1.0 g 4.7 g
    1. First we need a formula for ammonia.  You might wish to use Dalton's assumption of a 1:1 ratio or use the volume ratio to guess your own formula.

    2. Next adjust the weights so we have equal numbers of each kind of atom.  If you used Daltons formula of HN (one atom of Hydrogen for each atom of Nitrogen) then the weights Dalton measured already have equal numbers of atoms.  But if you decided on a formula such as H3N (three atoms of Hydrogen for each atom of Oxygen) then we will need to triple the the amount of Nitrogen and the measured weight of Nitrogen to calculate the weight of Nitrogen which would have the same number of atoms as the Hydrogen.

    3. Scale both weights so the Hydrogen weight equals exactly ONE.  This set won't be needed unless you reduced the hydrogen weight (say to 1/3) to match the number of Nitrogen atoms in the previous step.

    4. Add the weight of Nitrogen with the same number of atoms as in 1.0 g of Hydrogen to your list of atomic weights.

  3. Gay-Lussac noted that carbonic oxide gas can be prepared by distilling oxide of zinc and strongly calcined charcoal.  Today that is more common produced by burning charcoal briquettes in an abundance of air.  Since Carbon is a solid at room conditions so we can't know its volume as a gas, but Gay-Lussac calculated the volume of Oxygen compared the the volume of carbonic oxide gas produced.  If the gas is produced by burning charcoal, it needs to be done with excess Oxygen and then the remaining Oxygen measured and subtracted to determine the weight actually consumed.

    The reason for using excess Oxygen in the last investigation is that Carbon is also capable of forming a second compound when the Carbon is heated with very low concentrations of Oxygen.  Using the same weight of carbon, the volume of Oxygen consumed is half as much.
    Composition of compounds of Carbon with Oxygen
    data from M. Berthollet % calculated from densities
    volume Carbon volume Oxygen weight Carbon weight Oxygen
    for 100 carbonic oxide NA (a solid) 100 27.38 72.62
    for 100 carbonic oxide gas NA (a solid) 50 42.99 57.01
    So these are examples of two compounds with multiple proportions.  One has twice as much Oxygen as the other.
    1. First we need a formula for these two compounds.  Since we don't have volume ratios to give us a clue, we will either need to guess or use Dalton's assumption of a 1:1 ratio (CO) for one and 1:2 (CO2) for the other with twice as much Oxygen.  In either case we should hope to eventually get more information from other compounds which we hope will be logically consistent with our assumed formulae.  If it turns out inconsistent, we may need to return and try other formulae.

    2. Next adjust the weights so we have equal numbers of each kind of atom.  If you used CO (one atom of Carbon for each atom of Oxygen) then the weights as measured already have equal numbers of atoms.  But for the formulas CO2 (two atoms of Oxygen for each atom of Carbon) we will need to either double the the amount of Carbon and its measured weight or half the amount of Oxygen and its measured weight so we have weights of equal number of atoms.

    3. We already have an atomic weight for Oxygen from water, so scale both weights for the first compound until the Oxygen weight matches our atomic weight.  Add this weight of Carbon to our list of atomic weights.

    4. Do a similar scaling of the weights for the second compound until the Oxygen weight matches our atomic weight.  Check to see if this weight of Carbon matches what we just added to our list of atomic weights for the first compound.  If it doesn't search to figure out where we made an error.

  4. Composition of compounds of Nitrogen with Oxygen
    data from H. Davy % calculated using densities
    volume Nitrogen volume Oxygen weight Nitrogen weight Oxygen
    Nitrous oxide 100 49.5 63.30 36.70
    Nitrous gas 100 108.9 44.05 55.95
    Nitric acid 100 204.7 29.50 70.50
    Gay-Lussac noted that the first and the last of these calculated volume proportions differ only slightly from 100 to 50 and 100 to 200; it is only the second which diverges somewhat from 100 to 100. The difference, however, is not very great, and is such as we might expect as experimental error in experiments of this sort.  And furthermore, he presents additional data that burning the new combustible substance from potash in 100 parts by volume of nitrous gas, there remained over exactly 50 parts of Nitrogen, the weight of which, deducted from that of the nitrous gas (determined with great care by M. Berard at Arcueil), yields as a result that this gas is composed of equal parts by volume of Nitrogen and Oxygen.  So Gay-Lussac proposed the proportions by volume should be 50, 100, and 200 parts Oxygen.

    Repeat procedures from above to confirm that our atomic weights are logically consistent.

Compare your atomic weights with Dalton's list (above).

If you need course credit, use your observations recorded in your journal to construct a formal report.



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portions from a 1992 hypermedia stack
Lab A9 started 30 June 2007
latest revision 15 March 2009
by D Trapp
Mac made