# How did 19th century scientists measure atomic and molecular weight?

#### RPinPA

Found myself wondering about this recently, though I can't recall the context. When Mendeleev proposed the periodic table of elements, I believe that it was known that atomic weights of the known elements were multiples of hydrogen's atomic weight. Presumably also with substances like oxygen where the molecule is $O_2$, scientists were able to determine this and knew to divide the molecular weight by 2 to get the atomic weight.

How? What macroscopic measurement do you do that tells you the atomic / molecular weight of an element?

I'm really fascinated by 19th-century science and some of the amazing things scientists were able to do with what we would now consider primitive instruments. The Cavendish gravity experiment and the Michelson-Morley speed of light experiment are astonishingly precise. But I know nothing about chemistry in that era (and very little about it now actually).

A more modern molecular weight question which I'll piggy-back in here: I was reading an article on the history of plastics, and it mentioned that for one particular plastic scientists were struggling to increase the molecular weight of the polymer. How can that matter to the macroscopic properties? It's a similar question of what macroscopic measurement do you do that tells you the molecular weight?

#### TeethWhitener

Gold Member
A very important early development came with John Dalton’s discovery of the law of multiple proportions. The wiki link gives a good example. Basically, you take two compounds made of the same elements (like CO and CO2) and look at the mass of each element required to make each compound. It turns out they’re always in integer proportions (in the case above, you get a 2:1 ratio of oxygen in CO2 vs. CO). Do this with enough compounds (and noting that the alkanes CnH2n+2 do a lot of the legwork) and you can get enough info to put together a table with the relative atomic weights of each of the elements.

Note that it wasn’t a perfect science at first: for example, if you assume that all elements have an atomic mass that is an integer multiple of hydrogen (known as Prout’s hypothesis), and you do this exercise with chlorine, you get an atomic mass of 35.5. This is of course because of the 3:1 ratio of chlorine-35 and chlorine-37 isotopes but early 19th century scientists had no way of knowing about the neutron.

Another example of the pitfalls that befell some of the early researchers was Dalton’s assertion that the molecular formula of water was HO, not H2O (along with mistakes in the stoichiometries of several other compounds). This error was corrected by Amedeo Avogadro (though his work was not immediately accepted), who hypothesized that the same number of molecules of different gases occupy the same volume. So for example, 1 mole of hydrogen gas occupies the same volume as 1 mole of oxygen gas, even though their masses are different. By reacting hydrogen and oxygen, he found that it took two volumes of hydrogen to react with one volume of oxygen and deduced that the true chemical formula of water was H2O.

#### tnich

Homework Helper
I don't know for sure, but I suspect that atomic weights of elements other than hydrogen were deduced from observing the ratios of the elements consumed (or produced) in chemical reactions.

#### TeethWhitener

Gold Member
A more modern molecular weight question which I'll piggy-back in here: I was reading an article on the history of plastics, and it mentioned that for one particular plastic scientists were struggling to increase the molecular weight of the polymer. How can that matter to the macroscopic properties? It's a similar question of what macroscopic measurement do you do that tells you the molecular weight?
In answer to this question, larger molecules generally exhibit stronger intermolecular forces—this is why methane and ethane are gases, hexane and octane are liquids, and eicosane and triacontane are solids at room temperature. Likewise, longer polymer chains (higher molecular weight for a given polymer) have higher melting points in addition to other macroscopic properties, particularly mechanical properties.

#### RPinPA

Wonderfully informative answers, thank you so much!

#### hilbert2

Gold Member
There are things like the Graham's law of effusion and the equation of state of an ideal gas, which can be derived from the kinetic theory of gases, and contain mole mass as one variable. Those can be used for determining the relative mole masses of chemical compounds. To find the actual mass per atom or molecule, you also need to somehow detemine Boltzmann's constant $k_B$ which is related to the ratio of absolute temperature and the average kinetic energy of a molecule in an ideal gas.

#### epenguin

Homework Helper
Gold Member
Gravimetric stoichiometry, and the sort of questions that come up numerous in homework help.
Gay-Lussac law and Avogadro's hypothesis, idem.
How aware the early 19th century chemists were of elementary kinetic theory of gases that I believe had been worked out Bernoulli and others during the previous century I am not sure.
Other empirical relations like Dulong-Petit specific heat law with only crude understanding or theory.
This story of atomic masses is also true of molecular masses.
Some of the textbook methods, like freezing point depression, came in later than I thought – rather towards the end of the 19th century.
And I think the Gibbs' theoretical framework that incorporates and explains them was even later. His work is not easy reading and was published obscurely and you can understand it was not the sort of thing that could be absorbed overnight by chemists if they ever heard of it.
However, I would like to know of good books that are a guide to this history.

The gravimetric methods are the most precise, but mostly they only give you "equivalent" masses, i.e, The atomic mass divided by a simple fraction. You can then find out what the fraction is if from one of the other methods you can get just an approximate atomic mass.And by atomic masses all they could do in the 19th century was get relative atomic masses – i.e. essentially the mass of an atom relative to that of a hydrogen atom. Absolute masses, i.e. how many grams is an atom, how many atoms are there in a gram, had to wait for the for the early 20th century with the work of Perrin & Einstein and others.The very first estimate of this absolute scale which was correct within an order of magnitude, came a little bit earlier from the study of gas viscosity.

"How did 19th century scientists measure atomic and molecular weight?"

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