ScienceWeek

ON JOSEPH LOSCHMIDT (1821-1895)

Joseph Johann Loschmidt (1821-1895) is claimed by both chemistry and physics, made important contributions to both sciences, but received more recognition from physicists than from chemists. A child of poor peasants, Loschmidt was educated by local clergy who recognized his brilliance, and in 1839 he was admitted to the German University in Prague. He completed his university studies in Vienna in 1843, but he was unable to obtain a teaching post. So Loschmidt went into the chemical business, was not successful, and after 10 years of it declared bankruptcy. He then decided to return to science, and in 1856 he qualified as a teacher and obtained a post teaching chemistry in a high school, the Vienna Realschule. He began research in chemistry and theoretical physics and started publishing scientific papers. Before long, at the age of 47, he became an assistant professor of physical chemistry at the University of Vienna.

Loschmidt was the first to use double and triple lines to represent the double and triple bonds in organic molecules. He recognized that most "aromatic compounds" (so-called because they were obtained from fragrant substances) could be derived from benzene by replacing one or more hydrogen atoms by other atoms or groups. The term "aromatic" thus came to be applied to any hydrocarbon that has the benzene ring as part of its structure (although the definition of "aromatic" in chemistry is now expanded: see *Note #1). Loschmidt was the first to state that in alcohols containing several OH groups, each OH group is attached to a different carbon atom. He published partial explanations of the structures of several organic and inorganic compounds, including benzene, toluene, and ozone, and he also recognized that an element could have several valences. Loschmidt anticipated the ring structure of benzene, so that some historians claim that the assertion of Friedrich Kekule (1829-1896) that idea of the benzene ring came to him in a dream is probably fallacious, since Kekule most likely read Loschmidt's published paper on benzene and benzene derivatives.

All this chemistry aside, what Loschmidt is most famous for is his work in physics: he made perhaps the first accurate calculations of the size of air molecules and of the number of molecules in a gram-mole (the quantity now commonly called the Avogadro number). Loschmidt arrived at a size somewhat less than 10^(-7) centimeters for the diameter of the molecules in air, which is close to the accepted value of 0.3 x 10^(-7). In German-speaking countries, what is elsewhere called Avogadro's number is called "Loschmidt's number".

The following points are made by A. Bader and L. Parker (Physics Today 2001 March):

1) The molecular size determinations made by Loschmidt quickly brought him recognition, and were the basis for his professorship at the University of Vienna. In 1870, moving to another area of research, Loschmidt published the most accurate measurements yet made of the interdiffusion of two gases. James Clerk Maxwell (1831-1879), following Loschmidt's lead, used these data to calculate the molecular diameters of various gases. Loschmidt rose rapidly at the University of Vienna, becoming a full professor in 1872. Loschmidt and his younger university colleague, Ludwig Boltzmann (1844-1906), a future giant of 19th century physics) became good friends, and Loschmidt's critique of Boltzmann's attempt to derive the second law of thermodynamics from kinetic theory became famous as the "*reversibility paradox". This led Boltzmann to his statistical concept of entropy as a logarithmic tally of the number of microscopic states corresponding to a given thermodynamic state.

2) In an era when atoms and molecules were not yet fully confirmed as entities, an estimate of their size was of profound importance. By 1808, Joseph-Louis Gay-Lussac (1778-1850) had established that when different gases combine chemically, the combining volumes of the gases are in the ratio of simple integers. In 1811, Amadeo Avogadro (1776-1856) interpreted this observation as implying that the number of molecules in a liter of gas at a given temperature and pressure is the same for all gases. But Avogadro was never able to determine that number: before it could be calculated, one would need to know the characteristic size and mass of a molecule. An immediate consequence of Loschmidt's calculation of the diameter of a molecule was a reasonably good estimate of molecular mass and of the number of molecules per unit volume of a gas at standard temperature and pressure (STP). Loschmidt was the first to publish corrections to the ideal gas law, corrections due to both finite molecular size and time delays during collision, that were compared with experiment. The inclusion of collisional time delay allowed Loschmidt to fit the experimental data, but his modified gas law missed an important correction discovered years later --the weak attractive force between molecules first proposed by Johannes van der Waals (1837-1923).

3) Loschmidt's estimate of approximately 1 nanometer for the typical diameter of an air molecule was too high, but only by a factor of 3. At present, the "Loschmidt number" has come to mean simply Avogadro's number, the number of molecules in a mole, but Boltzmann originally coined the term "Loschmidt's number" to signify the number of molecules per cubic centimeter for an ideal gas at standard temperature and pressure. The modern value for this is approximately 2.7 x 10^(19) per cubic centimeter.

4) The main source of errors in Loschmidt's estimate of the molecular diameter were errors in the measurements of the mean free path and in the estimate of the density of liquid air. These uncertainties may have been on Loschmidt's mind when he devised a very accurate experimental method for measuring another quantity closely related to molecular size, namely the diffusion coefficient governing the rate interdiffusion of one gas into another. His experimental diffusion results were published in 1870. In Loschmidt's experiments, two gases were initially separated by a horizontal partition in a vertical cylindrical container, with the lighter gas on top. The partition was removed and the two gases were permitted to diffuse into each other for a certain time, after which the fraction of mixing was carefully measured. By comparing the experimental results with Maxwell's mathematical solution for the time dependence of interdiffusion in such a setup, Loschmidt was able to determine diffusion coefficients with greater accuracy than any previous measurements had achieved.

5) The authors point out that the prominent chemists of Loschmidt's time rejected or ignored his pioneering work on chemical structures. In contrast, Josef Stefan (1835-1893), James Clerk Maxwell, Ludwig Boltzmann, and other leading physicists were very receptive to Loschmidt's determinations of molecular size and mass, and to his later work in physics. In his eulogy to Loschmidt, Boltzmann said of his good friend: "His work forms a mighty cornerstone that will be visible as long as science exists... Loschmidt's excessive modesty prevented his being appreciated as much as he could and should have been." [*Note #2]

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Notes:

Note #1: In chemistry, the term "aromaticity" currently refers to stability. A compound is aromatic if it is significantly more stable than would be predicted on the basis of the most stable Lewis structural formula written for it. This special stability is related to the number of electrons contained in a cyclic conjugated system. All compounds that possess benzene rings possess special stability and are classified as "benzenoid aromatic compounds". Certain other compounds lack a benzene ring yet satisfy the criterion of special stability, and these compounds are classified as "nonbenzenoid aromatic compounds".

reversibility paradox: The reversibility paradox is most simply stated as follows: Let us assume that an isolated system does indeed evolve from an initial state to a final state of higher entropy. But it is a given that the microscopic laws of mechanics are invariant under time reversal. Therefore, there must also exist an entropy-decreasing evolution which is set in motion simply by taking the final state of the previous evolution as the new initial state and then reversing all the individual molecular velocities. This time-reversed evolution would seem to violate the 2nd law of thermodynamics. Boltzmann evidently took the reversibility paradox very seriously, and it led him to the realization that a statistical interpretation of the 2nd law of thermodynamics was essential. Boltzmann ultimately proposed the his famous expression for entropy (carved into his gravestone at the Vienna Central Cemetery): S = klogW, where (S) is entropy; (W) is the number of microstates compatible with the values of the thermodynamic variables characterizing the macroscopic state of a system; and (k) is what we call "Boltzmann's constant".

Note #2: Presently, 135 years after Loschmidt's determination of molecular size, some relevant approximate numerical magnitudes ranges for gases at ordinary temperature and pressure are as follows:

molecular diameter: 10^(-8) to 10^(-7) centimeters.

molecular number density: 10^(19) molecules per cubic centimeter

average molecular speed: 10^(4) to 10^(5) centimeters per second.

average distance between molecules: 10^(-7) 10^(-6) centimeters.

collision rate per molecule: 10^(9) to 10^(10) collisions per second.

average time between collisions: 10^(-10) to 10^(-9) seconds.

average distance traveled between collisions (mean free path): 10^(-5) to 10^(-4) centimeters.