Loschmidt number

Avogadro constant Na 6.0225-lO SmoM Number of particles per mol, formerly Loschmidt number... 

Loschmidt is remembered as a physicist for his determination of the Loschmidt number 61), the number of molecules in 1 mL of gas, but in 1861 he published a small booklet 62) in which he drew stmctural formulas for a large number of organic compounds. Two formulas of the Loschmidt type are reproduced in Figure 9. It is interesting to note that, in many ways, Loschmidt s formulae reflect Dalton s elemental symbols, and may, in fact, be based on Dalton s symbolism. 

Johann Josef Loschmidt (1821-1895) attended Prague University, and then at 21 went to Vienna to study first philosophy and mathematics, and then the natural sciences, physics and chemistry. After industrial ventures making potassium nitrate and oxalic acid among other products, he returned to Vienna as a concierge in the early 1850s, and then became a school teacher. Always attracted by theoretical problems, he is also known for his calculation in 1865 of the number of molecules in one mL of gas (the Loschmidt number ). In 1866, he became Privatdozent at the University... 

The number of molecules per cubic centimeter at standard temperature and pressure (STP), the Loschmidt number, is... 

A/l is Avogadro s or the Loschmidt number. A comparison between the energies in different units is given in Table 1.1. 

Johann Josef Loschmidt first calculated the value of Avogadro s number often referred to as the Loschmidt number in German-speaking countries Loschmidt constant now has another meaning). 

Loschmidt s constant (Loschmidt number) Symboi JVl. The number of particles per unit voiume of an ideai gas at STP. it has the value 2.686 763(23) x 10 m and was first worked out by the Bohemian physical chemist Joseph Loschmidt (1821-95). 

Nl Loschmidt number (the number of molecules in a gram-molecule)... 

N is the Loschmidt number while 0i and 02 are complex functions of the dipole moments and polarizabilities belonging to the molecule. The Kerr constant itself can be split into two terms of which one (Ki) merely expresses the anisotropy of the optical and electrical polarizability and is named the anisotropy term K, while the other represents the effect of possibly existing electric moments. This is called the dipole term K2. The two terms differ from each other in their dependence upon temperature the Kerr effect of dipole-free molecules is proportional to 1/T, that of dipole molecules is proportional to 1/T. ... 

N — Loschmidt number p == degree of polymerization, the corresponding work per ground mol will be... 

In this equation, R is the gas constant, T the absolute temperature, N the Loschmidt number and ri the viscosity of the solvent. 

With the mean free path thus calculated, it was possible to obtain a value for the number of molecules in unit volume, provided the diameter of the molecule was known. A method of estimating molecular diameters was suggested in 1865 by Johann Joseph Loschmidt (1821-1895), and the value he calculated for the number of molecules per cubic centimetre is sometimes called the Loschmidt number. It is now known that Loschmidt s value is too small by a factor of 30, This was due to Loschmidt using Mayer s value for the mean free path. Although Mayer s work was more recent than Maxwell s, his value for the mean free path was less accurate. 

Modern gas-diffusion medium in low-temperature fuel cells is typically a highly porous carbon paper with porosity in the range of sgdl = 0.6-0.8 and with the mean pore radius in the order of 10 pm (10 cm). By the order of magnitude, the mean free path of molecules in atmospheric pressure air is = l/(A LO-fci ), where Nl = 2.686 10 cm is the Loschmidt number (number of molecules in a cubic centimetre of atmospheric pressure gas at standard temperature) and akin — 10 cm is the molecular cross-section for kinetic collisions. With this data we get 3 10 cm, or 3 10 pm. Obviously, mean pore radius in the GDL is nearly 3 orders of magnitude greater than I f and the physical mechanism of molecule transport is binary molecular diffusion. 

Solution. Let us calculate first the number of molecules in 1 m of any gas at 1 atm and 0 C (which is called the Loschmidt number). This... 

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