Tuesday 16 December 2014

experimental physics - How was Avogadro's number first determined?


I read on Wikipedia how the numerical value of Avogadro's number can be found by doing an experiment, provided you have the numerical value of Faraday's constant; but it seems to me that Faraday's constant could not be known before Avogadro's number was as it's the electric charge per mole. (How could we know the charge of a single electron just by knowing the charge of a mole of electrons, without knowing the ratio of the number of particles in both?)


I just want to know the method physically used, and the reasoning and calculations done by the first person who found the number $6.0221417930\times10^{23}$ (or however accurate it was first discovered to be).


Note: I see on the Wikipedia page for Avogadro constant that the numerical value was first obtained by "Johann Josef Loschmidt who, in 1865, estimated the average diameter of the molecules in air by a method that is equivalent to calculating the number of particles in a given volume of gas;" but I can't access any of the original sources that are cited. Can somebody explain it to me, or else give an accessible link so I can read about what exactly Loschmidt did?



Answer



The first estimate of Avogadro's number was made by a monk named Chrysostomus Magnenus in 1646. He burned a grain of incense in an abandoned church and assumed that there was one 'atom' of incense in his nose at soon as he could faintly smell it; He then compared the volume of the cavity of his nose with the volume of the church. In modern language, the result of his experiment was $N_A \ge 10^{22}$ ... quite amazing given the primitive setup.


Please remember that the year is 1646; the 'atoms' refer to Demokrit's ancient theory of indivisible units, not to atoms in our modern sense. I have this information from a physical chemistry lecture by Martin Quack at the ETH Zurich. Here are further references (see notes to page 4, in German): http://edoc.bbaw.de/volltexte/2007/477/pdf/23uFBK9ncwM.pdf



The first modern estimate was made by Loschmidt in 1865. He compared the mean free path of molecules in the gas phase to their liquid phase. He obtained the mean free path by measuring the viscosity of the gas and assumed that the liquid consists of densely packed spheres. He obtained $N_A \approx 4.7 \times 10^{23}$ compared to the modern value $N_A = 6.022 \times 10^{23}$.


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