Avogadro constant - I can accept the number, if someone can show me how, over a hundred years ago, without having every really seen a molecule, this number could be derived. Obviously no one ever sat there and counted them but I find it hard to believe, they could have decided this without being able to see it.
"The charge on a mole of electrons had been known for some time and is the constant called the Faraday. The best estimate of the value of a Faraday, according to the National Institute of Standards and Technology (NIST), is 96,485.3383 coulombs per mole of electrons. The best estimate of the charge on an electron based on modern experiments is 1.60217653 x 10-19 coulombs per electron. If you divide the charge on a mole of electrons by the charge on a single electron you obtain a value of Avogadro’s number of 6.02214154 x 1023 particles per mole."