How Was Avogadro's Number Determined?

Introduction

• Avogadro's number is the number of particles in a mole.
• Contrary to popular belief, it was not discovered by Amadeo Avogadro.
• Avogadro was known for his hypothesis that equal volumes of different gases at the same temperature and pressure contain the same number of particles.

Historical Background

• Josef Loschmidt

  • An Austrian high school teacher, later professor at the University of Vienna.
  • Estimated the number of particles in a cubic centimeter of gas in 1865 using kinetic molecular theory.
  • This estimate is known as the Loschmidt constant, valued at 2.6867773 x 10^25 m^-3.

• Jean Baptiste Perrin

  • A French physicist who first used the term "Avogadro's number".
  • Estimated Avogadro’s number in 1909 using the study of Brownian motion.

Determination of Avogadro's Number

• Accurate determination requires measuring a quantity on both atomic and macroscopic scales with the same unit.

Robert Millikan's Contribution

• Measured the charge on an electron.
• The charge on a mole of electrons, known as the Faraday, was previously known.
• Current estimates:
  • Faraday: 96,485.3383 coulombs/mole of electrons.
  • Charge on an electron: 1.60217653 x 10^-19 coulombs/electron.
• Avogadro's number calculated as 6.02214154 x 10^23 particles per mole.

Modern Methods

• X-ray Diffraction Techniques
  • Involves measuring the density of an ultrapure sample both on macroscopic and atomic scales.
  • Uses x-ray diffraction to determine the number of atoms per unit cell and the distance between points defining the unit cell.

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These notes provide a comprehensive overview of how Avogadro's number was determined, highlighting key contributors and the methods used.