# Avogadro's Number Full

Fox and Hill, two noun-named professors at Georgia Tech, propose to define the kilogram in terms of a fixed value of Avogadro's number. Perhaps you and your students can determine why they chose the value they propose (602,214,141,070,409,084,099,072). Avogadro’s number is an absolute number: there are 6.022×10 23 elementary entities in 1 mole. This can also be written as 6.022×10 23 mol -1. The mass of one mole of a substance is equal to that substance’s molecular weight. Avogadro's number, or Avogadro's constant, is the number of particles found in one mole of a substance. It is the number of atoms in exactly 12 grams of carbon-12.This experimentally determined value is approximately 6.0221 x 10 23 particles per mole.

Contrary to the beliefs of generations of chemistry students, Avogadro’s number—the number of particles in a unit known as a mole—was not discovered by Amadeo Avogadro (1776-1856). Avogadro was a lawyer who became interested in mathematics and physics, and in 1820 he became the first professor of physics in Italy. Avogadro is most famous for his hypothesis that equal volumes of different gases at the same temperature and pressure contain the same number of particles.

The first person to estimate the actual number of particles in a given amount of a substance was Josef Loschmidt, an Austrian high school teacher who later became a professor at the University of Vienna. In 1865 Loschmidt used kinetic molecular theory to estimate the number of particles in one cubic centimeter of gas at standard conditions. This quantity is now known as the Loschmidt constant, and the accepted value of this constant is 2.6867773 x 10^{25} m^{-3}.

The term “Avogadro’s number” was first used by French physicist Jean Baptiste Perrin. In 1909 Perrin reported an estimate of Avogadro’s number based on his work on Brownian motion—the random movement of microscopic particles suspended in a liquid or gas. In the years since then, a variety of techniques have been used to estimate the magnitude of this fundamental constant.

### What Is Avogadro's Number

Accurate determinations of Avogadro’s number require the measurement of a single quantity on both the atomic and macroscopic scales using the same unit of measurement. This became possible for the first time when American physicist Robert Millikan measured the charge on an electron. 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 10^{23} particles per mole.

### 1 What Is Avogadro's Number

### Avogadro's Number Full

Another approach to determining Avogadro’s number starts with careful measurements of the density of an ultrapure sample of a material on the macroscopic scale. The density of this material on the atomic scale is then measured by using x-ray diffraction techniques to determine the number of atoms per unit cell in the crystal and the distance between the equivalent points that define the unit cell (see *Physical Review Letters,* 1974, 33, 464).