Solutions to Problems with Avogador’s Number and The Modern Periodic Law of Elements
Published: September 24, 2010


“Reason must be our last and final guide in everything.” -John Locke


In this essay, I propose to rationally demonstrate solutions to two problems. One is that Avogadro’s number is inaccurate. The other is that the modern periodic law of the elements is false. Avogadro’s number, which is given as 6.0221367 x 1023, is based upon measurement of the wrong particle and is much too small to represent the number of atoms or molecules contained in a mole (mol) or gram (g) of substance. The periodic law of the elements is a guide to constructing a periodic table of the elements, which arranges the elements in order of their increasing atomic mass, or atomic weights, or atomic numbers. The modern periodic law states that: “The properties of elements are periodic functions of their atomic numbers.”1 Even though the elements can be arranged in increasing order of the above named means, I will show that the properties of the elements are not the functions of any one of those means. Elements are substances, such as hydrogen, oxygen, carbon, iron, and sulfur, that cannot be broken down into other substances by chemical or physical means. My rationally demonstrated solutions will proceed as follows. In Section I, I will state Amedeo Avogadro’s law of molecule numbers in gases and explain what molecules are. In Section II, I will discuss chemists’ classification and measurement of matter using the gram and the mole. In Section III, I will discuss John Dalton’s “one-atom element” theory. In Section IV, I will discuss Dmitri Mendeleev’s periodic law. In Section V, I’ll discuss Joseph John Thomson’s great blunder in constructing a false model of the atom. In Section VI, I will propose a new Avogadro’s number and periodic law of the elements.

I will adhere to John Locke’s maxim: “Reason must be our last and final guide in everything.”2 I will also adhere to the rationalist’s basic belief that there is no truth in contradictory statements. I will accept this Ayn Rand’s definition of science: “Science is systematic knowledge gained by the use of reason based on observation.”3


Section I

In 1811, the Italian chemist Amedeo Avogadro (1776-1856) proposed that: “Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.”4 This is called Avogadro’s law. Molecules are compounds of two are more atoms. Atoms are the smallest particles of matter that can exist, the ultimate and smallest division of matter. Matter is anything that takes up (or occupies) space, has mass, and reacts to gravity. Mass is the amount of matter that makes up an object. Since matter is made up of atoms, it is the number of atoms that make up an object. Since it is impossible for atoms to come into existence out of nothing or pass away into nothing, they are eternal and indestructible. This means that they cannot be created or destroyed. If matter is repeatedly cut up, the end result will be uncuttable particles of matter. The ancient Greek Atomist Democritus (c.460- c.370) named these particles atoma, a Greek word meaning “uncuttables.” The singular of atoma is atomos, the word from which our English word “atom” is taken. It is very important to understand that since the word “atom” means “uncuttable,” if the description of a particle does not fit this definition of the atom, it cannot be an atom.

To be precise, Atomists call the objects made up of atoms “material objects.” As they explain, “Material objects are of two kinds, atoms and compounds of atoms. The atoms themselves cannot be swamped by any force, for they are preserved indefinitely by their absolute solidity. ” In 1811, Avogador named the compounds of atoms “molecules”, to distinguish them from individual atoms. He believed that molecules are diatomic particles, being made up of only two atoms.


Section II

I will reiterate: All matter is made up of atoms. As the American physicist Paul Brandwein,et al, explains, “Chemists sometimes classify matter as elements, compounds, and mixtures. For example, iron and sulfur are elements. When you stir together some iron and sulfur, you have a mixture. A compound forms when iron and sulfur are heated together.”5 Keep in mind that all elements are molecules, not single atoms. No element can be validly identified as being a kind of atom. Atoms are the fundamental particles from which nature forms, increases, and sustains all elements, and into which nature again resolves them when they disintegrate or decay. Atoms vary in size, shape, texture, and weight, but not in substance. Since atoms do not vary in substance, the elements cannot be identified on the basis of being different kinds of atoms. Thus, there are no such elements as a hydrogen atom, oxygen atom, carbon atom, etc.

There are only such elements as a hydrogen molecule, oxygen molecule, carbon molecule, etc. The elements can be identified by their varying molecular weights. The molecular weight of an element is the weight of the small sample, or single part, of the element that shows the quality, nature, or characteristic of the whole element. The sample is usually a gram unit of the element. A gram is a unit of mass or weight in the metric system, a decimal system of measurement in which each unit is multiplied by 10 to obtain the next larger unit, or divided by 10 to obtain the next smaller unit. Being able to visualize a gram of substance can be a little difficult. One gram equals 1/4 of a teaspoon, two grams equals 1/2 of a teaspoon, and four grams equals 1 tablespoon. The gram (g) is the standard unit of mass and weight in the International System of Units, which is abbreviated as SI (in French, Systeme International d’Unites). The metric system was conceived in 1670 by Gabriel Mouton (1618-94), the Vicar of St. Paul’s Church in Lyons, France, and an astronomer. It was adopted by the French Science Academy in 1791.

In 1901 or 1902, chemists replaced the gram with the “mole” (mol) for measuring large quantities of particles that are very difficult or impossible to count in grams. It is a fundamental unit of the International System of Units. The word “mole” is derived from the German word “mol”, a shortened form of “molekulargewicht”, the word from which our English term “molecular weight” is taken. One mole is an amount of substance containing Avogadro’s number of atoms or molecules. This number, also known as Avogadro’s constant, is equal to 602,214,199,000,000,000,000,000, or more simply 6.02214199 x 1023. This number, when rounded, reads six hundred sextillion. It was calculated by the French physicist Jean Baptiste Perrin (1870-1942), who showed that cathode rays were made of electrons with negative electric charge. He computed Avogadro’s number through several methods, without even knowing the size of an atom or a molecule. As you can see, it would be impossible to count to Avogadro’s number. The best way to understand how Avogadro’s number is a measure of a mole is to visualize a mole as a pile of atoms or molecules equal to a gram of substance.

It is important to understand that the concept of a mole did not exist in Avogadro’s time. Perrin just named his Avogadro’s number in honor of Avogadro’s name. However, Avogadro did not hold Perrin’s conceptions of the atom and the molecule. To him, an atom was the smallest particle of matter, and a molecule was made up of two of these atoms.

He believed that no particle could be smaller than an atom. Contrary to this view, Perrin believed that electrons and protons are subatomic particles. His Avogadro’s number was computed on the basis of this erroneous belief, which is the main reason why the number is not a correct quantity of atoms or molecules contained in a mole of substance.

It must be understood that atoms are infinitesimal particles, immeasurably small. The mass and weight of any atom will always be less than any assignable quantities, whether measured in grams or moles.


Section III

In 1808, the British chemist John Dalton (1766-1844) published his book entitled the “New System of Chemical Philosophy”. In this book, he stated his atomic theory as follows:

1. All substances are made up of atoms.
2. Atoms of the same elements always weigh the same, and they are also alike in their other characteristics.
3. Atoms of one element are different in weight from those of other elements.
4. Atoms of different elements combine to form compounds.
5. Atoms are indivisible.

I have read statements by various scientists claiming that they found flaws in these statements of Dalton’s atomic theory. I found none of the claims to be credible. I will explain why later. However, I did find a really serious blunder that Dalton made involving his conception of the relationship between atoms and elements. He regarded each element as being a different kind of atom. He failed to realize that the elements are aggregates of molecules, not single atoms. His belief that each element is an atom is called his “one atom-element” theory. I call this absurd theory his “one atom-element” problem. It has persisted in the science community to this very day.

Dalton carried out numerous experiments in a laboratory trying to find out if atoms of different elements had different masses. As the English physicist Christopher Cooper explains, “Dalton proposed that each element has its own unique atom and that each compound is formed by a certain combination of atoms. He showed that the weights of atoms relative to each other could be found by weighing the elements that combined in particular compounds. The comparative weight of an atom could be found, but not the actual weight- a given atom could only be said to be so many times heavier than, for example, one of hydrogen, the lightest atom.”6

From his experiments, Dalton found that the so-called hydrogen atom and so-called oxygen atom combine in a ratio of 1 to 7 to make water. It was later found that the ratio is 1 to 8. Dalton reasoned that the hydrogen atom is 7 times lighter than the oxygen atom. Since he did not know the weight of a hydrogen atom, he assigned it the arbitrary weight of 1. He could’nt say how much it weighed in pounds or grams.

Dalton’s “one atom- element” theory and his so-called “hydrogen atom”, with its arbitrary weight of 1, became the standard for determining the weights of the other elements, regarded as single atoms.


Section IV

In 1869, the Russian chemist Dimitri Mendeleev (1834-1907) proposed the following periodic law of the elements: “The properties of elements are periodic functions of their atomic weights.”7 Atomic weight is the pull of gravity on an atom’s mass. Gravity is the mutual force of attraction that draws two masses together. It is a fundamental property of the atom. According to the English physicist, astronomer, and mathematician Isaac Newton (1642-1727), “Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.”8 I will reiterate: Atoms are the smallest particles of matter that can exist; the ultimate and smallest division of matter. They are immeasurably small.

How did Mendeleev know the atomic weights of the elements? He didn’t! He simply accepted Dalton’s idea of arbitrarily assigning the number 1 to the weight of 1 hydrogen atom, the lightest of the elements. He then was able to arrange the other elements in order from lightest to heaviest in relation to the weight of the hydrogen atom. For example, 1 oxygen atom weighs 8 times more than 1 hydrogen atom; carbon weighs twelve times more; sulfur weighs 16 times more; and so on.

When Mendeleev arranged the elements in order of their increasing atomic weight, he was actually arranging them in order of their increasing atomic mass instead. I will reiterate: Atomic weight is the pull of gravity on an atom’s mass. The mass of an atom is the same throughout the universe, but its weight varies from planet to planet. The moon’s gravity attracts masses with only 1/6 the force of Earth’s gravity, which has a force of 10 newtons. One newton equals the force needed to increase or decrease the velocity of a 1 kilogram object by 1 meter per second per second. One kilogram (kg.) equals 10 newtons. To find the weight of an atom, you must multiply its mass in grams by 10 (ten) newtons. Mendeleev nor any of his contemporaries knew the mass and weight of an individual atom, only relative elemental mass and weight. Without knowledge of the mass and weight of atoms, Mendeleev’s periodic law of the elements could’nt be used to guide him in arranging the elements in order of atomic weight, which is the weight of an individual atom. He used his knowledge of the relative mass and weights of the known elements of his day to create his periodic table. The mass weight of a sample piece of an element is its molecular weight, not its atomic weight. Mendeleev arranged the elements in order of their increasing mass molecular weight. He did not know the mass and weight of an individual molecule. All elements are compounds of molecules. Keep this fact in mind as you read the next Section of this essay.


Section V

In 1897, the British physicist Joseph John Thomson’s (1856-1940) made the detrimental blunder of constructing a model of the atom, showing it to have an internal structure. While researching electrical currents inside cathrode ray tubes, he observed that the rays were deflected by an electric field. He erroneously theorized that the rays were streams of small subatomic particles. He called them corpuscles, a Latin word meaning “small bodies”. He figured that corpuscles accounted for about one- thousandth of the mass of a “hydrogen atom” (1/1836 or 1/1837). He did realize that there is no such thing as a hydrogen atom. All elements are molecules or compounds of molecules. Thomson’s corpuscles were later named “electrons.”

In 1909, it was determined that an electron has a mass of 9.110 x 10-28 grams, which is 1/1837 of the mass of a proton. The proton was discovered in 1886 by the German physicist Eugene Goldstein, who observed that a cathode ray emits streams of positively charged particles. These particles are called protons, and they have a mass of 1.673 x 10-24 grams. They are crowded into the nucleus of the thom, the name I give to Thomson’s false model of the atom. A thom is a compound of molecules that are made up of tinier molecules called protons, neutrons, electrons, and quarks.

The neutron was discovered in 1932 by the British experimental physicist, James Chadwick (1891-1974), during his study of artificial radioactivity. The neutron is an uncharged particle that has a mass slightly greater than that of the proton, 1.675 x 10-24 grams.

In many experiments in physics, the weight of the entire nucleus of the thom is important. The thom is identified by the total number of protons and neutrons in its nucleus. This number is a mass number. The only part of the nucleus that is important to chemists is the proton that holds the electrons in orbit around the nucleus. For this reason, thoms are commonly identified in chemistry by the number of protons in the nucleus, which makes up about 99.9 percent of the mass of the thom. I call this number the “protonic number” of the element, to distinguish it from the atomic number of an element.

Another reason for identifying thoms by the protonic number is the existence of isotopes. Isotopes are thoms of neutrons in the nucleus and thus have different thomic weight. The thomic weight of the element is the average weight of the mixture of the element’s isotopes. The weights of the two main isotopes, deuterium and tritium, in thomic mass units are 1.0078232 and 2.0141022, respectively. The two weights give the average thomic weight of hydrogen, 1.00797. The hydrogen thom contains one proton, no neutrons, and one electron. It is the only element with no neutrons in the nucleus of its thoms.

It takes 1.67492729 x 1030 protons to equal one gram of substance. Being able to visualize a gram of substance can be a little difficult for non-scientists. One gram of a substance equals ¼ of a teaspoon; two grams of substance equals 1/2 of a teaspoon; four grams of substance equals 1 teaspoon; and 12 grams of a substance equals 1 tablespoon. In the United States, people generally do not think of measurements in grams, but rather in ounces. One gram is equal to 28 ½ ounce.


Section VI

In the introduction, I said that I would propose a new Avogadro’s number and a new periodic law of the elements. My new Avogadro’s number will be based upon the following facts:

  1. All matter is made up of atoms.
  2. Atoms are the smallest particles of matter that can exist; the ultimate and division of matter.
  3. Atoms are the only elementary particles.
  4. Matter can be adequately measured in units called “grams.”
  5. Atoms can neither be created nor destroyed.
  6. Atoms cannot undergo change.
  7. Being the smallest particles of matter that can exist, atoms are smaller than electrons.
  8. According to Albert Einstein, the mass of an electron can be converted into energy, which is regarded as having no mass.
  9. Thoms are the smallest compounds of molecules that produce and retain the properties of elements.
  10. An element is a thom that cannot be broken down into substances by chemical means or physical means.

As I explained in Section V, it has been determined that an electron has a mass of 9.110 x 10-28 grams, which is 1/2837 of the mass of a proton, not an atom. Since electrons can be seen in the form of cathode rays, and since atoms cannot be seen, not even with a powerful electron microscope that can magnify a specimen up to a million times, I believe that it’s reasonable to assign the average atom with a mass one million times smaller than that of an electron. So, I say that an atom has a mass of 9.110 x 10-34 grams. One gram of matter, represented by the number 1, divided by the mass of an atom, equals 1 x 1033 atoms. This number can be written with a 10 followed by 33 zeros. This number can be rounded off to: 1 followed by 34 zeros. (10,000000000,000,000,0 00,000,000,000,000,000).

This is my new Avogadro’s number. It takes ten decillion atoms to make up 1 gram of matter. It takes one hundred quadrillion diatomic molecules to do the same. This shows that the Avogadro’s number given by Perrin: 6.0221367 x 1023 (602,214,199,000,000,000, 000,000) is smaller than my new number. According to it, rounded (6 followed by 23 zeros), it takes six hundred sextillion thoms (misnamed an atom) to make up 1 mole, or “gram mole”. My new Avogadro’s number is truly about atoms, not thoms.

In the past, I used the Up quark, or U quark, to figure out a new Avogadro’s number. The Up quark is the smallest quark with a charge of + 2/3 and a mass of 0.003 GeV/c2. The proton is made up of 3 quarks (2 Up quarks and 1 down quark). I arbitrarily estimated that the average atom has a mass 1 thousand times smaller than an Up quark. I thought that the mass of an Up quark would be equivalent to 1 x 1030 grams. I failed to think about the fact that mass in grams could not be equated with mass in GeV/c2. I no longer use the Up quark as a basis for trying to estimate the mass of an atom. I find the electron a more adequate basis.

Most physicists and chemists today believe that electrons are elementary particles, thinking that they cannot be divided into smaller parts and are not made up of smaller particles. If this were true, electrons would be atoms. Most physicists and chemists today also believe that the mass of electrons can be converted into energy, which has no mass. If this is true, they are not elementary particles. I argue that they are very tiny molecules whose masses are made up eternal and indestructible atoms.

I will reiterate: Nothing exist but atoms and molecules, except the void. Energy is nothing but the activity of atoms and molecules. I will propose my new periodic law of the elements on the basis of this fact: The properties of the elements are ultimately the functions of the gravitational interaction of their constituent atoms. Their properties are not functions of their atomic weight or atomic numbers. Their constituent atoms have weight and vary in number, but it was the gravitational interaction of their constituent atoms that brought them into being and sustains them. They can be arranged in order of their increasing mass or weight to construct a periodic table, but their natures can only be understood by studying the properties of their constituent atoms and their gravitational interactions.



Before this essay, Avogadro’s number was calculated on the basis of the mass of the hydrogen thom, erroneously called a “hydrogen atom.” The most current periodic law of the elements was based upon the protonic number of the nucleus of a thom, which vary in number. I predict that my new Avogadro’s number based upon a true atomic number of the “gram” and my new periodic law of the elements upon the gravitational interaction of the atoms of which all thoms (or elements) are composed, will become new cornerstones of physics and chemistry.


  1. Surendra Verma, The Little Book of Scientific Principles, Theories, & Things (New York: Sterling Publishing Co., Inc., 2005), p. 106.
  2. John Locke, Essay Concerning Human Understanding, 1689, Book IV, Chapter XIX.
  3. Quoted in Leonard Peikoff, Objectivism: The Philosophy of Ayn Rand (New York: Dutton, 1991), p. 35.
  4. Lucretius: On The Nature of The Universe, Translated by R.E. Latham And Revised With A New Introduction And Notes by John Godwin (London: Penguin Books, Ltd, 1951), Book Two, Verse 483, p.22.
  5. Paul Brandwein, Matter, Its Forms and Changes (New York: Harcourt Brace Jovanovich, Inc. 1972), p. 36.
  6. Christopher Cooper, Matter (New York: Dorling Kindersley, Inc., 1992), p. 34.
  7. Verma, The Little Book of Scientific Principles, Theories, & Things, p. 106.
  8. Isaac Newton, Philosophiae Naturalis Principia Mathematica, 1687, Book 3.