Size and Number of Molecules
It is interesting to view the particles of gas more intimately.
The velocity of a molecule of gas depends upon its mass. At the temperature of melting ice, hydrogen molecules have an average velocity of about one mile per second. Oxygen molecules being about sixteen times heavier travel about one fourth as fast as hydrogen molecules. These velocities are of the order of magnitude of projectiles fired from guns. It is fascinating to think of the nitrogen and oxygen molecules of the air about us moving between collisions with the velocities of bullets. They are striking our faces with these velocities and it is obvious that we should be thankful for their very small mechanical energy. We cannot conceive the smallness of the mass of a hydrogen molecule. Its mass is related to that of a baseball about as the mass of the baseball is to that of the Earth. There are about 102.5 molecules of hydrogen per ounce of the gas, or 10 million billion billion molecules or 10 trillion trillion molecules per ounce. The reader may take his choice of these numbers, but it is likely that the baseball comparison of relative mass gives a better idea of the size than the foregoing numbers. The diameter of the hydrogen molecule is less than ten billionths of an inch (8.5 X 10-9 inch). Particles must be a thousand times larger to be visible under the most powerful microscope.
Perhaps some idea of the number of molecules in an ounce of hydrogen gas might be obtained if we set out to count them.
There are about two billion persons on Earth. Suppose each was able to count 100 molecules per minute continuously. It would take the entire population of the Earth one hundred million years to count the molecules in an ounce of hydrogen gas. The mass of the Earth is again inconceivably greater than the mass of hydrogen weighing an ounce at the Earth’s surface, so it is seen that the number of molecules in the Earth alone is quite beyond comprehension. Similarly the greatest known distances in the stellar universe are inconceivably large. The human being is puny indeed and his mind can never comprehend the picture in its entirety. Nevertheless, we may enjoy knowing that there will always be awesome magnitudes to contemplate when we desire to exercise our imagination. There would be a maximum of about 7 billion molecules in a single row of them five feet long and it would take a person a lifetime to count the number in this short row of molecules in “single file.”
The Statistical Method
In dealing with molecules and other minute particles of matter which are shooting about as in the case of a gas confined in a vessel, we cannot arrive at any definite conclusion without studying averages. A single molecule, if we take averages, collides billions of times per second. If we direct our mind’s eye upon anyone molecule of a gas, we will find that its path is hap-hazard, unpredictable, and quite accidental. The same is true of the course of life of any human being. However, the insurance companies by observing a large number of persons can make sufficiently accurate predictions upon which to base a sound business. Anyone of us may die the next moment, or fall out of a window tomorrow, or collide with a street-car the next day. When an individual will marry, how many children he will have, or how much money he will acquire, only the future can tell us. No one can predict what will happen in a particular case, but from adequate records of a sufficient number of cases a safe prediction can be made based upon the” law of averages.” Many applications daily are now made of the results of statistics and science has successfully utilized the statistical method in various ways.
Maxwell (1841-1879) was the next great mathematical physicist after Newton to greatly change the course of scientific thought. Although he has greater scientific achievements to his credit, he placed the kinetic theory of gases on a firm foundation from which it has not been shaken, by developing the statistical method. He applied natural laws to the individual molecules, but without attempting to follow an individual he gave his attention to totality. It has been seen that the number of molecules in even a small quantity of matter is very great; therefore, we can have faith in the law of averages.
It is certain that the movements of molecules of a gas depend upon less complicated factors than the lives and activities of human beings. All molecules of the same element or gas have equal masses, with slight exceptions of no consequence at this time. The kinetic energy of anyone is determined by its mass and velocity. The mean velocity of the molecule, based upon the study of the combined effect of the billions of molecules, is a very definite and constant value for any given set of conditions. In fact, about all we must convince ourselves of in order to have faith in the statistical method as applied to gases, is that the rate of collision of molecules is constant for a given pressure, volume, temperature and gas.
Perhaps it will aid the reader to have faith if we revert momentarily to the number of molecules. A minute sphere two thousandths of an inch in diameter is about as small an object as we can see with the unaided eye at a distance of one foot. If this sphere were filled with gas at atmospheric pressure and of ordinary temperature, it would contain about 2000 billion molecules. Expressed in another way this number is equivalent to two million-million. Counting at the rate of 100 per minute for the usual working hours throughout a year, it takes a person a lifetime to count a billion. At this rate it would take 2000 persons their entire lifetime to count the molecules in that minute sphere two thousandths of an inch in diameter. Insurance can be safely based on the statistics of a number of persons, relatively few compared with the number of molecules in a sphere invisible to the unaided eye. Considering this fact along with the more complex vagaries of human beings as compared with those of molecules, it is seen that we can have utmost faith in the constancy of the results of the statisical method as applied to molecules of matter. Maxwell established these facts beyond question.
Brownian Movements
If we suspend in air an object easily visible to the unaided eye, it will be subjected to collisions from all directions, of molecules of the gases in the atmosphere. But we do not see it move here and there because it is being bumped from all directions. The number of molecules colliding with it per second is inconceivably large. Even in the smallest part of a second necessary for our consciousness to note a movement of this small suspended object, it would receive billions of impacts. The force upon it would be equal in all directions owing to the application of the law of averages so that even if it had no mass, it would not be moved appreciably.However, if we reduce the size of this suspended object, we should be able to arrive at a point where there is not a sufficient number of collisions from all directions for the effect to be equalized on all sides. In other words, the particle would be subjected to different forces from various sides and we would expect it to be bumped here and there in a haphazard fashion. Brown (1773-1858), a botanist, while examining under a microscope some liquids containing particles of pollen about one thousandth of an inch in diameter, noticed that these particles moved irregularly. He also noticed that the movements were more conspicuous for the smaller particles. Brown did not explain this, but, scientist that he was, he recorded his keen observations.With the establishment of any new principles and generalizations which are shown to be sound, many of the observed facts of past records are explained. Brown’s observations were to await the kinetic theory of matter before true light could be shed upon them. Hence, about fifty years later the Brownian movements were shown to be due to the impacts of molecules of the liquid in which the pollen particles were suspended. The same kind of movements have since been demonstrated in gases. It has been shown that fine particles of matter, such as gamboge suspended in water, obey the same laws that have been applied successfully to molecules. Some of this work has provided experimental foundation for the theory that the average energy of motion of the particles or molecules of a mass of matter depends only upon the temperature of the matter and not upon the mass of the particles. It was also shown that these particles, although very much larger than molecules, had an average energy of rotation equal to their average energy of translation. This also added support to the prevalent theory.
It is seen that the study of Brownian movements contributed much toward the establishment of the kinetic theory of matter.