Popular Science Monthly/Volume 15/August 1879/The Molecular Theory
|THE MOLECULAR THEORY.|
By LE ROY C. COOLEY, Ph. D.
THE idea that matter is an aggregate of minute particles, each of which possesses all the essential properties of the mass, is as old as Democritus, but it was left for the present century to crystallize the conception of the atom in clear and accurate expression. The atomic theory, revived and vitalized by the illustrious Dalton, has not simply been able to survive the conflicts in which many an older theory has been wrecked: it has itself been a prime mover of revolutions. It is doubtful whether without it the recent advances in chemical and physical science could have been made.
But the atom in chemistry is not the atom in physics; they are of a different order. When the idea of a chemical atom came to be clearly conceived so that atom could be defined, as it is, to mean the smallest particle of an elementary substance which can enter into the composition of a compound, the most natural, if not, indeed, the inevitable corollary would be that the compound itself must be made up of parts, each of which, containing only the minimum number of its constituent atoms competent to give it character, must be the smallest particle of that substance which can possibly exist. To distinguish this minutest portion of a substance from the chemical atoms of which it is composed, the French called it the molecule—literally the little mass; and this word molecule, homeless in the English language less than one hundred years ago, expresses an idea which now lies at the foundation of modern physics.
It has been said that the science of astronomy is the demonstration of the law of gravitation. Indeed, what evidence have we of the truth of Newton's grand generalization, except that it explains the phenomena of the skies? So, in the outset, we may say that the science of physics is the demonstration of the molecular theory of the constitution of matter, since it explains phenomena, suggests research, directs experiment, classifies and unitizes wide ranges of apparently diverse results, to an extent unparalleled by any other.
This theory boldly affirms a limit to the divisibility of matter, and thus seems to defy the logic of the metaphysician, who, passing the limit set by the necessary imperfections of manipulation, carries the process of subdivision mentally downward through the scale of littleness, until, finding no place where his conception of subdivision must halt, declares that no limit exists. But the physicist does not deny the logic of the metaphysician; he simply remembers that mental conceptions need not of necessity represent the realities of nature's processes, in the subdivision of matter. He claims that the line which may be mentally thrust through the minutest particle of matter is not a needle nor a knife—that it is the mathematician's line as immaterial as space—and that the thrusting of such a line can accomplish no division. He claims that, applicable as it may be to space, such logic need not bind the physicist who studies the constitution of bodies which inhabit space.
Therefore, unconcerned about the abstract question of divisibility, the physicist anxiously inquires whether the phenomena of the material world can afford any testimony in regard to the ultimate constitution of bodies. And the molecular theory may be regarded as an induction from a multitude of observed facts—a generalization reached by a careful comparison of many established principles. The object of the present paper is to present the theory in this light. To exhaust the evidence, however, by this method would be to present the science of modern physics complete, a task impossible at a single sitting.
The three fundamental conceptions embodied in the molecular theory are: the existence of molecules, the existence of molecular spaces, and the existence of molecular motions.
Now, there may be phenomena which declare the existence of molecules without touching the question of molecular space or of molecular motion, and proofs both of the existence of molecules and of molecular spaces may be altogether silent on the question of rest or motion. But notice: whatever evidence we have of the existence of intervals between the ultimate parts of a body is equally evidence of the existence of molecules, and whatever phenomena indicate the existence of motion among these interior parts of a body do equally affirm the existence both of molecules and of molecular spaces. If, then, the three classes of phenomena be presented as bearing first upon the molecule, second upon molecular spaces, and third upon molecular motion, the testimony will be continuous and cumulative.
First, then, as to the existence of molecules. We will confine our attention to two sources of evidence—the phenomena of divisibility and of chemical synthesis.
Is it possible, by continued subdivision, to reach a particle the division of which would put an end to the existence of the substance—not in the sense of annihilation, but, in other words, to reach a particle whose division compels a substance to suffer death by yielding up those identifying properties by which alone we distinguish it from other kinds of matter?
A piece of marble may be crushed and reduced to an almost impalpable powder, and yet, on examination, each little grain is found to be an angular block of stone, lacking no property of the original block except its size and form. The same may be said of other solids. Even ice, keep its temperature low enough, may be reduced to microscopic fineness, and each little particle, notwithstanding its minuteness, will be a block of ice. Nay, more; when by such mechanical means subdivision can be carried no further, we may resort to a gentle heat and find these microscopic blocks crumbling into fragments finer still; for what is melting but a process of division? In it, particles simply fall apart because the ties of cohesion are sundered by the heat, and the liquid is the same substance, differing from the impalpable powder only in the mobility due to its finer state of division. Now touch the liquid with a somewhat intenser heat. We find that the water is converted into steam, becoming invisible, and that the water-gas occupies a volume seventeen hundred times larger than did the water which it represents. However remarkable this change, yet it does not touch that which gives character to the substance. In all its essential properties it is water still. Furthermore, not the slightest addition or subtraction has been made. The process, in all its steps, from the original block of ice to the seventeen-hundred-fold volume of invisible vapor, is simply a process of division.
Now endeavor to carry the subdivision further. It may be that a fiercer heat will be a keener edge to cleave the invisible particles of water-gas. Thanks to Professor Chandler, who has taught us how to apply the requisite heat without at the time introducing a chemical attraction, so that we may be left confident that, whatever the result, it is accomplished by the same agents by which our previous subdivisions have been made.
In this experiment the steam is passed into a platinum flask, which is kept red-hot. From this flask a delivery tube conveys it to a jar designed to receive the products of the experiment. The invisible steam enters the platinum flask; an invisible gas also passes onward to be caught in the receiver; but afterward, on bringing a flame to the mouth of this receiver, an explosion declares that its contents are water-gas no longer—that a mixture of hydrogen and oxygen has taken its place. The steam particles are evidently broken by the heat. But mark the result: the fragments are no longer particles of water. The red heat has dissected the steam particles, and revealed the fact that they consist of still smaller pieces of hydrogen and oxygen.
In the form of steam, therefore, water is in its finest possible state of division, for to divide it further is to compel it to cease to exist as water. We are therefore entitled to declare that this substance consists of ultimate particles, which can not be divided without changing them into other kinds of matter. These are its molecules. Next, in the light of chemical synthesis, also, we may see the existence of these ultimate particles.
Hydrogen and oxygen are the inevitable constituents of water, and two volumes of hydrogen to one volume of oxygen are the invariable proportions. No human agency can obtain water by combining any other elements, nor by combining these in any other proportions.
These are facts confirmed by all experience. Nevertheless, it matters not how little oxygen is taken, provided only that the proper proportion of hydrogen is supplied. Then let us conceive the least possible portion of oxygen. Let the mind wrestle with the conception and reduce the volume of this gas until it is fixed at the smallest that can take part in a chemical action. Then conceive it combined with a volume of hydrogen twice as great. We may contemplate the infinitesimal droplet of water so produced, but to conceive a droplet any smaller is impossible, since this one contains no more than the least possible portions of its elements. To break this droplet of water would be to reduce it to fragments of hydrogen and oxygen. Again, then, do we find our minds in the presence of particles which can not be divided except at the sacrifice of their identity—in other words, in the presence of molecules.
But if molecules exist, the second question at once arises, Are they so closely packed as to constitute a continuous mass, or are they separated by intervening spaces?
A second class of phenomena directs our judgment here. We might detail the mathematical investigation by Cauchy, a third of a century ago, by which he demonstrated the impossibility of the dispersion of light in a substance whose minutest parts are absolutely homogeneous. It was proved that dispersion happens only on condition that "two contiguous portions of the medium, whose dimensions are moderately small fractions of a wave-length of light, are dissimilar." The molecules with intervening spaces would realize such dissimilarity.
But, confining ourselves to the experimental side of the problem, we find a variety of familiar phenomena ready to bear witness to this structure. Among them are porosity, expansion and change of physical condition, and the diffusion of vapors.
In regard to porosity, an old and homely experiment will give us a starting-point. We take a tall and narrow glass jar and fill it so completely with alcohol that the addition of a single drop will endanger an overflow. The jar appears to be full of a perfectly homogeneous liquor. But if a sheet of cotton wool, whose fibers have been previously well loosened, be at hand, fragment after fragment may, with care, be slowly introduced, without causing the overflow of a single drop, until the jar appears to be filled with moistened cotton instead of with alcohol. We have before us the surprising appearance of two bodies filling the same space at the same moment. Surely, however, we are not at liberty to adopt this explanation. For what should we call that which has no power to exclude another from the space which it occupies? To call it matter is to obliterate all distinction between matter and space. We are impelled to seek another explanation, and we find one more acceptable in the hypothesis that neither of the two bodies wholly fills the space which it appears to occupy—that spaces, too minute for even microscopic vision to detect, intervene between the ultimate particles of both, and to such an extent that these material particles of each find a habitation in the spaces of the other. Moreover, this experiment is but one of a large class, which all alike present the appearance of two or more bodies existing at the same time in the same place. And this phenomenon is a symbol which, translated, declares the existence of intervening spaces between the ultimate parts of which bodies of matter are composed. In regard to expansion and change of form, one of the most familiar and universal effects is the expansion of bodies by heat, and the most obvious classification of material objects is into three physical forms—the solid, the liquid, and the gaseous. We have only to admit the existence of molecules and of molecular spaces, and expansion can be defined at once to be the enlargement of these spaces under the influence of a force which drives the molecules asunder. Moreover, since distance is known to control the influence of attraction, it is plain that the melting of a solid and the vaporization of a liquid would be the necessary consequences of increasing the molecular distances, until cohesion is, in the one case nearly, and in the second case altogether, overcome. The existence of matter in three physical forms, and its changes from one to another under the influence of varying temperature, here find a most happy explanation.
But there follows a most important inference. If the gaseous form of matter is due to the separation of its molecules, then how enormously must their distances asunder exceed the diameters of the molecules themselves! For example, a cubic inch of water becomes about seventeen hundred cubic inches of steam. If this increase of volume is due to the enlargement of molecular spaces, how small a fraction of the vapor volume can consist of the material molecules! Can any experiment be brought to our relief, and furnish any solid ground on which we may stand and check the theory by testing the truth of this consequence? In "The New Chemistry," its author gives the following elegant description of an experiment on the diffusion of vapors:
"We have here a glass globe, provided with the necessary mountings—a stopcock, a pressure-gauge, and a thermometer, and which we will assume has a capacity of one cubic foot.
"Into this globe we will first pour one cubic inch of water, and in order to reduce the conditions to the simplest possible, we will connect the globe with our air-pumps and exhaust the air, although, as it will soon appear, this is not necessary for the success of our experiment. Exposing next the globe to the temperature of boiling water, the liquid will evaporate, and we shall have our vessel filled with ordinary steam. If, now, that cubic foot of space is really packed close with the material which we call water—if there is no break in the continuity of the aqueous mass, we should expect that the vapor would fill the space to the exclusion of everything else, or at least would fill it with a certain degree of energy which must he overcome before any other vapor could be forced in. Now what is the case? The stopcock of the globe is so arranged that we can introduce into it an additional quantity of any liquid on which we desire to experiment without otherwise opening the vessel. If, then, by this means, we add more water, the additional quantity will not evaporate, provided the temperature be kept at the boiling-point. Let us next, however, add a quantity of alcohol, and what do we find? Why, not only that this immediately evaporates, but we find that just as much alcohol-vapor will be formed as if no steam were present. The presence of the steam does not interfere in the least degree with the expansion of liquid alcohol into alcohol-vapor. The only difference which we observe is that the alcohol expands more slowly into the aqueous vapor than it would into a vacuum. If, now that the globe is filled with aqueous vapor and alcohol-vapor at the same time, each acting in all respects as if it occupied the space alone, we add a quantity of ether, we shall have the same phenomena repeated. The ether will expand and fill the space with its vapor, and the globe will hold just as much ether-vapor as if neither of the other two were present; and so we might go on, as far as we know, indefinitely. There is not here a chemical union between the several vapors, and we can not in any sense regard the space as filled with a compound of the three. It contains all three at the same time, each acting as if it were the sole occupant of the space."
Now these experimental results find an explanation nowhere else but in the inference, previously made, that molecular spaces do exist, and that they are so relatively large that the molecules of each gas find, in the spaces between the particles of all the others, abundant room to manifest all their characters.
If, now, we turn from vapors to the examination of permanent gases, we find a kindred action. Moreover, it is an action which not only confirms our evidence of the existence of molecules and molecular spaces, but, as we shall see in the sequel, in addition thereto suggests an answer to this important question in the history of molecules—are they in motion or at rest?
Hydrogen gas is sixteen times lighter than oxygen. Let us bring the open mouth of an inverted jar filled with hydrogen down upon the open mouth of a similar jar filled with oxygen. By this means we obtain a single cylinder of gas, the lower half of which consists of the heavier oxygen, and the upper half of the lighter hydrogen, the two gases being in contact only at their surfaces in the middle of the column. Their relative weights would lead us to expect them to maintain these positions; but the well-known properties of these gases enable us to learn that they do not. Neither one alone is explosive; their mixture is. Now, after a time, if we separate the jars and bring a flame to the mouth of the lower one, and then to the mouth of the upper one, two successive explosions occur, declaring that both jars contain a mixture of the gases. What must have happened? Evidently a portion of the heavier gas has risen into the upper jar, and a portion of the lighter gas has fallen into the lower jar, and this too, notwithstanding the fact that their difference in weight is more than a third greater than that of lead and water. A further study of this phenomenon reveals the significant fact that just as much of each gas diffuses into the space of the other as would expand into a vacuum of the same size. In fact each gas is, at all temperatures, a vacuum to every other. This fact remains an unsolved mystery, except we admit the existence of molecules and of molecular spaces far outmeasuring the molecules themselves.
Vapors and permanent gases are, therefore, not unlike in this respect. But when we compare this diffusion of the latter with the production and commingling of the former, as shown in the globe experiment, we discover this difference: whereas the molecules of the vapor are driven into mixture by the application of heat, those of the permanent gases spring spontaneously each into the spaces of the other without it. Plainly there exists among the molecules of the gases at low temperature an energy to drive them asunder, such as must be introduced by artificial means among those of vapors to enable them to manifest the same action in the same degree. We need to say, "in the same degree," for even liquids do spring into the gaseous form and mingle their vapors with other gases at common temperatures. This is evaporation. And when we remember, further, that many solids, notably ice, camphor, iodine, yield vapors to the atmosphere on similar exposure thereto, we can feel justified in saying that there exists in gaseous and liquid and solid bodies alike an energy by which their molecules are urged asunder.
This molecular energy bears the closest relationship to heat. Of this the facts already stated are sufficient evidence. Every variation in one is accompanied by a corresponding variation in the other. Whenever heat is expended this molecular energy in the body receiving it is increased. Whenever a body of gas, freed from opposing pressures, expands, in obedience to this molecular agency, its own temperature is reduced. Moreover, the most exact quantitative relation can be traced. This molecular energy and heat are, therefore, correlative. All this is suggested by the facts of expansion, vaporization, and diffusion. But I have no time to give even an outline of the classic researches of Rumford, Mayer, Joule, and others, which prove that heat and molecular energy is the energy of molecules in motion.
Molecules, molecular space, and molecular motions—these three conceptions stand as the modern translation of the symbols on which the facts in regard to the constitution of matter are written. According to the theory, in every material body these three fundamental elements are embodied. It consists of particles which can not be divided without changing the nature of the substance, separated by distances in comparison with which their own diameters are sometimes as insignificant as are the diameters of planets in comparison with their immense solar distances, and finally in motion, inconceivably rapid, and never ceasing. Such is the molecular theory of matter, in its most general form of expression. And in this form it seems destined to do for the science of physics what has been done for chemistry by the atomic theory, and for astronomy by the theory of gravitation. It seems competent to bring all branches into harmonious relation as constituents of a single science. It may do this even if the mathematical measurements of the magnitudes it describes should prove to be beyond the reach of human skill.
But, if molecules exist, what are their masses and their diameters? If they are not in contact, what is the measure of their separation; and, if in motion, with what velocity? These are legitimate subjects of research suggested by the theory itself, and no less important in the science of physics than the problems of astronomical magnitudes are in astronomy. It is, therefore, not strange that the best intellects among experimental and mathematical philosophers should be found bending their energies toward the solution of these problems. Already very wonderful progress has been made, and numerical values are assigned to these molecular magnitudes, in some cases with great confidence in their accuracy, and in other cases provisionally, awaiting better and more extended means of research. For example, Dr. Joule tells us that the hydrogen molecule is darting through the molecular spaces of this gas at the rate of 6,099 feet a second; and Clerk Maxwell, that the molecules of oxygen move at the more sluggish rate of about 1,525 feet a second. We are further informed that the distance from center to center of the molecules of a gas is probably about 800000 of an inch. Different methods of investigation agree tolerably well in pointing to 30000000 f a millimetre as a fair approximation toward the diameter of a molecule—that is to say, about 760,000,000 of these bodies lying side by side would bridge the space of a single inch.
These magnitudes are of an order which only modern science has ever asked the intellect of man to contemplate. The human mind thus discovers its position between two infinities. It is able, through the agency of the senses, to acquaint itself directly with a very limited range of phenomena, but, planting itself upon this little fragment of solid ground, it reaches into space, and by observations and by computations made upon them becomes acquainted with the infinitely great; while in the other direction it pierces the recesses of minute bodies, and by observations and computations there it becomes acquainted with the infinitesimal. The results attained in both directions are alike incomprehensible. Who can, for example, accurately conceive the distance described as 1,000,000 miles? Even he who has made the circuit of the world can not rely on this extended experience to enable him to see the beginning, middle, and end of 1,000,000 miles in their true proportions. Yet this is a little more than the one-hundredth part of our distance from the sun, from which we get the light and heat on which our lives depend. What, then, shall we say of those sidereal spaces to measure which this solar distance is taken as the unit! The astronomer contemplates magnitudes and distances and motions expressed by figures of such vast array, that the power of enumeration is almost staggered, and our capacity to comprehend values is altogether overwhelmed by them. But let us reduce the unit of measure from the mile to the inch, and then let us take the reciprocals of these enormous values obtained by the astronomer in his study of the planetary composition of the universe, and we shall have before us the order of measurements which engage the attention of the physicist who studies the molecular composition of matter. If we are not dismayed by the one, let us not be by the other. In one case our conceptions are pictures in miniature; in the other they must be pictures enlarged. But it is no more difficult to picture the distance between two minute bodies, when measured by the hundred-millionths of an inch, than it is to picture it between two greater ones when measured by the hundred millions of miles. To comprehend the real magnitude is, in both cases, impossible, and our belief in the existence of either must depend on our faith in the infallibility of mathematical processes and on the observations upon which they are based. But granting the existence of such evidence to sustain it, neither can be called incredible, however it may transcend our comprehension, for credulity consists, not in believing, but believing without evidence.
- Read before the Poughkeepsie Society of Natural Science, December, 1878.
- By J. P. Cooke, Jr., "International Scientific Series," D. Appleton & Co.