VOL.2, No. 11
THELAWOF AVOGADRO
1061
THE LAW OF AVOGADRO ABRAHAMHENWOOD, CENTRAL HIGHSCHOOL, PHIIADELPHIA, PA.
The law of Avogadro is a fundamental principle of modern chemistry. I n spite of this fact, however, i t remains more or less an article of faith, to be justified by its works. While it is true that it has been amply so justified it would seem very much more satisfactory to the student if it were clearly and explicitly shown upon what firmly established laws of nature i t depends and how i t may be deduced from them. Avogadro, in his classic memoir, puts it forth as an ex catlzedra hypothesis which affords an explanation of the law of Gay Lussac on the combining volumes of gases. That chemists were not convinced of its validity is shown by the fact that forty-seven years went by before Cannizzaro's pamphlet led Lothar Meyer to say, "the scales fell from my eyes, my doubts disappeared, and a feeling of tranquil security took their place." These considerations have led me to attempt what may be regarded as a deductive proof. Let N be the number of molecules of a gas in the volume V ; n the number of molecules in unit volume of the gas. Then we may write N = nV
Now if N1 molecules of a gas whose volume is V l interact with N2 mole, have cules of a second gas whose volume is V Z we N, = nr Vc N, = n,V,
and by division
. NdNa = n h X VdV*
or VdVg
= */nl
X NJNZ.
If temperature and pressure be constant V J V zis a ratio whose terms are small integers (Law of Gay Lussac). Thus the hydrogen-oxygen ratio is 2/1. Nl/N2 is also a ratio whose terms are small integers. This follows from the law of combining masses, thus: The combining mass of a n element is the mass of that element which combines with (or displaces) an arbitrarily chosen fixed mass of a selected standard element, oxygen, for example. It is found by experiment that the composition of any substance can be expressed by small integral multiples of these combining masses of the constituent elements. Since one or more combining masses taken together constitute an atomic mass and further one or more atomic masses constitute a molecular mass, it follows, a fortiori, that NJN2 is a ratio whose terms are small integers. , nl is not Reverting now to the equation V,/V2 = m/nl X N I / N ~suppose equal to nz. Then the result of multiplying N,/Nz, a ratio whose terms are
small integers, by iza/nl cannot give in all cases a ratio whose terms are small integers, as is required by the fact that this product is equal to V,/V2, a ratio whose terms are small integers. For example, suppose nt = 2153 X lo', ne = 1879 X lo', a possible case; and further let N1/N2 = 1/2, then V1/Vz = 1879/2153 X 1/2 = 1879/4306 which is not a Gay-Lussac ratio. Therefore, n, cannot be not equal to m,i. e., n, is equal to nzwhich is Avogadro's law. I t is to be noted that the law depends not on Gay-Lussac's law alone but to an equal degree on the Law of Combining Masses. This is a point that is not brought out in the text-books. Furthermore it is evident that the law only holds exactly for ideal gases. In this respect it is on the same plane as the laws of Boyle, Charles, and Gay-Lussac.
