88 STATISTICAL PHYSICS- The extension of Avogadro's law: equal volumes of solutions at the same p and
T contain the same number of solute molecules. This number is equal to the
number of gas molecules at the same (gas) pressure p and the same T. Hence,
for one gram-mole
where R is the gas constant. Thus, after van 't Hoff, the liquid phase offered
a new way of measuring the gas constant and, consequently, new possibilities
for the determination of Avogadro's number.'The fact that the dissolved molecules of a diluted solution exert on a semi-
permeable membrane—in spite of the presence of the solvent—exactly the same
pressure as if they alone were present, and that in the ideal gas state—this fact is
so startling that attempts have repeatedly been made to find a kinetic interpreta-
tion that was as lucid as possible', Ehrenfest wrote in 1915 [El]. Einstein briefly
discussed the statistical derivation of van 't HofFs laws in 1905 [E2]; more impor-
tant, however, are the applications he made of these laws.
In 1901, van 't Hoff became the first to receive the Nobel prize for chemistry.
The presentation speech delivered on that occasion illustrates vividly that, at the
beginning of the twentieth century, molecular reality had become widely accepted
among chemists as well as physicists: 'He proved that gas pressure and osmotic
pressure are identical, and thereby that the molecules themselves in the gaseous
phase and in solutions are also identical. As a result of this, the concept of the
molecule in chemistry was found to be definite and universally valid to a degree
hitherto undreamed of [N3].5c. The Doctoral Thesis
In his PhD thesis, Einstein described a new theoretical method for determining
molecular radii and Avogadro's number. From a comparison of his final equations
with data on sugar solutions in water, he found thatThe printed version of his thesis [E3] carries the dedication 'to my friend Marcel
Grossman' and gives April 30, 1905, as the completion date. Einstein did not sub-
mit his dissertation to the dean of the philosophical faculty, Section II, at the
University of Zurich until July 20 [E4]. This delay may have had its technical
reasons. More important, probably, was the fact that, between April and July,
Einstein was rather busy with other things: during those months he completed his
first papers on Brownian motion and on the special theory of relativity. The thesis
was rapidly accepted. On July 24* the dean forwarded to the faculty for their
'Einstein later recalled that, after having been told that the manuscript was too short, he added one
sentence, whereupon it was accepted [S2]. I have found no trace of such a communication, nor is it
clear to me when this exchange could have taken place.