( COSTRIBUTIOSFROM THE KEXT CHEMICALLABORATORYOF THE UNIVERSITY OF CHICAGO. )
A KEJV PROOF O F THE FOR1\IULX d = - - -
OZT'
L
BY FELIX LEXGFELD
T h e ordinary student of chemistry has a rather vague conception of thermodynamjcs, and therefore in van 't Hoff's' demonstration of the relation between the lowering of the freezingpoint of a solution (or the rise of the boiling-point) and certain physical constants of the solvents, he does not know why work is equal to d T S L T iz '
and hence it loses its entire meaning. T h e following modification of van 't Hoff's demonstration has been found of real yalue with such students. Let a solution containing gz gram-molecule solute in S grams solvent be put into a cj-linder provided with a semipermeable end and with a movable piston. 9 t T - d T the freezing-point of the solution let freeze out a quantitj. of the solvent that originally contained one gram-molecule solute, i-iz.? S 11
grams.
If L' be the latent heat of fusion of the solvent at
the temperature T - dT, there will be evolved
x 12
L' calories.
Separate the solid from the solution and bring the whole to the temperatiire T, the melting-point of the solvent. T o do this n calories must be added. Allow the solvent to melt. If its latent heat of fusion at the temperature T be I,, it will absorb N ~
11
L calories.
X o w bring the liqaid solvent into contact with
Zeit. phys. Cherii.
I,
496 (1887).
500
Felit- Leitgfeld
the solution a t the semi-permeable inembralie with the pressure on the solution equal to the osmotic pressure. Raising the piston under this constant presstire the solvent paises through the diaphragm, mixing with the solution. T h e work done on the piston is equal to the osmotic pressure P into the volume of the solvent V. A s 1- is the volume that contained one graininolecule solute PV = RT, or if we express R iii thermal units, I i o r k = PV = 2T. Bring the whole to the origiiial temperature T - dT, thus coming back to the starting-point. Dyring this last process (r calories are evolved. sorbed and
c
L’--
ITe therefore have b
(
I, ~- n calories ab-
)
) calories are evolved.
T h e work done
must be the difference between these, or as n and b are practically equal, we may consider
2T =
N 71
( L - I
