210 OUTLINES OF PHYSICAL CHEMISTRY
then there would be n unitary molecules dissolved in the solution, and the osmotic pressure would be normal. Bat a certain fraction x of this number of molecules suffers hydrolytic decomposition, and only (1 — x) n molecules remain unchanged, whilst the #n dissociated molecules give #n times n 1 free ions. The osmotic pressure is, therefore, not determined by n particles, but by (1 — x) n + n x n material particles ; and as the osmotic pressure is i times too large we may write
t -«(i-«)» + »*»,n. (n _i )g .
N v '
In this equation i and n are known and # can be calculated :
��# =
��iT^T
��As a rule (at any rate for binary electrolytes) the value found for x by either of these methods is the same.
But as direct osmotic experiments are extremely diffi- cult to carry out, it would be dangerous to make them serve as the basis of a theoretic system.
This would be a serious objection were it not that a mathematical relation exists between the osmotic pressure of a solution and its boiling and freezing points. 2 The boiling-point or the freezing-point of a solution being known, we can calculate its osmotic pressure, and so the direct determination of this pressure is quite superfluous. Besides, all the observed facts tend to show that there is a direct connection between osmotic methods and boiling and freezing point methods. Thus, if the osmotic pressure of a solution is regular, its rise in boiling-point and its
1 n is the number of ions of which the molecule is composed.
- See the chapter, ' Theoretical Relations/ on p. 127. There the
relationships between osmotic pressure and the vapour tension, the boiling-point, and the freezing-point of a very dilute solution con-
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