van't Hoff Factor and Degree of Dissociation

The discussion of colligative properties of electrolytes in the preceding sections is based on the fact that the electrolytes are completely dissociated in their aqueous solutions. This is approximately true for solutions of strong electrolytes, and not for weak electrolytes, which dissociate to a small extent. The weak electrolytes involve the concept of degree of dissociation ($\alpha$), which changes the van't Hoff factor. (Throughout this discussion the book typesets the degree of dissociation with the proportionality glyph $\propto$ -- semantically it is the Greek letter alpha, $\alpha$, and we write it so.)

Relation between van't Hoff factor and degree of dissociation : Consider an electrolyte $\mathrm{A_xB_y}$ that dissociates in aqueous solution as

Initially: 1 mol, 0, 0. At equilibrium: $(1-\alpha)$ mol, $(x\alpha)$ mol, $(y\alpha)$ mol.

If $\alpha$ is the degree of dissociation of the electrolyte, then the moles of cations are $\alpha x$ and those of anions are $\alpha y$ at equilibrium. We have dissolved just 1 mol of electrolyte initially: $\alpha$ mol of the electrolyte dissociates, and $(1-\alpha)$ mol remains undissociated at equilibrium.

Total moles after dissociation:

where $n = x + y$ = moles of ions obtained from the dissociation of 1 mole of electrolyte. …