# What is the van't Hoff factor?

Jun 20, 2017

It is the effective number of solute particles per formula unit of the added solute.

The van't Hoff factor $i$ is the multiplier seen in any of the following situations, indicating the effective number of particles after considering the dissociated solute:

• osmotic pressure increase, $\Pi = i M R T$
• freezing point depression, $\Delta {T}_{f} = - i {K}_{f} m$
• boiling point elevation, $\Delta {T}_{b} = i {K}_{b} m$
• vapor pressure reduction (implicit; easier to see conceptually)

(note: for vapor pressure reduction, $i$ is implicit; it is easier to see that the greater number of particles per formula unit of solute, the more the nonvolatile solute blocks the solvent from vaporizing, hence lowering its vapor pressure even more, as expected.)

We generally approximate $i$ to be the number of particles at 100% dissociation. Of course, nothing dissociates 100%, and we have deviations shown below.

• If the solute is a strong electrolyte, then $\boldsymbol{i \text{ >> } 1}$, indicating high percent dissociation.

For instance, ${\text{MgCl}}_{2}$ has $i \approx 2.7$, compared to the ideal $3.0$, so it does not dissociate 100% to form ${\text{Mg}}^{2 +}$ and ${\text{Cl}}^{-}$. See the remark about ion pairing below.

• Weak electrolytes have $i$ close to but still greater than $1$.

For example, glucose has $i \approx 1.0$, a pretty much ideal nonelectrolyte. On the other hand, acetic acid has $i$ somewhere around $1.01$ ~ $1.2$, depending on its concentration because it is a weak electrolyte.

[Strong electrolytes are not as influenced by changes in initial concentration.]

• And if the electrolyte has some ion-pairing going on, it might have some contribution to decrease $i$, but that would be beyond the scope of general chemistry classes.

For example, ${\text{FeCl}}_{3}$ has $i \approx 3.4$, much less than the ideal $4$, due to ion pairing to form ${\text{FeCl}}^{2 +}$ and ${\text{FeCl}}_{2}^{+}$.