2.2 Van’t Hoff Factor
 (1904) - 1901 Nobel Prize winner in Chemistry; Figure from [Wikipedia](https://upload.wikimedia.org/wikipedia/commons/3/33/Jacobus_van_%27t_Hoff_by_Perscheid_1904.jpg)](https://upload.wikimedia.org/wikipedia/commons/3/33/Jacobus_van_%27t_Hoff_by_Perscheid_1904.jpg)
Figure 2.6: Jacobus Henricus van’t Hoff Jr. (1904) - 1901 Nobel Prize winner in Chemistry; Figure from Wikipedia
Many ionic compounds dissociate when dissolved in water, resulting in dissolved ions in solution. These are called electrolytes.
Those that do not form ions when dissolved in solution are called non-electrolytes. It is important to track the number of resulting solute particles that end up in solution. For example, when one particle of NaCl dissolves in water, the resulting number of dissolved solute particles is two and can be seen with the ionic equation.
\[\mathrm{NaCl}(s) \longrightarrow \mathrm{Na^+}(aq) + \mathrm{Cl^-}(aq)\]
The ratio of dissolved particles for NaCl is 2:1 (two resulting particles for every one particle dissolved).
Non-electrolytes, however, do not dissociate and the resulting number of dissolved particles equals the number of particles introduced into the solution. A sugar molecule such as sucrose (C12H22O11) is a non-electrolyte. If one molecule of sucrose is dissolved in water, the resulting number of solute particles in solution is one.
\[\mathrm{C_{12}H_{22}O_{11}}(s) \longrightarrow \mathrm{C_{12}H_{22}O_{11}}(aq)\]
The ratio of dissolved particles for non-electrolytes is 1:1 (one resulting particle for every one particle dissolved).
Practice
Three moles of NaCl are dissolved in water. How many solute particles (in mol) are there?
500.0 g of MgSO4 (m.m. = 120.366 g mol–1) is dissolved in water. How many solute particles (in mol) are there?
Solution
Problem 1
\[\mathrm{NaCl}(s) \longrightarrow \mathrm{Na^+}(aq) + \mathrm{Cl^-}(aq) \qquad i =2\] \[3~\mathrm{mol~NaCl} \times 2 = 6~\mathrm{mol~particles}\]
Problem 2
\[\mathrm{MgSO_4}(s) \longrightarrow \mathrm{Mg^{2+}}(aq) + \mathrm{SO_4^{2-}}(aq) \qquad i = 2\] \[500.0~\mathrm{g~MgSO_4} \left(\dfrac{\mathrm{mol}}{120.366~\mathrm{g}} \right ) \times 2 = 8.31~\mathrm{mol~particles}\]
The van’t Hoff Factor (i) is simply the ratio for different substances.
| Substance | Solute | iideal | ireal |
|---|---|---|---|
non-electrolyte |
no dissociation |
1 |
1 |
NaCl |
Na+ + Cl– |
2 |
1.9 |
MgSO4 |
Mg2+ + SO42– |
2 |
1.3 |
MgCl2 |
Mg+ + 2Cl– |
3 |
2.7 |
K2SO4 |
2K+ + SO42– |
3 |
2.6 |
FeCl3 |
Fe + 3Cl– |
4 |
3.4 |
- iideal assumes complete dissociation (a good approximation for dilute solutions)
- ireal is the actual measured ratio (i decreases as concentration increases due to ion pairing) – Values measured for a 0.05 m concentration
Ion Pairing
Ionic compounds dissociate when dissolved in solution. At very low concentrations, these ions are not very likely to “find” each other in a vast ocean of solvent particles. However, at higher concentration, the probability of the ions finding each other increases. Ions of opposite charge will be attracted to each other and form ion pairs, thereby decreasing the number of dissolved particles slightly.
iideal assumes no ion pairing whereas ireal is the actual ratio of dissolved solute particles at some concentration.
\[i_{\mathrm{real}}~~<~~i_{\mathrm{ideal}}~~~\text{at increasing concentration}\]