Chemistry · Ch 2 — Solutions

van't Hoff Factor (i)

2.11.1

van't Hoff Factor (i)

To obtain the colligative properties of electrolyte solutions by using the relations for nonelectrolytes, van't Hoff suggested a factor $i$ . It is defined as the ratio of the colligative property of a solution of an electrolyte to the colligative property of a nonelectrolyte solution of the same concentration. Thus,

i = \frac{\text{colligative property of electrolyte solution}}{\text{colligative property of nonelectrolyte solution of the same concentration}}

= \frac{(\Delta T_f)}{(\Delta T_f)_0} = \frac{(\Delta T_b)}{(\Delta T_b)_0} = \frac{(\Delta P)}{(\Delta P)_0} = \frac{(\pi)}{(\pi)_0} \qquad \text{...(2.22)}

where the quantities without subscript refer to electrolytes, and those with subscript 0 refer to nonelectrolytes.

The van't Hoff factor $i$ is also defined in an alternative, but exactly equivalent, manner:

i = \frac{\text{actual moles of particles in solution after dissociation}}{\text{moles of formula units dissolved in solution}} \qquad \text{...(2.23)}

= \frac{\text{formula mass of substance}}{\text{observed molar mass of substance}} = \frac{\mathrm{M_{theoretical}}}{\mathrm{M_{observed}}} \qquad \text{...(2.24)}

Thus, $i$ is equal to 1 for a nonelectrolyte, 2 for $\mathrm{KNO_3}$ and NaCl, 3 for $\mathrm{Na_2SO_4}$ and $\mathrm{CaCl_2}$ , and so forth. The colligative properties of these electrolytes are, therefore, twice and thrice, respectively, those of nonelectrolytes of the same concentration. …

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