# Anomalous Colligative Properties

Anomalous colligative properties are colligative properties that deviate from the norm. Chemist Jacobus van't Hoff was the first to describe anomalous colligative properties, but it was Svante Arrhenius who succeeded in explaining anomalous values of colligative properties.

### Introduction

Colligative Properties are the properties of solutions that rely only on the number(concentration) of the solute particles, and not on the identity/type of solute particles, in an ideal solution (e.g., vapor pressure lowering, freezing point depression, boiling point elevation and osmotic pressure). There is a direct relationship between the concentration and the effect that is recorded. Therefore, the colligative properties are helpful when characterizing the nature of a solute after it is dissolved in a solvent.

There are some solutes that produce a greater effect on colligative properties than what is expected. Arrhenius explained this by using the following equation:

$\Delta{T_f} = -K_f \times m = -1.86 \; ^{\circ}C \; m^{-1} \times 0.0100 \; m = -0.0186 \; ^{\circ}C \tag{1}$

The expected freezing point for this solution would be: - 0.0186 $$^{\circ}C$$. Lets say that this solution was that of urea, the measured freezing point is close to -0.0186 $$^{\circ}C$$. If it were to be a solution of NaCl, then the measured freezing point would then be -0.0361 $$^{\circ}C$$. According to Van't Hoff the factor, $$i$$ is the ratio of the measured value of a colligative property to that of the expected value if the solute is a nonelectrolyte. Now, for 0.0100 m NaCl, it would be:

$i = \dfrac{measured \; \Delta{T_f}}{expected \; \Delta{T_f}} \tag{2}$

For the solute urea $$i$$ = 1. For a strong electrolyte like NaCl that produces 2 moles of ions in a solution/ mole of solute dissolved, the effect on the freezing point depression would be expected to be twice as much as that for a nonelectrolyte. The expected $$i$$ = 2. This leads the colligative properties to be rewritten as demonstrated in the table below.

Original Rewritten
$$\pi = M \times RT$$ $$\pi = i \times M \times RT$$
$$\Delta{T_f} = -K_f \times m$$ $$\Delta{T_f} = -i \times K_f \times m$$
$$\Delta{T_f} = -K_b \times m$$ $$\Delta{T_f} = i \times K_b \times m$$

We can just substitute 1 for $$i$$ for nonelectrolytes and for strong electrolytes, find the value of $$i$$.

### Resources

1. Petrucci, Harwood, Herring, Madura. General Chemistry, Principles & Modern Applications 9th Edition. Upper Saddle River, NJ: Pearson Education, Inc., 2007.
2. Zumdahl, Steven S. Chemistry 4th Edition. New York: Houghton Mifflin,1997.

### Contributors

• Nathalie Interiano (UCD)