What is Abnormal Molar Mass: Van't Hoff Factor, Applications and Exam Tips

Let us discuss the key principle. Questions based on this are covered in NCERT solutions of this chapter. Anyone who plans to sit in the exam must practice those questions. Let us now talk about this principle.

The van't Hoff factor ( $i$  ) is defined as:

$$i=\frac{\mathrm{Observed} \mathrm{colligative} \mathrm{property}}{\mathrm{Normal} \mathrm{colligative} \mathrm{property}}=\frac{\mathrm{Actual} \mathrm{number} \mathrm{of} \mathrm{particles}}{\mathrm{Number} \mathrm{of} \mathrm{particles} \mathrm{without} \mathrm{association}/\mathrm{dissociation}}$$

For non-electrolytes without association/dissociation, $i=1$ . For association, $i<$  1 ; for dissociation, $i>1$

• Non-electrolytes like glucose or sucrose don't dissociate in water, so they have i = 1. One molecule dissolves to produce one particle.
• Strong electrolytes dissociate completely. Sodium chloride (NaCl) gives i = 2, calcium chloride (CaCl₂) gives i = 3, and aluminum sulfate [Al₂(SO₄)₃] theoretically gives i = 5.
• Weak electrolytes only partially dissociate, so their Van't Hoff factors fall between 1 and their theoretical maximum. For instance, acetic acid might have i = 1.1 instead of the theoretical maximum of 2.

Association occurs when solute molecules combine to form larger species, reducing the number of particles in solution. This decreases the colligative property, leading to a higher observed molar mass. The topic is also useful from IISER and IIT JAM point of view and understanding it with the help of an example will be beneficial for entrance exam aspirants.

Acetic Acid in Benzene

Acetic acid $\left({\mathrm{C}\mathrm{H}}_3\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}\right)$ dimerizes in benzene via hydrogen bonding: $2{\mathrm{C}\mathrm{H}}_3\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}\rightleftharpoons {\left({\mathrm{C}\mathrm{H}}_3\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}\right)}_2$

Normal molar mass: $60\mathrm{g}/\mathrm{m}\mathrm{o}\mathrm{l}$ ; observed molar mass: $120\mathrm{g}/\mathrm{m}\mathrm{o}\mathrm{l}$  (dimer). If degree of association ( $\alpha$  ) is 0.8 for a trimer ( $3A\to A_3$  ), the effective molality decreases, reducing colligative effects.

Van't Hoff Factor for Association

For $nA\to A_n$  with degree of association $\alpha$ : $i=1+\left(\frac{1}{n}-1\right)\alpha =1-\alpha \left(1-\frac{1}{n}\right)$

For trimerization ( $n=3$ ): $i=1-\frac{2}{3}\alpha$

Dissociation occurs when ionic solutes break into ions, increasing the number of particles. This increases the colligative property, leading to a lower observed molar mass. Those preparing for NEET and CUET exams must learn this concept in detail. An example has been given below to help students learn what exactly is dissociation.

Example: KCl in Water

KCl dissociates completely in water: $\mathrm{K}\mathrm{C}\mathrm{l}\rightleftharpoons {\mathrm{K}}^{+}+{\mathrm{C}\mathrm{l}}^{-}$

Normal molar mass: $74.5\mathrm{g}/\mathrm{m}\mathrm{o}\mathrm{l}$ ; observed molar mass: $37.25\mathrm{g}/\mathrm{m}\mathrm{o}\mathrm{l}$ (two particles). For partial dissociation, the degree of dissociation ( $\alpha$ ) determines $i$ .

Van't Hoff Factor for Dissociation

For an electrolyte $A_x{B}_y\to x{A}^{y+}+y{B}^{x-}$  with degree of dissociation $\alpha$ , where $n=x+y$  : $i=1+(n-1)\alpha$

For ${\mathrm{K}}_2{\mathrm{S}\mathrm{O}}_4(n=3)$ : $i=1+2\alpha$

The van't Hoff factor modifies colligative property equations:

• Relative lowering of vapor pressure: $\frac{P^0-P_s}{P^0}=i{X}_B$
• Boiling point elevation: $\mathrm{\Delta }{T}_b=i{K}_{b}m$
• Freezing point depression: $\mathrm{\Delta }{T}_f=i{K}_{f}m$
• Osmotic pressure: $\pi =iCRT$

Abnormal molar mass is used in the following ways:

• Chemical Analysis: Determining molecular masses of unknown solutes using colligative properties.
• Electrolyte Solutions: Calculating degree of dissociation for salts in water, e.g., NaCl in IV fluids.
• Industrial Processes: Understanding behavior of solutes in non-aqueous solvents, e.g., carboxylic acids in organic synthesis.
• JEE Main Problems: Numerical calculations of $i,\alpha$ , or molar mass from experimental data.

Students must remember these points while learning about abnormal molar mass. These will be helpful for them while solving questions:

• Memorize van't Hoff factor formulas for association and dissociation (NCERT, Page 56).
• Practice problems involving partial dissociation (e.g., ${\mathrm{K}}_2\left[\mathrm{F}\mathrm{e}(\mathrm{C}\mathrm{N}{)}_6\right]$ ) or association in non-polar solvents.
• Understand how $i$ affects all colligative properties.
• Solve past JEE Mani questions on abnormal molar masses to master numerical accuracy.