# Van't Hoff Factor Equation and Abnormal Molar Mass

## Van’t Hoff Factor

Some solute particles undergo association or dissociation in solution which causes a change in their colligative property as well as in their molar mass. Colligative properties are properties that are dependent on the ratio of the number of solute to solvent particles present in the solution. The extent to which particles undergo association or dissociation is calculated through Van’t Hoff factor.

This factor is named after Jacobus Henricus Van't Hoff, the Dutch physical chemist, who earned the first Nobel Prize in chemistry. It is important to remember that the calculated value for electrolytic solutions of the Van't Hoff factor is typically lower than the expected value (due to the pairing of ions). The higher the charge on the ions, the higher the deviation.

Here, you will learn about van't Hoff factor, how to calculate van't hoff factor, and abnormal molar mass.

### Abnormal Molecular Mass

Do You Know What is Abnormal Molar Mass?

The molar mass calculated through the colligative properties is sometimes different from that of experimentally determined molar mass is known as abnormal molar mass. This abnormal molar mass is due to the solute particles that undergo association or dissociation.

There are four types of colligative properties by which molar mass can be calculated-

1. Relative lowering of vapor pressure

2. Elevation in boiling point

3. Depression in freezing point

4. Osmotic Pressure

Van't Hoff explained that solute dissociates into ions when solutes are dissolved in a solvent. The dissociation of solute molecules into ions results in an increase in the number of particles and thus affects the colligative properties, as the colligative properties depend only on the number of solute particles.

Some compounds tend to be associated in the aqueous state and the amount of ions/molecules found in the solution is smaller than the total number of molecules for those molecules. Thus, for those substances that dissociate in solution, the molar mass measured will always be less than the real mass, and the real mass will always be less than the molar mass observed for those substances that associate in solution.

It is Possible to Describe the Abnormality in Molecular Mass as Follows:

1. A rise in the number of particles results from the dissociation of solute molecules into several ions. This, in essence, increases the solution's colligative properties.

2. Since the molar mass is inversely proportional to the colligative properties, it tends to have a lower value than predicted.

3. The total number of particles in the solution decreases as solvent particles interact with each other, contributing to a decrease in colligative properties.

4. The molar mass values obtained are higher than expected in this case

### What is Van’t Hoff Factor?

Vant Hoff factor denoted by the symbol ‘i’ measure the extent of association or dissociation of solute in a solution.

Let’s see How to calculate Van’t Hoff factor-

Van’t Hoff Factor Formula-

i = $\frac{\text{Observed Colligative Property}}{\text{Normal or Theoretical Colligative Property}}$

i = $\frac{\text{Normal Molar Mass}}{\text{Observed Molar Mass}}$

i = $\frac{\text{Actual Number of Particles}}{\text{Observed Number of Particles}}$

These three formula shows the Van't Hoff Equation

### Van't Hoff Law for Dissociated Solutes -

When 1 mole of NaCl is dissolved in 1 Kg of water, if all NaCl molecules dissociate in water, the resulting solution would contain 1 mole of Cl-ions and 1 mole of Na+ ions (a total of 2 moles of ions in the solution). But we consider only 1 mol of NaCl to be present in the solution when measuring the molar mass using the colligative properties.

So how to calculate van t Hoff factor-

i = $\frac{\text{Observed Colligative Property}}{\text{Normal or Theoretical Colligative Property}}$

i= $\frac{2}{1}$ = 2

So in case, the dissociation value is greater than 1- the number of solute increases, colligative property increases, and decreases in the molar mass of the solute. Hence colligative property is inversely proportional to the molar mass of the solute.

This shows the relation between van’t hoff factor and degree of dissociation.

### Van't Hoff Law for Associated Solutes-

Example -A solution of acetic acid in benzene. Dimerization of acetic acid in benzene occurs. So 2 molecules of acetic acid combine to form one.

2CH3COOH+ benzene(CH3COOH)2

i=1/2=0.5

The value of  ‘i’ is smaller than 1, so the quantity of solute decreases thus the colligative property, and hence the mass of solute increases.

### Did You Know?

Osmotic pressure is one of the colligative property which plays a major role in a biological cell. An important factor that affects cells is osmotic pressure. Osmoregulation is an organism's homeostasis process for osmotic pressure to achieve equilibrium.

• Hypertonicity is the presence of a solution that causes the shrinkage of cells.

• The presence of a solution that causes cells to swell is hypotonicity.

• Isotonicity is the presence of a solution that does not cause any change in the volume of cells.

If the cell within accumulates water when a biological cell is in a hypotonic environment, water flows into the cell via the cell membrane, allowing it to expand. The cell wall limits expansion in plant cells, resulting in pressure from within on the cell wall called turgor pressure.