Van't Hoff Factor Equation and Abnormal Molar Mass

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 the 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 Abnormal Molar Mass Is?

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-

Relative Lowering of Vapour Pressure

The phenomenon where the addition of a non-volatile solute to a solvent leads to the vapour pressure getting lower is called relative lowering of vapour pressure. The relation between the pressure of the solution, the vapour pressure of the pure solvent and the mole fraction of the solute was discovered by a French Chemist.

He observed that it is mainly the concentration of the solute particles which was responsible for the lowering of vapour pressure. 

As per the laws devised by scientists, 

Decrement in Vapour Pressure = Vapour Pressure of Pure Solvent – Vapour Pressure of Solvent. 

This equation is used to determine the ultimate molar mass of a solute.

Elevation in Boiling Point

The vapour pressure of a solute decreases as a non-volatile solute is added to a solvent. The boiling point of such a solution is always greater than the pure solvent that it is added to. This is because the pressure of vapour is in direct proportion to the temperature of the solution. For the solution to boil, the solution’s temperature has to be raised. This phenomenon is called the elevation of boiling point.

Formula: ΔT = iKbm

(ΔT= change in temperature, i = the Van’t Hoff factor, m = the molality, Kb = the molal boiling point constant)

Depression in Freezing Point 

Decreasing the vapour pressure of a solution results in a decrease of the freezing point of the solution. The freezing point of a solution can be identified as a point at which the vapour pressure of the substance is equal in the liquid and vapour state.

As per the law, the freezing point for a given dilute solution stays directly proportional to the molality of the solute.

Formula: ΔT = iKfm

(ΔT= change in temperature, i = the Van’t Hoff factor, m = the molality, Kf = the molal freezing point constant)

Osmotic Pressure

Osmosis is the flow of solvent molecules from the pure solvent to the solution through a membrane. This flow does not stop until equilibrium is reached. This process occurs through a membrane that contains small pores that allow small solvent molecules like water to pass through. Such membranes are called semipermeable membranes (SPM).

The solvent’s flow across the semipermeable membrane to the solution side can be stopped by applying extra pressure on the solution. This pressure is known as the osmotic pressure of the solution.

Thus, the osmotic pressure of a solution is the excess pressure applied to the solution to prevent osmosis.

Osmotic pressure depends on the concentration of the solution, and when it comes to dilute solutions, this pressure is directly proportional to the molarity of the solution at a certain temperature.

Π = C R T =  (n²/V) R T

(Π is osmotic pressure, C is molarity, R is gas constant, T is temperature, V is a volume of solution in litres, n is the number of moles of solute).

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 the Van't Hoff Factor?

The Van't Hoff factor denoted by the symbol ‘i’ measures 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 = \[\frac{Observed\:Colligative\:Property}{Normal\:or\:Colligative\:Property}\]

i = \[\frac{Normal\:Molar\:Mass}{Observed\:or\:Molar\:Mass}\]

i = \[\frac{Actual\:Number\:of \: Particles}{Observed\:Number\:of \: Particles}\]

These three formulas show 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 = \[\frac{Observed\:Colligative\:Property}{Normal\:Or\:Colligative\:Property}\]

i = \[\frac{2}{1}\] = 2

So in case, the dissociation value is greater than 1- the number of solutes increases, colligative properties increase, 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 the 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 = \[\frac{1}{2}\] = 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 properties 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 preshttps://www.vedantu.com/biology/turgorsure.