Van't Hoff Factor

Some chemical substances when used as solutes undergo dissociation or association in solution. This causes a change in their molar Mass and various Colligative properties. This can be explained by Van't Hoff Factor. It was named after Dutch physical Chemist Jacobus Henricus Van't Hoff, Jr. He was the first winner of the Nobel Prize in Chemistry. 

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To have a better and clear understanding of the Van't Hoff Factor, you need to understand the Colligative properties of solutions and Abnormal molar Mass first. So, let’s start with a brief explanation of what are Colligative properties and what is Abnormal molar Mass. 

What is Abnormal Molar Mass? 

Molar Mass can be defined as the Mass of a sample of that compound divided by the amount of substance in that sample, measured in Moles. 

When the molecular mass of a solute is calculated from the Colligative properties of solution (In which that solute has been dissolved), are sometimes found to differ from experimentally obtained values. This value is called the Abnormal molar Mass of that solute. The reason behind this is that some solutes when dissolved in solutions get dissociated into ions or associate into larger Molecules. 

What are Colligative Properties? 

In Chemistry, Colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent Molecules in a solution and not on the nature of the chemical species present. Colligative properties include following four main properties –

• Relative lowering of vapor pressure (depends on mole fraction of solute)

• Elevation of boiling point

• Depression of freezing point 

• Osmotic pressure 

Van't Hoff Factor

Van't Hoff Factor is the measure of the effect of solute on various Colligative properties of solutions. Colligative properties such as relative lowering in vapor pressure, osmotic pressure, boiling point elevation and freezing point depression are proportional to the quantity of solute in the solution. Van't Hoff Factor is the ratio between the actual concentration of particles produced when the substance is dissolved, and the concentration of a substance as calculated from its Mass. It is denoted by ‘i’. 

If we take one liter of water and dissolve 1mole of sugar in it then its Colligative properties will not change but if dissolve 1 mole of salt in 1L of water then its Colligative properties will change as 1 mole of NaCl will dissociate into 1 mole Na+ and 1 mole Cl-. So, for NaCl solutions theoretical and experimental data will differ. In this situation to rectify or to measure the change in Colligative properties of the solution, we need the Van't Hoff Factor. Various formulae of calculating Van't Hoff Factor are given below –

\[ i = \frac{\text{Observed colligative property}}{\text{Normal or theatrical colligative property}}\]

\[ i = \frac{\text{Normal molar mass}}{\text{Observed molar mass} }\]

\[i = \frac{\text{Actual number of particles}}{\text{Expected Actual number of particles}}\]

Van't Hoff Factor for Dissociated Solutes – let’s understand it by using NaCl solution. 1 mole of Sodium chloride dissolved in 1L water and gives 1 mole of sodium and 1 mole of chloride ions. At time 0, when dissociation did not start –

                             NaCl                  🡪               Na+           +            Cl-

At t=0                  1 mole                                  0 mole                 0 mole 

At time t, when dissociation is completed –

                             NaCl                  🡪               Na+           +            Cl-

At t=t                  0 mole                                 1 mole                  1 mole 

\[ i = \frac{\text{Observed colligative property}}{\text{Normal or theatrical colligative property}}\]

On keeping the values from equation in the above formula –                                                                                    

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

For dissociation, in absence of association, the value of i is greater than 1. 

In Case of Dissociation – the quantity of solute increases,the  Colligative property increases, molar Mass of solute decreases. 

Van't Hoff Factor for Associated Solutes – let’s understand it by using the example of the solution of acetic acid in benzene. Dimerization of acetic acid takes place in benzene. So, if we take 2 Molecules of acetic acid in benzene then it becomes 1. 

\[ 2CH_{3}COOH + Benzene \rightarrow  (CH_{3}COOH)_{2} \]

Thus, at t=0, when association did not start, 2 moles of acetic acid is present. While at time t, when the association is completed, 1 mole of acetic acid is present. As we know Van't Hoff Factor –

\[ i = \frac{\text{Observed colligative property}}{\text{Normal or theatrical colligative property}}\]

On keeping the values -

\[ i = \frac{1}{2} = 0.5\]

Thus, in case of association value of i is smaller than one, the quantity of solute decreases, Colligative property decreases, Molar Mass of solute increases.

Van't Hoff Factor for Associated Solutes and dissociated solutes can be summarized in tabulated form as follows –

Physical Significance of ‘i’

The value of 'i' determines the physical concentration of solute particles in a solution.

It is found that if the solute particles are associated in a solution, ‘i’ happens to be less than 1. We can understand this through carboxylic acids such as acetic acid (ethanoic acid) or benzoic acid which are known to form dimers in benzene, which divides the number of solute particles by half the number of acid Molecules.

However, if the solute particles dissociate in the solution, ‘i’ will be greater than 1 (e.g. salts dissolved in water such as sodium chloride in water, potassium chloride in water, magnesium chloride in water, etc.).

And in cases where the solute particles neither dissociate nor associate in a solution, ‘i’ equals 1 (e.g. glucose in water).

The value of i can be obtained simply from the actual number of particles in solution after dissociation divided by the number of formula units initially dissolved in solution. In other words, the number of particles per formula unit of the solute when a solution is dilute is 'i' value for the solution.

This quantity can be related to the osmotic coefficient g by the relation: i= ng

Contributions of Chemist Van't Hoff:

In Organic Chemistry: Van 't Hoff first gained popularity in the field of organic Chemistry. In 1874, he explained the phenomenon of optical activity in solutions by emphasizing that the chemical bonds between carbon atoms and the neighboring atoms were directed towards the corners of a regular tetrahedron. The resultant three-dimensional structure that was created would explain the isomers found in nature. He shares the credit for this work in stereoChemistry with the French chemist Joseph Le Bel, who independently came up with the same idea.  Van 't Hoff later published his theory, which today is regarded as the foundation of stereoChemistry.

In Physical Chemistry: In 1884, Van 't Hoff went on to publish his works on a different aspect of Chemistry, the chemical kinetics, in the paper titled "Studies in Chemical Dynamics". Through his research, he described a novel method for determining the order of a reaction using graphics. He also applied the laws of thermodynamics to chemical Equilibrium attained in solutions and introduced the modern age concept of chemical affinity. In 1886, he worked on the  similarity between the behaviour of dilute solutions and gases. He also contributed to Svante Arrhenius's theory of dissociation of electrolytes and provided experimental evidence for the Arrhenius equation. Finally, in the year 1901, he received the first Nobel Prize in Chemistry for his work with dilute solutions. His work aptly demonstrated that very dilute solutions follow mathematical laws that closely resemble the laws describing the behavior of gases.

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