Van't Hoff Factor

Some chemical substances when used as solutes undergo dissociation or association in solution. This causes 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 van’t Hoff factor, you need to understand 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 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 –

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 

                                              

On keeping the values from equation in the above formula –

                                                                                    

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

In case of dissociation – quantity of solute increases, 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. 

2CH3COOH + Benzene 🡪 (CH3COOH)2

Thus, at t=0, when association did not start, 2 moles of acetic acid is present. While at time t, when association is completed, 1 mole of acetic acid is present. As we know van’t hoff factor –

On keeping the values -

 

Thus, in case of association value of i is smaller than one, 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 –


Quantity of Solute 

Colligative Property 

Molar mass of Solute 

Van’t Hoff Factor (i)

Dissociation 

Increases 

Increases 

Decreases 

i>1

Association 

Decreases 

Decreases 

Increases 

i<1


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