Abnormal Molar Masses: Van’t Hoff Factor & Colligative Properties

Abnormal molar masses are those values that, when calculating molar masses, turn out to be either on the higher or lower side, usually varying from experimentally predicted ones. These are calculated using the colligative properties. Simply, the theoretical values of molecular mass often differ from the experimentally determined values. Thus, these values are called Abnormal Molar Masses.

Some of the colligative properties include:

• Elevation of Boiling Point
• Lower Vapor Pressure
• Freezing Point Depression
• Easiness Of Osmotic Pressure

The term “Abnormal” suggests the abnormality of the calculation of molar masses, which is also known as the Van’t Hoff factor. The Van’t Hoff factor is “the ratio of the particle concentration that forms when a substance is dissolved to the concentration of the substance by mass.”

Key Terms: Solutions, Solubility, Colligative Property, Atomic Mass, Solute, Van’t Hoff Factor, Molar Mass, Association, Dissociation, Mass Spectrometry

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Van’t Hoff Factor

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The Van’t Hoff factor defines the effect of solutes on the colligative properties of solutions. The symbol used to donate the same is “i”. The Van’t Hoff factor can be defined as:

The extent to which a substance associates or dissociates in a solution is referred to as the Van’t Hoff factor.

• For instance, when a non-electrolytic substance gets dissolved in water, the value of “i”, in a majority of the cases will be 1.
• However, in the formation of a solution in water due to an ionic compound, the value of “i” will remain the same as the total number of ions available in one formula unit of the substance.
• For instance, the Van’t Hoff factor of CaCl₂ will be 3 on getting dissociated into one Ca²⁺ ion and two Cl^– ions.
• However, some of these ions associate with each other in the solution, which will result in a decrease in the total number of particles present in the solution.
• This factor is named after a famous scientist who won the first Nobel Prize in chemistry - Jacobus Henricus Van’t Hoff.
• It is important to note that the measured value of the Van’t Hoff factor for electrolytic solutions will be less as compared to the estimated value.
• The more the charge on the ions, the more the deviation will be.

Van’t Hoff factor Formula

The following are some formula used for Van’t Hoff factor:

• \(i = \frac{Observed\ Colligative\ Property}{Normal\ or\ Theoretical\ Colligative\ Property}\)
• \(i = \frac{Normal\ Molar\ Mass}{Observed\ Molar\ Mass}\)
• \(i = \frac{Actual\ Number\ of\ Particles}{Expected\ Actual\ Number\ of\ Particles}\)

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Effects of Association/Dissociation

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The effects of Association/Dissociation can be explained as:

• Association means the joining of two or more particles in order to create one single entity.
• An example of the association of two particles is the dimerization of carboxylic acids on getting dissolved in benzene.
• Dissociation means the splitting of a molecule into many multiple ionic entities.
• For example, sodium chloride (NaCl) dissociates into Na⁺ and Cl^– ions when they get dissolved in water. 

The effects of the association or dissociation of a solute on the solution, their respective colligative properties, and Van’t Hoff factor can be further differentiated as:

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Abnormal Molar Masses

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The theoretical molecular mass values, when calculated from the colligative properties of solutions, often differ from the experimentally acquired values. Thus, these values are often called abnormal molar masses.

Molecular masses of the solute are determined taking the help of colligative properties easily such as:

• Relative Lowering In Vapour Pressure
• Boiling Point Elevation
• Freezing Point Depression
• Osmotic Pressure

All these values are referred to as Abnormal Molar Masses.

The abnormality in the molecular mass occurs when:

• The dissociation of solute molecules into many ions will witness a surge in total particles, which in turn, will further increase the colligative properties of the solution.
• Since the molar mass is inversely proportional to the colligative properties, the overall value will be lower as expected.
• When solute particles get associated with each other, the total number of particles in the solution will decrease, which further will lower the overall colligative properties.
• In this case, the molar mass values achieved will be more than predicted.

Abnormal Molar Masses & Van't Hoff Factor

Association of Solute Particles

Some solute molecules start to get linked inside the solution, meaning that they have fewer amount of solute particles in the solution.

• As colligative properties differ with solute particles in the solution, they will keep on decreasing with the solute particles.
• Since the colligative properties are inversely proportional to the molecular mass of the solute, the molar mass of the solute will be much.

Dissociation of Solute Particles

Some solute molecules namely electrolytes dissociate into two or more ions/particles on getting dissolved in a solution.

• It results in a further surge in solute particles in the solution, further increasing the colligative properties of solutions.
• Since the colligative properties and molecular mass of the solute differ inversely, the molar mass of the solute will be less.

To Describe the Abnormality in Molecular Mass: 

• The rise in the number of particles causes the dissociation of solute molecules into ions, thus increasing the solution's colligative properties. 
• Knowing that molar mass is inversely proportional to the colligative properties, it generally has a lower value than the one predicted. 
• The total number of particles in the solution can be observed to decrease as solvent particles interact with one another, leading to colligative property decrement. 
• The molar mass values which are acquired are higher than expected herein.

The precise value of the molar mass can be acquired considering that the following conditions are met:

• The solutions should be diluted: The solutions that help determine colligative properties shouldn’t be too concentrated. In concentrated solutions, The particles, in concentrated solutions, are known to interact with one another as well as with the solvent. Thus, vapour pressure, alongside other conjugate properties, is based on the nature of the solute, and not only the number of solute particles.
• The required solute is not separate or collaborative in the solution: The derivative equations that further aid for the measurement of the colligative properties are for non-electrolyte solutes which don’t undergo dissociation or have an association solution. However, certain issues in the determination of the molar mass can take place when solutes dissociate or associate with dissolution in a solvent. This happens because the number of molecules in a solution varies due to the addition or dissociation of solute molecules.

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Colligative Properties of Solutions

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With an intention to decide the colligative properties for solutions that undergo association and dissociation, a Dutch physical chemist, Jacobus Henricus van’t Hoff, in 1880, introduced the concept of Van’t Hoff Factor (i).

The concept was introduced to understand the association and dissociation problem while calculating the molar mass of the solute. The Van’t Hoff factor is represented by ‘i’ and is obtained while dividing normal mass with an abnormal mass of solute. Thus,

Calculating “i”:

First of all, we write an equation of the solute being associated or dissociated. 

For Dissociation

In case of Dissociation:

i = 1 + (n – 1) α

Here,

• n = number of particles dissociated
• α = degree of dissociation

Thus, 

Initial Moles = 1 mole and 0 moles

⇒ When at equilibrium = 1 – α and nα

⇒ Total number at equilibrium = 1 – α + nα

⇒ Hence, i = 1 – α + \(\frac{nα}{1}\)

Therefore, α = \(\frac{i - 1}{n - 1}\)

For Linking or Association

In case of Association:

i = 1 + (1/n – 1) α

Here,

• n = number of particles dissociated
• α = degree of dissociation

The derivation obtained is:

nα → α_n 

⇒ Initial Moles: 1 mole and 0 moles

⇒ At equilibrium 1 – α  and  α/n

⇒ Total moles = 1 – α + α/n

Therefore, \(\alpha = n \frac{1 - i}{(n - 1)}\)

• For solutes depicting association, the Van’t Hoff factor will always remain lesser than 1.
• For solutes showing dissociation, the Van’t Hoff factor will be more than 1. 
• For instance, both KCl and NaCl have Van’t Hoff factor 2.
• For particles showing neither dissociation nor association, the Van’t Hoff Factor will be 1.

The modified equations referred to while determining molar mass in case of association or dissociation is:

• Vapour Pressure of Relatively Lowering Solvent, \(\frac{p_1º – p_1}{p_1º } = \frac{i.n_2}{n_1} \)
• Boiling Point Elevation, Δ T_b = i K_b m where K_b is the elevation constant and m is the molality of the solute
• Freezing Point Depression Δ T_f = i K_f m where K_f is the depression constant and m is the molality of the solute

Did You Know? Osmotic pressure plays a major role in the biological cell. One of the most important factors known to affect cells is Osmotic Pressure. Osmoregulation is a homeostasis process followed by an organism for osmotic pressure in order to achieve equilibrium.  Hypertonicity can be expressed as the presence of a solution which causes cell shrinkage.  Hypotonicity is the presence of a solution which causes cells to swell. Isotonicity can be defined as the presence of a solution which causes no change in the volume of cells.

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Things to Remember

• Molar mass is the total number of moles that is present in a solution after the dissociation or association of solute.
• If the molar mass is below or above the expected value, it is called an abnormal molar mass.
• Van’t Hoff factor provides detailed information on the effect of solutes on the colligative properties of solutions. 
• For solutes depicting association, the Van’t Hoff factor will always remain lesser than 1.
• For solutes showing dissociation, the Van’t Hoff factor will be more than 1. 
• For particles showing nor dissociation or association, the Van’t Hoff Factor will be 1.

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Important Chemistry Topics
Avogadro's Law	Atomic Mass of Elements	Theoretical Yield Formula
Concentration of a Solution	Percent by Weight Formula	Dalton's Law of Partial Pressure
Difference between Molar Mass and Molecular Mass	Pressure of an Ideal Gas	Difference between Mixture and Solution
Solutions Important Questions	Solutions MCQ	Ncert Solutions of Chapter 2 Solutions

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Previous Years Questions

1. Calculate the molecular weight of the solute.​
2.  For this process, which of the following statement is true?​
3. Then the vapour pressure of a solution containing 1 mole of a strong electrolyte (AB2) in 99 moles of the solvent at 293 K is (assume complete dissociation of solute)​
4. The number of millimoles of the gas dissolved in one litre of water is
5. Molarity of 0.2NH₂SO₄ is​
6. The degree of dissociation (α) of a weak electrolyte AxBy is related to van?t Hoff factor (i) by the expression​
7. If glucose of 36g weight is dissolved in 2kg of H₂O then, change in boiling point (ΔTb) at 1.013 bar will be (Kb for H₂O is 0.52Kkgmol⁻¹)​
8. Volume of acid required to make 1 litre of 0.1MH₂SO₄ solution is:​
9. With increase in temperature, which one of these changes?
10. What would be the freezing point of aqueous solution containing 17g of C₂H₅OH in 1000g of water?