Van't Hoff Factor and Abnormal Molar Mass

Van't Hoff factor was discovered by Jacobus Henricus van't Hoff in the year 1887 when he was developing the theory of chemical equilibria he proposed the concept of van't Hoff factor and his work developed the idea of colligative properties of solutions which are influenced by the number of particles in the solution which leads to the formulation of van't Hoff factor. The scientists Water Nernst and Friedrich Ostwald studied the behavior of solutions then they came to understand the colligative properties and the influence of solute particle behavior on these properties. They observe that the molar mass of the solutes P article when calculated from the colligative properties measurement could be different from the expected value due to the dissociation and association of the molecules.

This Story also Contains

1. Van't Hoff factor(i) or Abnormal Colligative Property
2. Some Solved Examples
3. Summary

Van't Hoff factor(i) or Abnormal Colligative Property

If a solute gets associated or dissociated in a solution, the actual number of particles is different from expected or theoretical consideration.

We know, that:

Colligative property $\propto$ number of particles

Thus, we can say that:

$\begin{aligned} & \mathrm{i}=\frac{\text { Observed number of solute particles }}{\text { Number of particles initially taken }} \\ & \mathrm{i}=\frac{\text { Observed value of colligative property }}{\text { Theoretical value of colligative property }}\end{aligned}$

Again, we have:

Colligative property $\propto \frac{1}{\text { molecular mass of solute }}$

Thus;

$\mathrm{i}=\frac{\text { Theoretical molecular mass of solute }}{\text { Observed molecular mass of solute }}$

van't Hoff Factor for dissociation of solute

Suppose we have the solute A which dissociates into n moles of A. Then the dissociation occurs as follows:

$\mathrm{A}_{\mathrm{n}} \rightarrow \mathrm{nA}$

At time t = 0 1 0

At time t = t 1 - $\alpha$ n$\alpha$

At time t = 0, initial number of solute particles = 1

And, at time t = t, observed number of solute particles = 1 - $\alpha$ + n$\alpha$

= 1 + (n-1)$\alpha$

Thus, we know that:

$\mathrm{i}=\frac{\text { observed number of solute particles }}{\text { initial number of solute particles }}$

$\mathrm{i}=\frac{1+(\mathrm{n}-1) \alpha}{1}$

where n = number of solute particles

$\alpha$ = Degree of dissociation

For strong electrolytes, the degree of dissociation is taken to be unity.

Using the above equation, the van’t Hoff factor and the degree of dissociation can be related which can be further related to the theoretical and observed colligative properties.

Calculation of Extent of Association in an Electrolytic Solution

Suppose we have a solute A and it associates into (A)_n. Then the association occurs as follows:

$n A \rightarrow(A)_n$

At time t = 0 1 0

At time t = t 1 - $\beta$ $\beta$/n

Now, the initial number of solute particles = 1

And, the observed number of solute particles = $1-\beta+\frac{\beta}{n}$

$=1+\beta\left[\frac{1}{n}-1\right]$

Thus, van't Hoff factor is given as:

$i=1+\beta\left[\frac{1}{n}-1\right]$

where, $\beta$ is the degree of association

Using the above equation, the van’t Hoff factor and the degree of association can be related which can be further related to the theoretical and observed colligative properties.

Recommended topic video on (Vant Hoff Factor)

Some Solved Examples

Example.1

1. Which of the following is not a colligative property?

1)Osmotic pressure

2)Elevation in B.P.

3) (correct)Vapour pressure

4)Depression in the freezing point

Solution

As we have learned,
Colligative Properties -
Properties that depend on a number of solute particles and are independent of the nature of the solute are known as colligative properties.
wherein it is due to the addition of non-volatile solute to solvent.

Vapour pressure is not a colligative property.

Hence, the answer is the option (3).

Example.2

2. Which of the following is a colligative property?

1) (correct)Osmotic pressure

2)Boiling point

3)Vapour pressure

4)Freezing point

Solution

As we have learned,
Colligative Properties -
Properties that depend on a number of solute particles and are independent of the nature of the solute are known as colligative properties. It is due to the addition of non-volatile solute to solvent.

Osmotic pressure is a colligative property.
Hence, the answer is the option (1).

Example.3

3. Which of the following will have the highest boiling point at 1 atm pressure

1)0.1M NaCl

2)0.1M sucrose

3) (correct)0.1 M BaCl₂

4)0.1 M glucose

Solution

All have the same concentration, So they can be compared by the number of ions.

1) 0.1 M NaCl , Number of ions - Na⁺ + Cl^- = 2
2) 0.1 M sucrose , Number of ions - sucrose = 1
3) 0.1 M BaCl₂ (Correct) , Number of ions - Ba²⁺ + 2Cl^- = 3
4) 0.1 M glucose , Number of ions - sucrose = glucose

BaCl₂ gives maximum ion. Hence, it shows the highest boiling point.

Hence, the answer is the option (3).

Example.4

4. The osmotic pressure of a dilute solution of an ionic compound $X Y$ in water is four times that of a solution of $0.01 \mathrm{MBaCl}_2$ in water. Assuming complete dissociation of the given ionic compounds in water, the concentration of $X Y\left(\right.$ in mol $\left.L^{-1}\right)$ in solution is :

1) $4 \times 10^{-2}$

2) (correct) $6 \times 10^{-2}$

3) $4 \times 10^{-4}$

4)$16 \times 10^{-4}$

Solution

Osmotic Pressure - Osmotic Pressure ($\pi$) is excess pressure developed on the solution side due to osmosis.

Vant Hoff factor (i) -

In the case of electrolytes, the observed colligative property is different from the theoretical colligative property. The ratio is defined by the Vant Haff factor

- wherein

$i=\frac{\text { observed }}{\text { theoritical }}$

Given, $\pi_{x y}=4 \pi_{\mathrm{BaCl}_2}$

$\begin{aligned} & i_1 C_1 R T=4 i_2 C_2 R T \\ & 2[x y]=4 \times 3 \times[0.01] \\ & {[x y]=2 \times 3 \times 0.01=6 \times 10^{-2} M}\end{aligned}$

Hence, the answer is the option (2).

Example.5

5. Which one of the following aqueous solutions will exhibit the highest boiling point?

1) (correct)$0.01 \mathrm{MNa}_2 S \mathrm{SO}_4$

2)0. $01 \mathrm{M} \mathrm{KNO}_3$

3)0.015M Urea

4)0.015 M glucose

Solution

Elevation in Boiling point $\propto i \times m$

For Na₂SO₄, i = 3, will be the highest among these given aqueous solutions.

So, In 0.01 M Na₂SO_4, the $i \times m$ value will be 0.03 which is the highest of the given options.

Hence, the answer is the option (1).

Example.6

6. Which of the following solution in water possesses the lowest vapour pressure?

1)0.1 M NaCl

2) (correct)0.1 M BaCl₂

3)0.1 M KCl

4)None of these

Solution

BaCl₂ gives maximum ion hence it shows the lowest vapour pressure.
Hence, the answer is the option (2).

Summary

Van't hoff factor and the abnormal molar mass are connected to each other as They are developed by the almost same scientist and They give us a deeper understanding of how solute affects the colligates properties. This factor tells us that the behavior of solute in the solvent is very important to accurately determine the properties of solutions and their molar masses. Their Applications are as follows the accurate determination of molar mass is important in pharmaceutical chemistry as in the formulation of the drug design. The Van't hoff factor helps to determine the electrolyte behavior in accordance with the physiological conditions and it is also necessary to ensure the proper osmotic balance to avoid any complications in the intravenous solution for designing the drug.