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The Van’t Hoff factor for \[0\cdot 1M\]$Ba{{\left( N{{O}_{3}} \right)}_{2}}$ solution is $\text{2}\cdot \text{74}$ The degree of dissociation is:

Last updated date: 13th Jun 2024
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Hint: The Van’t Hoff factor is used to determine the degree of dissociation. It is a measure of deviation from ideal behavior. With the increasing concentration of solute, the Van’t Hoff factor decreases because ionic compounds generally do not totally dissociate in aqueous solution.

Formula used: $i=1+2\alpha $ where i= Van’t Hoff Factor
  $\alpha $= degree of dissociation

Complete answer: or Complete step by step answer:
The solution It is defined as the ratio of the concentration of particles formed when a substance is dissolved to the concentration of the substance by mass. The extent to which a substance associates or dissociates in a solution is described by Van’t Hoff Factor. This Factor is represented by ‘$i$ ’ and is named after Dutch physical chemist Jacobus Henricus Van’t Hoff.
For an Electrolytic solution, the value of $i$ is generally higher than the predicted value (due to pairing of ions).
Association: It is the joining of two or more particles to form one entity ($i$ is less than 1).
Dissociation: It refers to the splitting of a molecule into multiple iconic entities ($i$ is greater than 1).
Given compound, $Ba{{(N{{O}_{3}})}_{2}}\text{ dissociates into B}{{\text{a}}^{2+}}\text{ and 2N}{{\text{O}}^{-3}}$ . Using,
$i=1+2\alpha $
$\Rightarrow 2\cdot 74=1+2\alpha $
$\Rightarrow 2\cdot 74-1=2\alpha $
$\Rightarrow 1.74=2\alpha $
$\Rightarrow \alpha =\dfrac{1\cdot 74}{2}=0\cdot 87$
$\Rightarrow \alpha =87%$

So, the correct answer is “Option B”.

Additional Information:
Colligative properties: These 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 vapor pressure lowering, boiling point elevation, freezing point depression and osmotic pressure.
The Van’t Hoff Factor (i) is a measure of the effect of a solute on colligative properties.
i.e. $i=\dfrac{measured\text{ value of concentration of particles}}{calculated\text{ value of concentration from its mass}}$

 Concepts regarding colligative properties, Van’t Hoff Factor and degrees of dissociation and association should be clear. Dissociating the compound into ions according to their respective changes should be learnt. Van’t Hoff Factor is more than the 1 for the strong electrolytes which will dissociate and form more than one ion. It is less than 1 then it will tend to associate.