Question

Van’t Hoff factor of \[Ca{(N{O_3})_2}\]is:
A. 1
B. 2
C. 3
D. 4

Answer 1

Hint: Van't Hoff factor quantifies the extent to which a solute is dissociated or associated. Van 't Hoff factor deviation tends to be greatest when ions have multiple charges.

Complete Step by Step Solution:
1. A ratio of normal molar mass to experimentally determined molar mass or the ratio of observed colligative property to calculated colligative property.
2. The expressions for the Van’t Hoff factor are given below:
\[i = \dfrac{{Normal\,molar\,mass}}{{Abnormal\,molar\,mass}}\]
\[i = \dfrac{{Observed\,colligative\,property}}{{Calculated\,colligative\,property}}\]
\[i = \dfrac{{Total\,number\,of\,moles\,of\,particles\,after\,association/dissociation}}{{Number\,of\,moles\,of\,particles\,before\,association/dissociation}}\]
3. Based on the Van’t Hoff value, the molecules are
If \[i > 1\], then molecules are said to have dissociated
If \[i = 1\], then molecules have neither associated nor dissociated
If \[i < 1\], then molecules have associated
4. The general formula to calculate the Van’t Hoff factor:
\[i = 1 + alpha(X + Y - 1)\]
Where X is the number of cations and Y is the number of anions.
5. The dissociation of \[Ca{(N{O_3})_2}\]is expressed by an equation:
\[Ca{(N{O_3})_2}(aq) \to C{a^{2 + }}(aq) + 2NO_3^ - (aq)\]

In the given equation,
Degree of dissociation = 1
Number of cation = 1
Number of anions = 2

Applied these values in the general formula to calculate Van’t Hoff factor:
\[i = 1 + 1\left( {1 + 2 - 1} \right) = 3\]
The Van’t Hoff factor is three for the given compound.
Option (C) is the correct answer.

Additional information:
1. Dissociation: The separation of the ionic crystal lattice that occurs when a solid ionic compound is dissolved in water
2. Abnormal mass is the experimentally determined molar mass, and colligative properties are derived by assuming the non-volatile solute is neither associative nor dissociative.

Note: When the solute present in the solution gets dissociated or associated, the observed value of colligative properties differs from the theoretically calculated value.