Question

What is the Van’t Hoff factor of $N{{a}_{3}}P{{O}_{4}}$ in a 0.40 m solution whose freezing point is -2.6$^{\circ }C$.

Answer 1

Before answering this question, we should first know about the Van’t Hoff factor. The ratio between the number of particles of solute and the number of particles that are produced in a solution after solute is being dissolved in the solution is the Van't Hoff factor.

Complete answer:
Van’t Hoff factor of $N{{a}_{3}}P{{O}_{4}}$is-
Generally, we will assume the value of Van’t Hoff factor of $N{{a}_{3}}P{{O}_{4}}$ to be 4
The number of ions that are produced per formula unit of solute in Ionic compounds.
When Sodium phosphate is kept in an aqueous solution, It dissociates and produces positive ions i.e Sodium cations ($N{{a}^{+}}$) and negative ions i.e Phosphate anions ($PO_{4}^{3-}$).
$N{{a}_{3}}P{{O}_{4}}(aq)\to 3N{{a}^{+}}(aq)+PO_{4}^{3-}(aq)$
As 4 ions are produced by every formula unit of sodium phosphate so we assume the van’t Hoff factor to be 4 but that’s not the case.
Freezing point depression equation is :
$\Delta {{T}_{f}}=i.\,{{K}_{f}}.\,b$
In which,
$\Delta {{T}_{f}}$- freezing point depression
i – Van’t Hoff factor
${{K}_{f}}$- cryoscopic constant of the solvent
b – molality of the solution.
The cryoscopic constant of water is 1.86 $^{\circ }C\,Kg\,mo{{l}^{-}}^{1}$.
The freezing point depression can be seen as –
$\Delta {{T}_{f}}=T_{f}^{\circ }-{{T}_{f}}$
In which,
$T_{f}^{\circ }$- the freezing point of the pure solvent
${{T}_{f}}$- the freezing point of the solution
In this : $\Delta {{T}_{f}}={{0}^{\circ }}C-(-{{2.6}^{\circ }}C)={{2.6}^{\circ }}C$
Now, we put all the values in the formula to obtain the result
$\Delta {{T}_{f}}=i.\,{{K}_{f}}.\,b$
$i=\dfrac{\Delta {{T}_{f}}}{{{K}_{f}}.\,b}$
$i=\dfrac{{{2.6}^{\circ }}C}{{{1.86}^{\circ }}\,C\,Kg\,mo{{l}^{-1}}\times \,0.40\,mol\,K{{g}^{-1}}}$
i = 3.5
Our expected value of Van’t Hoff factor was 4 but the observed value of Van’t Hoff factor that is obtained is 3.5

Note:
The expected Van’t Hoff factor will always be greater than the observed Van’t Hoff factor. It occurs because some ions form solvation cells by binding. This is the reason the expected value is greater than the number of ions produced per formula unit.