Question

A 0.0020M aqueous solution of an ionic compound $Co{{(N{{H}_{3}})}_{5}}(N{{O}_{2}})Cl$freezes at -0.00732°C. Number of moles of ions which 1 mole of ionic compound produces on being dissolved in water will be: $\left[ {{K}_{f}}=1.86{}^\circ C/m \right]$
(a) 1
(b) 2
(c) 3
(d) 4

Answer 1

Van’t Hoff factor is the number of splitting or forming of ions of the solute in a solution. To solve this, you can use the relation of the Van’t Hoff factor with the dissociation constant and find out the correct answer.
For dissociation, $i=1+\alpha \left( n-1 \right)$ and for association, $i=1-\left( 1-\dfrac{1}{n} \right)\alpha$.
Also, for calculating depression in freezing point $\left( \Delta {{T}_{f}} \right)$ will be calculated using the formula: $\Delta {{T}_{f}}=i\times {{K}_{f}}\times m$

Complete step by step solution:
We have been provided with an aqueous solution of an ionic compound $Co{{(N{{H}_{3}})}_{5}}(N{{O}_{2}})Cl$ with concentration: 0.0020M, and freezing point: -0.00732°C.
Now, depression in freezing point $\left( \Delta {{T}_{f}} \right)$ is given by: $\Delta {{T}_{f}}=i\times {{K}_{f}}\times m$,
Where, $i=$Vant Hoff factor
${{K}_{f}}=$ cryoscopic constant (for water: 1.86°C/m),
m= molality of solution
In this question, we have been given $\Delta {{T}_{f}}=0-(-0.00732)$,
So, depression in freezing point comes out to be: $\Delta {{T}_{f}}=0.00732$,
Now, as we need to calculate number of moles of ions, so for that we will be calculating Van't Hoff factor(i) using the formula:$i=\dfrac{\Delta {{T}_{f}}}{{{K}_{f}}\times m}$,
Keeping the values, we would get: $i=\dfrac{0.00732}{1.86\times 0.0020}$,
So, Van't Hoff Factor comes out to be: $i=1.86\approx 2$,
So, the compound $Co{{(N{{H}_{3}})}_{5}}(N{{O}_{2}})Cl$ in solution will dissociate into $\left[ C \right.o{{(N{{H}_{3}})}_{5}}(N{{O}_{2}}{{\left. ) \right]}^{+}}$ and $C{{l}^{-}}$,
So, the number of moles of ions that is n comes out to be: n=2.

Therefore, option (b) is correct.

Note: Non-electrolytes dissolved in water have the value of i equal to 1. Ionic compounds dissolve in water and thus the Van’t Hoff factor is the number of ions in a formula unit of the substance.
Van't Hoff Factor for dissociation is: $i=1+\alpha (n-1)$.