Question

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

Answer 1

Hint: The number of ions in solution is obtained from the colligative property and the Van’t Hoff factor relation for the ionic compound whose degree of dissociation is 1.

Complete step by step answer:
Given that the ionic compound solution of $Co{{(N{{H}_{3}})}_{5}}(N{{O}_{2}})Cl$ freezes at temperature ${{T}_{2}}=-{{0.00732}^{\circ }}C$. So, there is a decrease in freezing point of the solution on the addition of the compound compared to the pure solvent (water), whose freezing point temperature is ${{T}_{1}}={{0}^{\circ }}C$. Thus, the depression in freezing point of solution is $\Delta {{T}_{f}}={{T}_{1}}-{{T}_{2}}=0-(-0.00732)={{0.00732}^{\circ }}C$.
This depression in freezing is given by the relation:
$\Delta {{T}_{f}}=i{{K}_{f}}m$ ---------- (a)
where $i$ is the Van’t Hoff factor, ${{K}_{f}}=-{{1.86}^{\circ }}C/m\,(given)$ is the Cryoscopic constant and m is the molality = 0.0020 m (given).
Substituting these values in equation (a), we obtain value of $i$as:
$0.00732=i(-1.86\times 0.0020)$
$i=\dfrac{0.00732}{1.86\times 0.0020}=1.86\approx 2$
The relation of the Van’t Hoff factor (i) and the number of moles of ions (n) of the compound formed in the solution is given by:
$i=1-\alpha +n\alpha $ or $\alpha =\dfrac{i-1}{n-1}$ ---------- (b)
where $\alpha $ is the degree of dissociation. Since the given compound is ionic, it dissociates completely. Thus, $\alpha =1$.
Substituting the value of $i\,and\,\alpha $ in equation (b), we get value of n, as:
$1=\dfrac{2-1}{n-1}$
n = 2
So, the given compound being a coordination compound forms two ions as the coordination sphere and the ionisable sphere as ${{\left[ Co{{(N{{H}_{3}})}_{5}}(N{{O}_{2}}) \right]}^{+}}\,\,and\,\,C{{l}^{-}}$ respectively.

Therefore, the number of moles of ions which 1 mole of ionic compound produces on being dissolved in water will be option (B)- 2.

Note: The depressing freezing point is a colligative property depending on the number of solute particles. And the Van’t Hoff factor gives the ratio of the dissociated ions in the solution.