CrCl$_3$.xNH$_3$ can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of 0.558°C. Assuming 100\% ionization of this complex and coordination number of Cr is 6, the complex will be:

Question

$W$ g of a non-volatile electrolyte solid solute of molar mass $M\,\text{g mol}^{-1}$ when dissolved in $100\,\text{mL}$ water decreases vapour pressure of water from $640\,\text{mm Hg}$ to $600\,\text{mm Hg}$. If aqueous solution of the electrolyte boils at $375\,\text{K}$ and $K_b$ for water is $0.52\,\text{K kg mol}^{-1}$, then the mole fraction of the electrolyte $(x_2)$ in the solution can be expressed as ___.
(Given: density of water $=1\,\text{g mL}^{-1}$, boiling point of water $=373\,\text{K}$)

Answer 1

The problem concerns determining the structure of a coordination complex by analyzing its ionization and the resulting freezing point depression.

Given a 0.1 molal solution with a freezing point depression ($\Delta T_f$) of 0.558°C, the formula for freezing point depression, $\Delta T_f = i \cdot K_f \cdot m$, is applied. Here, $i$ represents the Van't Hoff factor, $K_f$ is the cryoscopic constant (1.86 °C kg/mol for water), and $m$ is the molality.

The Van't Hoff factor ($i$) is calculated as: $i = \frac{\Delta T_f}{K_f \cdot m} = \frac{0.558}{1.86 \cdot 0.1} \approx 3$. This indicates that the complex dissociates into 3 ions.

Considering the coordination number of Cr is 6, each potential complex structure is evaluated for its dissociation:

[Cr(NH$_3$)$_6$]Cl$_3$ yields 1 complex ion and 3 Cl$^-$ ions, totaling 4 ions, which is inconsistent with $i = 3$.

[Cr(NH$_3$)$_4$]Cl$_2$Cl yields 1 complex ion and 3 Cl$^-$ ions, totaling 4 ions, which is inconsistent with $i = 3$.

[Cr(NH$_3$)$_5$]Cl$_2$ yields 1 complex ion and 2 Cl$^-$ ions, totaling 3 ions, which is consistent with $i = 3$.

[Cr(NH$_3$)$_3$]Cl$_3$ yields 1 complex ion and 3 Cl$^-$ ions, totaling 4 ions, which is inconsistent with $i = 3$.

Therefore, the complex structure [Cr(NH$_3$)$_5$]Cl$_2$ is confirmed as correct, as it aligns with the experimentally derived Van't Hoff factor of $i = 3$.

The identified correct structure is [Cr(NH$_3$)$_5$]Cl$_2$.

CrCl\(_3\).xNH\(_3\) can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of 0.558°C. Assuming 100\% ionization of this complex and coordination number of Cr is 6, the complex will be:

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The Correct Option is C

Solution and Explanation

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