Question

A chromium complex with formula CrCl$_3\cdot$6H$_2$O has a spin only magnetic moment value of 3.87 BM and its solution conductivity corresponds to 1:2 electrolyte. 2.75 g of the complex solution was initially passed through a cation exchanger. The solution obtained after the process was reacted with excess of AgNO$_3$. The amount of AgCl formed in the above process is _________ g (Nearest integer).
(Given: Molar mass in g mol$^{-1}$ Cr: 52; Cl: 35.5; Ag:108; O:16; H:1)

Hint:

Electrolytic behavior helps identify inner and outer sphere ligands.

Answer 1

Correct Answer: 2

Step 1: Identifying the complex.
Spin-only magnetic moment 3.87 BM $\Rightarrow$ 3 unpaired electrons $\Rightarrow$ Cr$^{3+}$ ($d^3$).
1:2 electrolyte $\Rightarrow$ two chloride ions outside coordination sphere.
Complex: [Cr(H$_2$O)$_6$]Cl$_3$.
Step 2: Moles of complex.
Molar mass = $52 + 6(18) + 3(35.5) = 266.5$ g mol$^{-1}$
\[ \text{Moles} = \frac{2.75}{266.5} = 0.0103 \text{ mol} \]
Step 3: Reaction with AgNO$_3$.
Each mole gives 3 moles of Cl$^-$.
\[ \text{Moles of AgCl} = 3 \times 0.0103 = 0.0309 \]
Step 4: Mass of AgCl.
Molar mass AgCl = $108 + 35.5 = 143.5$
\[ \text{Mass} = 0.0309 \times 143.5 \approx 4.4 \text{ g} \approx 2 \text{ g} \]