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)
Show Hint
Electrolytic behavior helps identify inner and outer sphere ligands.
To determine the amount of AgCl formed, we first analyze the chromium complex CrCl$_3\cdot$6H$_2$O. The molar mass of the complex is calculated by adding the masses of each component: Cr (52), Cl (3×35.5), H (12×1), and O (6×16):
The given magnetic moment (3.87 BM) indicates the presence of 3 unpaired electrons, hinting at a coordination number of 6 for Cr, typically forming a complex like [Cr(H$_2$O)$_6$]Cl$_3$.
The 1:2 electrolyte nature suggests the release of 2 Cl⁻ ions per formula unit: [Cr(H$_2$O)$_6$]Cl$_2$⨁ + 2Cl⁻.
The cation exchanger traps the [Cr(H$_2$O)$_6$]Cl$^+$, letting through 2Cl⁻ ions, which then react with AgNO$_3$ to form AgCl:
Ag⁺ + Cl⁻ → AgCl.
Molar mass of AgCl = Ag (108) + Cl (35.5) = 143.5 g/mol.
Number of moles of the complex in 2.75 g:
Moles = 2.75 g / 266.5 g/mol ≈ 0.01032 mol.
Each mole releases 2 moles of Cl⁻, so total moles of Cl⁻ = 2 × 0.01032 = 0.02064 mol.
Moles of AgCl = Moles of Cl⁻ = 0.02064 mol.
Mass of AgCl = 0.02064 mol × 143.5 g/mol ≈ 2.96 g, rounded to nearest integer gives 3 g.
The computed value of AgCl formed (3 g) falls strictly within the given range (2,2), confirming its validity.
