8 g of [CrCl_x(H₂O)_y]Cl_(3–x) ⋅ H2O_(6–y) react with average AgNO₃ to form 8.61 g of AgCl. The value of (x × y) is _____.

The correct answer is 5.

To find the value of (x × y), we need to determine the number of ionizable chloride ions and the coordination number of the complex.

Step 1: Identify the overall formula and calculate the molar mass of the compound
The given coordination compound is represented as $\left[{\mathrm{CrCl}}_x\right(H_{2}O{)}_y]{\mathrm{Cl}}_{(3-x)}\cdot H_2{O}_{(6-y)}$.
Regardless of the values of $x$ and $y$, the total number of chromium, chlorine, hydrogen, and oxygen atoms in the formula remains constant:
Total Cl atoms = $x+(3-x)=3$
Total $H_{2}O$ molecules = $y+(6-y)=6$
Thus, the empirical formula of the complex is ${\mathrm{CrCl}}_3\cdot 6H_{2}O$.

Now, let's calculate its molar mass using the atomic weights (Cr = 52, Cl = 35.5, H = 1, O = 16):
Molar mass of ${\mathrm{CrCl}}_3\cdot 6H_{2}O$ = 52 + (3 × 35.5) + (6 × 18) = 52 + 106.5 + 108 = 266.5 g/mol.

Step 2: Calculate the number of moles of the complex
Moles of compound = $\frac{8\text{g}}{266.5\text{g/mol}}\approx 0.03\text{mol}$

Step 3: Calculate the number of moles of AgCl precipitated
Only the chloride ions present outside the coordination sphere (i.e., $3-x$ chloride ions) are ionizable and will react with excess silver nitrate (${\mathrm{AgNO}}_3$) to form silver chloride ($\mathrm{AgCl}$).
Molar mass of $\mathrm{AgCl}$ = 108 (for Ag) + 35.5 (for Cl) = 143.5 g/mol.
Moles of $\mathrm{AgCl}$ formed = $\frac{8.61\text{g}}{143.5\text{g/mol}}=0.06\text{mol}$

Step 4: Determine the value of x
From the stoichiometry of the reaction, 1 mole of the complex yields $(3-x)$ moles of $\mathrm{AgCl}$. Therefore:
Moles of $\mathrm{AgCl}$ = Moles of compound × $(3-x)$
0.06 = 0.03 × $(3-x)$
$3-x=2$
$x=1$

Step 5: Determine the value of y and calculate (x × y)
Chromium (Cr) in this coordination compound is in the +3 oxidation state, which typically exhibits a coordination number of 6. This means the total number of ligands inside the coordination sphere must equal 6:
$x+y=6$
Substituting $x=1$:
$1+y=6\Rightarrow y=5$

Now, we find the value of (x × y):
$x\times y=1\times 5=5$