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Ratio of Moles of Complex Reacted and AgCl Formed

5.33 g5.33\text{ g} of CrCl3⋅6H2O\mathrm{CrCl_3 \cdot 6H_2O}, which is a 1:31 : 3 electrolyte, is dissolved in water and is passed through a cation exchanger. The chloride ions in the eluted solution, on treatment with AgNO3\mathrm{AgNO_3} results in 8.61 g8.61\text{ g} of AgCl\mathrm{AgCl}. The ratio of moles of complex reacted and moles of AgCl\mathrm{AgCl} formed is ________ ×10−2\times 10^{-2}. (Nearest integer) [Molar mass in g mol−1Cr:52,Ag:108,Cl:35.5,H:1,O:16\text{g mol}^{-1} \mathrm{Cr} : 52, \mathrm{Ag} : 108, \mathrm{Cl} : 35.5, \mathrm{H} : 1, \mathrm{O} : 16]

Official Numerical Answer33

Topics & Concepts

Coordination CompoundsCoordination CompoundsMole Concept

Step-by-Step Solution

To determine the ratio of the moles of the complex reacted to the moles of AgCl\mathrm{AgCl} formed, we calculate the moles of each substance step-by-step:

Step 1: Calculate the molar mass of the complex CrCl3⋅6H2O\mathrm{CrCl_3 \cdot 6H_2O} Molar Mass of CrCl3⋅6H2O=52+3(35.5)+6(18)\text{Molar Mass of }\mathrm{CrCl_3 \cdot 6H_2O} = 52 + 3(35.5) + 6(18) =52+106.5+108=266.5 g mol−1= 52 + 106.5 + 108 = 266.5\text{ g mol}^{-1}

Step 2: Calculate the moles of the complex reacted Moles of complex (ncomplex)=MassMolar Mass=5.33 g266.5 g mol−1=0.02 mol\text{Moles of complex } (n_{\text{complex}}) = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{5.33\text{ g}}{266.5\text{ g mol}^{-1}} = 0.02\text{ mol}

Step 3: Calculate the molar mass of AgCl\mathrm{AgCl} Molar Mass of AgCl=108+35.5=143.5 g mol−1\text{Molar Mass of }\mathrm{AgCl} = 108 + 35.5 = 143.5\text{ g mol}^{-1}

Step 4: Calculate the moles of AgCl\mathrm{AgCl} formed Moles of AgCl(nAgCl)=MassMolar Mass=8.61 g143.5 g mol−1=0.06 mol\text{Moles of }\mathrm{AgCl } (n_{\mathrm{AgCl}}) = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{8.61\text{ g}}{143.5\text{ g mol}^{-1}} = 0.06\text{ mol}

Step 5: Find the ratio of moles of complex reacted to moles of AgCl\mathrm{AgCl} formed Ratio=ncomplexnAgCl=0.020.06=13≈0.3333\text{Ratio} = \frac{n_{\text{complex}}}{n_{\mathrm{AgCl}}} = \frac{0.02}{0.06} = \frac{1}{3} \approx 0.3333

Expressing this ratio in the form x×10−2x \times 10^{-2}: Ratio=33.33×10−2\text{Ratio} = 33.33 \times 10^{-2}

Rounding off to the nearest integer gives 33.

Ratio of Moles of Complex Reacted and AgCl Formed | Chemistry PYQ Solution - JEE Challenger