`A,B` and `C` are three complexes of chromium(III) with the empirical formula `H_(12)O_(6)C_(13)Cr` All the three complexes not react with concentrated `H_(2)SO_(4)` whereas complexes `B` and `C` lose `6.75%` and `13.5%` of their original mass respectively, on treatment on treatment with conectrated `H_(2)SO_(4)` Identify `A,B` and `C` .

Explanation

The data suggests that the complexes are hydrate isomers. As the complex A does not lose any molecle of `H_(2)O` on heating with conc. `H_(2)SO_(4)` this means that no molecules of `H_(2)O` are Outside the co-ordinate sphere. The structure of the complex A is : `[CrH_(2)O_(6)]Cl_(3)`
As B loses `67.5%`of weight on heating with conc. `H_(2)SO_(4)` , therefore actual loss in weight.
= 6.75 / 100 `xx` 266.5 = 18 amu
This means that the isomer B has one molecule of `H_(2)` existing as monohdrate . [B] : `[Cr(H_(2)O)_(5)Cl]Cl_(2).H_(2)O` .
As C loses 13.5% of weight on heating which is twice the loss in the first case, this shows that the isomer C exists as a dihydrate. [C] : `[CrH_(2)O_(4)Cl_(2)]Cl.2H_(2)O`.