Question

The two isomers $ X $ and $ Y $ with the formula $ Cr{{({{H}_{2}}O)}_{5}}ClB{{r}_{2}} $ were taken for experiment on depression in freezing point. It was found that one mole of $ X $ gave depression corresponding to $ 2 $ moles of particles and one mole of $ Y $ gave depression due to $ 3 $ moles of particles. The structural formulae of $ X $ and $ Y $ respectively are

• A. $ [Cr{{({{H}_{2}}O)}_{5}}Cl]B{{r}_{2}};[Cr{{({{H}_{2}}O)}_{4}}B{{r}_{2}}]Cl.{{H}_{2}}O $
• B. $ [Cr{{({{H}_{2}}O)}_{5}}Cl]B{{r}_{2}};[Cr{{({{H}_{2}}O)}_{3}}ClB{{r}_{2}}.2{{H}_{2}}O] $
• C. $ [Cr{{({{H}_{2}}O)}_{5}}Br]BrCl;[Cr{{({{H}_{2}}O)}_{4}}ClBr]Br.{{H}_{2}}O $
• D. $ [Cr{{({{H}_{2}}O)}_{5}}Cl]B{{r}_{2}};[Cr{{({{H}_{2}}O)}_{4}}ClBr]Br.{{H}_{2}}O $
• E. $ [Cr{{({{H}_{2}}O)}_{4}}B{{r}_{2}}]Cl.{{H}_{2}}O;[Cr{{({{H}_{2}}O)}_{5}}Cl]B{{r}_{2}} $

Answer 1

Answer: (E)

One mole of X gave depression corresponding to 2 moles of particles, ie., on ionization X gives 2 moles of ions, thus it contains only one ion outside the coordination sphere and its structural formula is
$ [Cr{{({{H}_{2}}O)}_{4}}B{{r}_{2}}]Cl.{{H}_{2}}O $
While Y gives 3 moles of ions, so it contains two ions outside the coordination sphere and its structural formula is $ [Cr{{({{H}_{2}}O)}_{5}}Cl]B{{r}_{2}} $
$ [Cr{{({{H}_{2}}O)}_{4}}B{{r}_{2}}]Cl.{{H}_{2}}O\xrightarrow[{}]{ionisation} $
$ \underbrace{{{[Cr{{({{H}_{2}}O)}_{4}}B{{r}_{2}}]}^{+}}+C{{l}^{-}}}_{2\,ions}+{{H}_{2}}O $
$[Cr{{({{H}_{2}}O)}_{5}}Cl]B{{r}_{2}}\xrightarrow{ionisation}\underbrace{{{[Cr{{({{H}_{2}}O)}_{5}}Cl]}^{2+}}+2B{{r}^{-}}}_{3\,ions} $