Q102P - Chemistry: Molecular Nature Of Matter And Change

Question

Rank the following in order of increasing $\mathbf{∆}$ and energy of light absorbed: ${\mathbf{\left[}\mathbf{Cr}{\left({\mathrm{NH}}_3\right)}_{\mathbf{6}}\mathbf{\right]}}^{\mathbf{3}\mathbf{+}}\mathbf{,}{\mathbf{\left[}\mathbf{Cr}{\left(H_{2}O\right)}_{\mathbf{6}}\mathbf{\right]}}^{\mathbf{3}\mathbf{+}}\mathbf{,}{\mathbf{\left[}\mathbf{Cr}{\left({\mathrm{NO}}_2\right)}_{\mathbf{6}}\mathbf{\right]}}^{\mathbf{3}\mathbf{+}}$

Step-by-Step Solution

Answer

The final answer in increasing order is: ${\left[\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{3+}<{\left[\mathrm{Cr}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}<{\left[\mathrm{Cr}{\left({\mathrm{NO}}_2\right)}_6\right]}^{3+}$

Step 1: Given Information

Given compounds are:

${\left[\mathrm{Cr}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+},{\left[\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{3+},{\left[\mathrm{Cr}{\left({\mathrm{NO}}_2\right)}_6\right]}^{3+}$

Step 2: Concept Introduction

The stronger field the ligand is, the bigger the energy of light absorbed. Spectrochemical series (from weak-field to strong-field ligands): 

${\mathbf{I}}^{\mathbf{-}}\mathbf{<}{\mathbf{Cl}}^{\mathbf{-}}\mathbf{<}{\mathbf{F}}^{\mathbf{-}}\mathbf{<}{\mathbf{OH}}^{\mathbf{-}}\mathbf{<}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{<}{\mathbf{SCN}}^{\mathbf{-}}\mathbf{<}{\mathbf{NH}}_{\mathbf{3}}\mathbf{<}\mathbf{en}\mathbf{<}{\mathbf{NO}}_{\mathbf{2}}^{\mathbf{-}}\mathbf{<}{\mathbf{CN}}^{\mathbf{-}}\mathbf{<}\mathbf{CO}$

Step 3: Solution

We can now quickly formulate the answer to this problem using the spectrochemical series and the information above:

${\left[\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{3+}<{\left[\mathrm{Cr}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}<{\left[\mathrm{Cr}{\left({\mathrm{NO}}_2\right)}_6\right]}^{3+}$