Question

Rank the following in order of decreasing$(∆)$and energy of light absorbed:${\left[\mathrm{Cr}{\left(\mathrm{en}\right)}_3\right]}^{\mathbf{3}\mathbf{+}}\mathbf{,}{\left[\mathrm{Cr}{\left(\mathrm{CN}\right)}_6\right]}^{\mathbf{3}\mathbf{-}}\mathbf{,}{\left[{\mathrm{CrCl}}_6\right]}^{\mathbf{3}\mathbf{-}}$

Short answer

The final answer in decreasing order is${\left[\mathrm{Cr}{\left(\mathrm{CN}\right)}_6\right]}^{3-}>{\left[\mathrm{Cr}{\left(\mathrm{en}\right)}_3\right]}^{3+}>{\left[{\mathrm{CrCl}}_6\right]}^{3-}$

Step-by-step solution

Given Information 

Given compounds are

$$\begin{gathered} {\left[\mathrm{Cr}{\left(\mathrm{en}\right)}_3\right]}^{3+} \\ {\left[\mathrm{Cr}{\left(\mathrm{CN}\right)}_6\right]}^{3-} \\ {\left[{\mathrm{CrCl}}_6\right]}^{3-} \end{gathered}$$

Concept Introduction

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

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

Solution

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

${\left[\mathrm{Cr}{\left(\mathrm{CN}\right)}_6\right]}^{3-}>{\left[\mathrm{Cr}{\left(\mathrm{en}\right)}_3\right]}^{3+}>{\left[{\mathrm{CrCl}}_6\right]}^{3-}$