question_answer

The correct decreasing order of \[E_{{{M}^{3+}}/{{M}^{2+}}}^{\Theta }\] values for the following elements is

I. Co (Z = 27)

II. Mn (Z = 25)

III. Fe (Z = 26)

IV. Cr (Z = 24)

 

A) I > II > III > IV  

B) IV >III > II > I   

C) II > I > III > IV  

D) III >IV > I > II

Correct Answer: A

Solution :

[a]              values of the above element are:             I.             II.             III.             IV. Exceptional high positive , value cannot be explained satisfactorily by electronic configuration. \[Co\,(Z=27)=3{{d}^{7}}4{{s}^{2}};\]           \[C{{o}^{2+}}=3{{d}^{7}},\] \[C{{o}^{3+}}=3{{d}^{6}}\] \[C{{o}^{3+}}(3{{d}^{6}})+{{e}^{\Theta }}\xrightarrow{{}}C{{o}^{2+}}(3{{d}^{7}})\] The stabilities of \[{{d}^{6}}\] and \[{{d}^{7}}\] configuration cannot be compared. The extra stability of \[C{{o}^{2+}}({{d}^{7}})\] configuratior. and high positive \[{{E}^{\bigcirc -}}_{(C{{o}^{3+}}/C{{o}^{2+}})}\] value is related to the highest negative enthalpy of hydration \[({{\Delta }_{hyd}}.{{H}^{\Theta }})\]. In \[3d\]series, size of \[C{{o}^{3+}}\] ion is 61 pm, therefore charge density is very high. Hence have highest negative \[{{\Delta }_{hyd}}.{{H}^{\Theta }}\] value. The comparatively high positive value for \[{{E}^{\bigcirc -}}_{(M{{n}^{3+}}/M{{n}^{2+}})}=+1.57V,\] is due to very stable \[({{d}^{5}})\] configuration of \[M{{n}^{2+}}\]ion.             \[Mn(Z=25)=3{{d}^{5}}\,4{{s}^{2}},\]  \[M{{n}^{2+}}=3{{d}^{5}},\] \[M{{n}^{3+}}=3{{d}^{4}}\]             \[M{{n}^{3+}}(3{{d}^{4}})+{{e}^{\bigcirc -}}\underset{(Stable\,\,configuration)}{\mathop{\xrightarrow{{}}M{{n}^{2+}}(3{{d}^{5}})}}\,\] The comparatively low positive value for \[{{E}^{\bigcirc -}}_{(F{{e}^{3+}}/F{{e}^{2+}})}=+0.77V,\] is due to stable configuration of \[F{{e}^{3+}}(3{{d}^{5}})\] ion. \[Fe(Z=26)=3{{d}^{6}}4{{s}^{2}},\]     \[F{{e}^{2+}}=3{{d}^{6}},\] \[F{{e}^{3+}}=3{{d}^{5}}\] \[\underset{(Stable\,\,confiuration)}{\mathop{F{{e}^{3+}}(3{{d}^{6}})+{{e}^{\bigcirc -}}}}\,\xrightarrow{{}}F{{e}^{2+}}(3{{d}^{6}})\] Although from electronic configuration, reduction of \[F{{e}^{3+}}\] \[({{d}^{5}})\] to \[F{{e}^{2+}}\] \[({{d}^{6}})\] is not very favourable yet low positive \[{{E}_{red}}^{\bigcirc -}\] value favours the reduction of \[F{{e}^{3+}}\] to \[F{{e}^{2+}}\] ion to some extent Due to high charge density of \[F{{e}^{3+}}\] ion, high (negative) hydration enthalpy \[({{\Delta }_{hyd}}.{{H}^{\bigcirc -}})\] favours the reduction of \[F{{e}^{3+}}\]to \[F{{e}^{2+}}\] ion. The comparatively high negative \[{{E}^{\bigcirc -}}_{(C{{r}^{3+}}/C{{r}^{2+}})}=-0.41V,\] is due to more stable configuration of \[C{{r}^{3+}}\] ion having a half- filled \[{{t}^{3}}_{2g}\] level. \[\underset{\begin{smallmatrix}  (More\,\,stable\,\,{{t}^{3}}_{2g} \\  configuration) \end{smallmatrix}}{\mathop{C{{r}^{3+}}(3{{d}^{3}})+{{e}^{\bigcirc -}}}}\,\xrightarrow{{}}\underset{\begin{smallmatrix}  (Less\,\,stable \\  configuration) \end{smallmatrix}}{\mathop{C{{r}^{2+}}(3{{d}^{4}})}}\,\] So, the decreasing order of . \[{{E}^{\bigcirc -}}_{{{M}^{3+}}/{{M}^{2+}}}\] values are \[(I)>(II)>(III)>(IV)\]