Consider the following statements for the self‐exchange electron transfer reaction in [Cr(H2O)6]2+/3+ a. σ* orbitals are only involved in electron transfer b. It involves large inner‐sphere reorganization energy c. It involves no change in M–L bond lengths d. Rate of self‐exchange electron transfer is fast The correct statements are
a and b
The question concerns the self-exchange electron transfer reaction between hexaaquachromium(II) and hexaaquachromium(III) ions:
\[ \text{[Cr(H}_2\text{O)}_6\text{]}^{2+} + \text{[Cr(H}_2\text{O)}_6\text{]}^{3+} \rightleftharpoons \text{[Cr(H}_2\text{O)}_6\text{]}^{3+} + \text{[Cr(H}_2\text{O)}_6\text{]}^{2+} \]To evaluate the given statements, let's first consider the electronic configurations of the metal ions in an octahedral aqueous environment:
- Chromium(II) (\(\text{Cr}^{2+}\), d\(^4\)): In a weak field (like water), it is high spin: \(\text{t}_{2\text{g}}^3 \text{e}_\text{g}^1\). The electron being transferred is the one in the \(\text{e}_\text{g}\) orbital.
- Chromium(III) (\(\text{Cr}^{3+}\), d\(^3\)): In a weak field, it is high spin: \(\text{t}_{2\text{g}}^3 \text{e}_\text{g}^0\). The \(\text{e}_\text{g}\) orbital is empty and accepts the electron.
Now, let's analyze each statement:
Orbital Involvement in Electron Transfer
Statement a: "σ* orbitals are only involved in electron transfer".
The \(\text{e}_\text{g}\) orbitals in an octahedral complex are antibonding ($\sigma^*$) combinations of metal d orbitals and ligand $\sigma$ orbitals. Since the electron transfer in this reaction involves the movement of an electron from the \(\text{e}_\text{g}\) orbital of \(\text{Cr}^{2+}\) to the \(\text{e}_\text{g}\) orbital of \(\text{Cr}^{3+}\), and the \(\text{e}_\text{g}\) orbitals are $\sigma^*$ in character, $\sigma^*$ orbitals are directly involved in the transfer process. This statement is considered correct.
Inner-Sphere Reorganization Energy
Statement b: "It involves large inner-sphere reorganization energy".
Inner-sphere reorganization energy is the energy required to distort the geometry of the reactants and products to match the geometry of the transition state. The key difference between \(\text{Cr}^{2+}\) (\(\text{e}_\text{g}^1\)) and \(\text{Cr}^{3+}\) (\(\text{e}_\text{g}^0\)) lies in the occupation of the antibonding \(\text{e}_\text{g}\) orbitals. The presence of an electron in an antibonding orbital (\(\text{e}_\text{g}\) in \(\text{Cr}^{2+}\)) weakens and lengthens the metal-ligand bonds compared to when the orbital is empty (\(\text{e}_\text{g}\) in \(\text{Cr}^{3+}\)). The difference in $\text{Cr-O}$ bond lengths is significant (approximately 2.0-2.1 Å for \(\text{Cr}^{3+}\) and 2.4-2.5 Å for \(\text{Cr}^{2+}\)). This substantial structural difference between the reactant and product requires a significant amount of energy (reorganization energy) to reach the transition state configuration. Therefore, the inner-sphere reorganization energy is large. This statement is correct.
Metal-Ligand Bond Lengths
Statement c: "It involves no change in M–L bond lengths".
This statement is incorrect. As explained above, the \(\text{Cr}^{2+}-\text{O}\) bond lengths are considerably longer than the \(\text{Cr}^{3+}-\text{O}\) bond lengths due to the occupation of the antibonding \(\text{e}_\text{g}\) orbital in \(\text{Cr}^{2+}\). The electron transfer process involves a transition between these two different geometries, hence there is a significant change in metal-ligand bond lengths.
Rate of Self-Exchange Electron Transfer
Statement d: "Rate of self-exchange electron transfer is fast".
The rate of electron transfer is related to the reorganization energy. A large reorganization energy creates a higher activation barrier, resulting in a slower reaction rate. Because the [Cr(H2O)6]2+/3+ self-exchange reaction has a large inner-sphere reorganization energy, its rate is known to be quite slow compared to other redox systems with smaller geometric changes. This statement is incorrect.
Based on the analysis, the correct statements are a and b.
Important Questions from Electron Transfer Reactions
In 3‐iron ferredoxins, the number of sulfide bridges and cysteinyl ligands, respectively, are:
The second order rate constants for the outer sphere self- exchange electron transfer reactions for [Ru(NH3)6]2+/[Ru(NH3)6]3+ and [Co(NH3)6]2+/[Co(NH3)6]3+ are 9.2 × 102 M-1 sec-1 and ≤ 10-9 M-1 sec-1, respectively.
The correct rationale for the above data is
In the following electron transfer reactions, the one in which the bridging ligand comes from the reductant is
Of the following assertions regarding the mechanism of electron transfer,
A. An outer-sphere mechanism involves electron transfer from the reductant to the oxidant, with the coordination shells or spheres of each staying intact.
B. In the inner-sphere mechanism, the reductant and oxidant share a ligand in their inner or primary coordination sphere which assists in electrons being transferred.
C. In the inner-sphere mechanism, an oxidant possesses at least one ligand capable of binding simultaneously to two metal ions.
D. In the inner-sphere mechanism, ligands of reductant are substitutionally inert.
The correct statements are
- The water exchange rates for the complex ions follow the order
