Question

The complex \(\left[\mathrm{Ru}(\mathrm{EDTA})\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{-}\) undergoes substitution reactions with several ligands, replacing the water molecule with the ligand. \(\left[\mathrm{Ru}(\mathrm{EDTA})\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{-}+\mathrm{L} \longrightarrow[\mathrm{Ru}(\mathrm{EDTA}) \mathrm{L}]^{-}+\mathrm{H}_{2} \mathrm{O}\) The rate constants for several ligands are as follows: $$ \begin{array}{ll} \hline \text { Ligand, } \mathrm{L} & k\left(M^{-1} s^{-1}\right) \\ \hline \text { Pyridine } & 6.3 \times 10^{3} \\ \text { SCN }^{-} & 2.7 \times 10^{2} \\ \mathrm{CH}_{3} \mathrm{CN} & 3.0 \times 10 \\ \hline \end{array} $$ (a) One possible mechanism for this substitution reaction is that the water molecule dissociates from the complex in the rate-determining step, and then the ligand \(\mathrm{L}\) fills the void in a rapid second step. A second possible mechanism is that \(L\) approaches the complex, begins to form a new bond to the metal, and displaces the water molecule, all in a single concerted step. Which of these two mechanisms is more consistent with the data? Explain. (b) What do the results suggest about the relative basicities of the three ligands toward Ru(III)? (c) Assuming that the complexes are all low spin, how many unpaired electrons are in each?

Short answer

The associative mechanism is more consistent with the given rate constants as they vary significantly with different ligands: Pyridine > SCN⁻ > CH₃CN, indicating that ligand substitution reactions are faster for more basic ligands. Assuming low spin complexes, there will be one unpaired electron in each Ru(III) complex, as the 5 d-electrons will occupy the t₂g orbitals first in octahedral complexes.

Step-by-step solution

Examine the Rate Constants

The given rate constants for the ligand substitution reactions with the different ligands are: Pyridine: \(6.3 \times 10^{3} \mathrm{ M^{-1} s^{-1}}\) \(\mathrm{SCN^{-}:}\) \(2.7 \times 10^{2} \mathrm{ M^{-1} s^{-1}}\) \(\mathrm{CH_3CN:}\) \(3.0 \times 10 \mathrm{ M^{-1} s^{-1}}\) We are evaluating two possible mechanisms: 1. Dissociative mechanism: The water molecule dissociates first, and then the ligand \(\mathrm{L}\) fills the void in a rapid second step. 2. Associative mechanism: \(\mathrm{L}\) approaches the complex, forms a new bond to the metal, and displaces the water molecule all in a single concerted step.

Determining the Mechanism

The given rate constants indicate that ligands compete with one another for binding to the metal center. If the mechanism was dissociative, rate constants would not depend heavily on the ligands competing for binding. On the other hand, if the mechanism is associative, we would expect a greater dependence on ligand properties since the reaction occurs via a concerted step involving the ligand/catalyst complex. In this case, the rate constants vary by orders of magnitude when different ligands are used, which is more consistent with the associative mechanism than with the dissociative mechanism. Therefore, we can conclude that the associative mechanism is more consistent with the given rates. #(b) Relative Basicities of Ligands#

Comparison of Basicities

The given rate constants indicate that the ligand substitution reactions are faster for the more basic ligands: - Pyridine: \(6.3 \times 10^{3} \mathrm{ M^{-1} s^{-1}}\) - \(\mathrm{SCN^{-}:}\) \(2.7 \times 10^{2} \mathrm{ M^{-1} s^{-1}}\) - \(\mathrm{CH_3CN:}\) \(3.0 \times 10 \mathrm{ M^{-1} s^{-1}}\) Considering the faster reaction rate for more basic ligands, we can deduce the relative basicities as follows: Pyridine > \(\mathrm{SCN^{-}}\) > \(\mathrm{CH_3CN}.\) #(c) Unpaired Electrons in the Complexes#

Determine Unpaired Electrons

Assuming low spin complexes for each ligand substitution reaction, note that the complexes formed will be \(\mathrm{Ru(III)}\) complexes with the general form: \(\left[\mathrm{Ru}(\mathrm{EDTA})\left(\mathrm{L}\right)\right]^{-}\). The \(\mathrm{Ru(III)}\) ion has 5 d-electrons, and in a low spin complex, the electrons will be paired in the d orbitals available, minimizing the number of unpaired electrons. In this case, since the complexes are octahedral, the five electrons will occupy the t\(_{2g}\) orbitals first. Therefore, there will be one unpaired electron in the last t\(_{2g}\) orbital for all the \(\mathrm{Ru(III)}\) complexes. So, the number of unpaired electrons in each complex is: 1.

Key concepts

Mechanisms of Ligand Substitution

In ligand substitution reactions, there are two prominent mechanisms that describe how ligands replace one another in a metal complex.
The first is the **dissociative mechanism**, where a ligand, such as a water molecule, leaves the metal center before a new ligand binds. This creates an intermediate state where the metal is unsaturated, and only then does the new ligand attach.
The second is the **associative mechanism**, in which an incoming ligand approaches the metal complex, begins forming a bond, and simultaneously displaces the old ligand, such as water, in a single concerted step. This mechanism suggests the reaction proceeds directly and in one step with no intermediate formation.

The rate of ligand substitution can often help differentiate between these two mechanisms. When significant changes in rate constants are observed with different ligands, as seen in the original exercise, this behavior aligns more with an associative mechanism, implying that ligand properties significantly influence the reaction.

Reaction Rate Constants

Reaction rate constants provide insight into how fast a chemical reaction proceeds and are denoted in units such as \( M^{-1} s^{-1} \), indicating molar change per second.
In ligand substitution reactions, these constants tell us how rapidly ligands are replaced within a complex. They can vary greatly depending on the nature of the incoming ligands.
For instance, in the given example, pyridine has a high rate constant of \(6.3 \times 10^{3}\), meaning it effectively competes for the binding site on the metal. In comparison, SCN ions and acetonitrile, with lower rate constants, react more slowly.

The variation in these constants highlights that the substitution mechanism is likely associative, as it depends heavily on ligand identity and properties. Faster constants often suggest a more favorable interaction between the new ligand and the metal center, facilitating quicker replacements.

Basicity of Ligands

Basicity refers to a substance's ability to accept protons; in the context of ligand substitution, it indicates a ligand's capacity to donate electrons to a metal center.

• Pyridine, with the highest reaction rate, is also the most basic, efficiently donating electrons to the metal.
• SCN^- follows, and though less basic than pyridine, it is still more effective than CH₃CN.
• Finally, CH₃CN is the least basic, as reflected by its lower reaction rate.

The pattern observed in the step-by-step solution clearly suggests that the speed of substitution correlates with ligand basicity. Thus, the ability of the ligand to donate electron density plays a crucial role in the rate of substitution, with more basic ligands typically facilitating faster reactions.

Unpaired Electrons

Unpaired electrons in a complex relate to the magnetism and electronic configuration of a metal center.
In the case of the Ru(III) ( ext{d}^{5}) ion, it's pivotal to consider its low-spin state to understand its electronic configuration.
In low-spin octahedral complexes, electrons fill the t_2g orbitals first, minimizing electron repulsion and leaving fewer electrons unpaired. For Ru(III) with five d-electrons, four will fill these lower energy orbitals, and one electron will remain unpaired.

This single unpaired electron means such complexes possess a paramagnetic character, which plays a role in their reactivity and the energy required to facilitate the substitution reactions discussed earlier. Understanding how these unpaired electrons affect the properties of the complex is crucial when predicting the behavior of transition metal complexes in reactions.

Transition Metal Complexes

Transition metal complexes are entities where transition metals bond with various ligands, forming coordination compounds with distinctive properties and structures.
These metals, like Ru(III) in our example, often have partially filled d-orbitals, which provide the flexibility for diverse bonding and coordination patterns.
Transition metals can accommodate various ligands, leading to different coordination geometries, electronic configurations, and magnetic properties.

The stability and reactivity of these complexes make them paramount in industrial applications and biological systems. Their ability to undergo ligand substitution reactions provides insight into their dynamic chemistry, allowing for innovative developments in catalysis, medicine, and material science. Understanding their behavior, especially concerning electron configurations and ligand interactions, expands our ability to manipulate these complexes for various applications.