Problem 101 - Chemistry: The Central Science

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. In all cases, the ruthenium stays in the \(+3\) oxidation state and the ligands use a nitrogen donor atom to bind to the metal. $$ \left[\operatorname{Ru}(\mathrm{EDTA})\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{-}+\mathrm{L} \longrightarrow[\operatorname{Ru}(\mathrm{EDTA}) \mathrm{L}]^{-}+\mathrm{H}_{2} \mathrm{O} $$ The rate constants for several ligands are as follows: (a) One possible mechanism for this substitution reaction is that the water molecule dissociates from the Ru(III) in the rate-determining step, and then the ligand L binds to Ru(III) in a rapid second step. A second possible mechanism is that L approaches the complex, begins to form a new bond to the Ru(III), 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 donor ability of the nitrogens of the three ligands toward Ru(TII))? (c) Assuming that the complexes are all low spin, how many unpaired electrons are in each?

Step-by-Step Solution

Answer

The data is more consistent with Mechanism 2, where L approaches the complex, begins to form a new bond to Ru(III), and displaces the water molecule in a single concerted step. The relative donor ability of the nitrogen atoms towards Ru(III) is Pyridine > SCN > CH3CN. Assuming all complexes are low spin, each complex has 2 unpaired electrons.

Step 1: Compare the two mechanisms with the given data

In this step, we will look at the rate constants for different ligands and determine which of the two given mechanisms is more consistent with the data. Mechanism 1 suggests that the rate-determining step is the dissociation of the water molecule, followed by a rapid second step where the ligand L binds to Ru(III). In this case, the rate of the reaction should be independent of the nature of the ligand. Mechanism 2 suggests a single concerted step where L approaches the complex, begins to form a new bond to Ru(III), and displaces the water molecule. In this case, the rate of the reaction would be influenced by the nature of the ligand. Given the rate constants: - Pyridine: \(k = 6.3 \times 10^3 M^{-1}s^{-1}\) - SCN: \(k = 2.7 \times 10^2 M^{-1}s^{-1}\) - CH3CN: \(k = 3.0 \times 10 M^{-1}s^{-1}\) The rate constants for different ligands are not the same, which means the nature of the ligands influences the reaction rate. Therefore, the data is more consistent with Mechanism 2.

Step 2: Relative donor ability of nitrogen atoms towards Ru(III)

To analyze the relative donor ability, we can look at the rate constants. A higher rate constant indicates faster binding of the ligand to Ru(III) and stronger donor ability. From the given data, the order of donor ability is: Pyridine > SCN > CH3CN

Step 3: Calculating the number of unpaired electrons in each complex

Since all complexes are assumed to be low spin, we can calculate the number of unpaired electrons based on the oxidation state of Ru(III). Ru(III) has an electron configuration of [Kr] 4d^5. Since the complexes are low spin, three of the five electrons in the 4d subshell will pair up, leaving two unpaired electrons. Therefore, each complex has 2 unpaired electrons.

Key Concepts

Ligand Substitution

Ligand substitution in coordination chemistry involves replacing one ligand in a metal complex with another. In the context of the given exercise, we are dealing with the substitution of a water molecule by different nitrogen-donor ligands in the complex \[ \left[ \text{Ru} (\text{EDTA})(\text{H}_2 \text{O}) \right]^− \].

Here's how the process works:

• The water molecule (\(\text{H}_2\text{O}\)) that is initially bound to the ruthenium ion in the complex is displaced by a new ligand (\(\text{L}\)).
• Different ligands can replace the water molecule depending on their ability to donate electrons to the metal center.
• The nature and strength of the binding depend on the characteristics of the ligand involved in the substitution.

This process requires an understanding of the metal's electron configuration and how they accommodate different ligands.

Rate Determining Step

The rate-determining step in a chemical reaction is the slowest step that limits the overall rate of reaction. In the given exercise, two mechanisms are hypothesized for the ligand substitution reaction.

• The first mechanism involves an initial step where the water molecule dissociates from the \(\text{Ru}(\text{III})\), which is followed by a rapid binding of the ligand (\(\text{L}\)). If this were the rate-determining step, the reaction rate would not significantly vary with different ligands.
• In the second proposed mechanism, the ligand approaches the complex and displaces the water molecule in a concerted fashion. Since this process occurs in one step, the reaction rate would depend greatly on the identity of the ligand.

Given that the rate constants for different ligands differ, with pyridine having the highest rate constant, the second mechanism is deemed more consistent with the observed data.

Oxidation State

In coordination complexes, the oxidation state of the metal is key to understanding its chemistry and interactions with ligands. For the complex discussed in the exercise, ruthenium remains in the \(+3\) oxidation state throughout the substitution reactions.

• An oxidation state of \(+3\) indicates that ruthenium has lost three electrons in forming the complex, which generally leads to a \([\text{Kr}] 4d^5\) electronic configuration.
• Maintaining the same oxidation state in different ligand complexes implies that the nature of the ligands does not change the electron count on ruthenium.
• Understanding this oxidation state helps predict the Lewis acidity and potential reactivity of the complex.

Thus, the intact oxidation state assures that the substitution reactions are permutations of ligands around the same central metal ion.

Electron Configuration

Electron configuration provides a map of how electrons are distributed around the nucleus of a metal ion in a complex. For the ruthenium ion in our example, which is in a \(+3\) oxidation state, the electron configuration is \([\text{Kr}] 4d^5\).

• The notation \([\text{Kr}]\) indicates that electrons in the lower energy, inner-shell, have the same arrangement as krypton.
• The presence of five electrons in the \(4d\) subshell reflects partial filling, which typically implicates a degree of electron pairing, especially in low spin configurations.
• Since the complexes are assumed to be low spin, three of the five \(4d\) electrons pair up, leaving two unpaired electrons.

Understanding the electron configuration is essential in predicting the magnetic properties and the chemical behavior of the complexes.