Problem 73 - Chemistry: The Central Science in SI Units, Global Edition

Question

The molecule dimethylphosphinoethane \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{PCH}_{2} \mathrm{CH}_{2}\right.\) \(\mathrm{P}\left(\mathrm{CH}_{3}\right)_{2},\) which is abbreviated dmpe] is used as a ligand for some complexes that serve as catalysts. A complex that contains this ligand is \(\mathrm{Mo}(\mathrm{CO})_{4}(\) dmpe \()\). (a) Draw the Lewis structure for dmpe, and compare it with ethylenediamine as a coordinating ligand. (b) What is the oxidation state of Mo in \(\mathrm{Na}_{2}\left[\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}(\) dmpe \()\right] ?(\mathbf{c})\) Sketch the structure of the \(\left[\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}(\text { dmpe })\right]^{2-}\) ion, including all the possible isomers.

Step-by-Step Solution

Answer

(a) The Lewis structure of dmpe is (\(CH_3)_2PCH_2CH_2P(CH_3)_2\), with phosphorus (P) atoms as donor atoms. In ethylenediamine, nitrogen (N) atoms act as donors. Both ligands have a flexible carbon chain between donor atoms to fit various metal coordination sites. (b) The oxidation state of Mo in Na2[Mo(CN)2(CO)2(dmpe)] is +2. (c) There are two main isomers for the \([Mo(CN)_2(CO)_2(dmpe)]^{2-}\) ion: 1. Trans isomer: CN and CO ligands occupy opposite positions, while the P atoms of the dmpe ligand are cis to each other. 2. Cis isomer: CN and CO ligands are both in cis positions, and P atoms of dmpe are again in cis positions.

Step 1: (a) Drawing Lewis Structure of dmpe

First, draw the Lewis structure of dmpe: (\(CH_3)_2PCH_2CH_2P(CH_3)_2\). 1. Start with the central atoms: Two P atoms and two C atoms. 2. Attach the \(CH_2\) groups to the central P and C atoms, forming a P-C and a C-P single bond. 3. Attach the two \(CH_3\) groups to each P atom, forming single bonds. 4. Add non-bonding electron pairs to P atoms to complete their octets, while C and H atoms will have a complete octet by sharing the electrons in the bonds formed. Now that the Lewis structure is drawn, it can be compared with ethylenediamine. Ethylenediamine: \(H_2NCH_2CH_2NH_2\) Both dmpe and ethylenediamine have two donor atoms. In dmpe, the donor atoms are two P atoms, while in ethylenediamine, the donor atoms are two N atoms. Both ligands have a flexible chain of C atoms between the donor atoms, which can adjust their conformation to fit various metal coordination sites.

Step 2: (b) Calculating Oxidation State of Mo

To solve the problem, we need to determine the oxidation state of Mo in Na2[Mo(CN)2(CO)2(dmpe)]. Each Na ion contributes a +1 charge, so the complex ion has a net -2 charge. Let's denote the oxidation state of Mo as \(x\). Then, we can write the following equation: \[x \; - 2 \times 2 \; - 4 \times 1 + 0 = -2\] Here, -2 represents the charge contributed by each CN ligand, -4 represents the total charge contributed by CO ligands, and 0 is dmpe's charge as it is a neutral ligand. Solving for \(x\), we get \(x = 2\). Thus, the oxidation state of Mo in the given complex is +2.

Step 3: (c) Sketching Isomers of the Complex Ion

Now, we need to sketch the structure of the \([Mo(CN)_2(CO)_2(dmpe)]^{2-}\) ion, including all possible isomers. First, draw the central Mo atom surrounded by the attached ligands (two CN, two CO, and one dmpe). The isomers can vary depending on the positions of both CN and CO ligands. There are two main possibilities: 1. Isomer 1: Trans isomer (opposite positions) - Place CN and CO ligands at the opposite sites (trans) of the octahedral coordination sphere. - Attach dmpe ligand by coordinating the P atoms to the Mo atom, in a manner that P atoms are cis to each other. 2. Isomer 2: Cis isomer (adjacent positions) - Place both CN ligands in cis positions (next to each other in the same plane) and CO ligands in cis positions as well. - Attach dmpe ligand by coordinating the P atoms to the Mo atom, again with P atoms in cis positions. These two isomers differ in the relative arrangement of the ligands surrounding the Mo atom in the \([Mo(CN)_2(CO)_2(dmpe)]^{2-}\) ion.

Key Concepts

Ligand

A ligand is a molecule that binds to another, typically larger, molecule, often a metal ion, in coordination chemistry. Ligands can be a crucial part of forming coordination complexes. When ligands bind, they donate electron pairs to the metal center, stabilizing the complex and altering its chemical behavior.

Ligands can be classified in various ways:

• Monodentate: Ligands such as Cl⁻ or NH₃ that have only one donor atom and bind through just one end.
• Bidentate or Polydentate: Ligands like ethylenediamine (en) or dmpe, which can form two or more bonds with the metal center through multiple donor sites, providing added stability to the complex.

In the case of dimethylphosphinoethane (dmpe), it is a bidentate ligand because it uses its two phosphorus atoms to coordinate with the metal center. This characteristic helps make the metal complex it's involved with more stable.
When evaluating or predicting the behavior of a coordination complex, paying attention to the ligand's nature can help in understanding how the overall complex will interact with its environment.

Oxidation State

The oxidation state of a metal in a coordination complex is a hypothetical charge that the metal would have if all ligands and electron donations were removed. It is an important concept in coordination chemistry as it affects the reactivity, color, and magnetic properties of the complex.

To determine the oxidation state of a metal in a complex, such as Mo in \\(\mathrm{Na}_{2}\left[\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}(\text{dmpe})\right]\), we use the following steps:

• Identify the charges of known components: Na⁺ has a charge of +1, CN⁻ has a charge of -1, and CO and dmpe as neutral ligands contribute 0.
• Set up an equation where the sum of these charges equals the overall charge of the complex, which is -2 in this case.

The calculation yields an oxidation state of +2 for Mo. Knowing this state allows chemists to predict how the complex might react with other species or environmental conditions.

Isomerism

Isomerism is a phenomenon where compounds with the same chemical formula can exist in different structures or arrangements, leading to different properties. In coordination chemistry, isomers commonly arise due to the varied spatial arrangement of ligands around the central metal atom.

In the complex \\([\mathrm{Mo}(\mathrm{CN})_{2}(\mathrm{CO})_{2}(\text{dmpe})]^{2-}\), we can have several coordination isomers:

• Cis-trans isomers: Differ based on the positioning of certain ligands in the complex. For example, CN ligands can be adjacent (cis) or opposite (trans) to each other.
• For this specific complex, when ligands like CO and CN vary in their respective positions, such as being adjacent or opposite, they constitute different isomers.

Understanding isomerism is crucial in predicting the reactivity and interaction of the complex with other substances. Some isomers might interact more favorably with specific reactants, making them key players in certain reactions, especially catalytic ones.

Lewis Structure

Lewis structures provide a simplified representation of the bonding between atoms in a molecule. They show how electrons are distributed within a compound, using dots to signify lone pairs and lines for covalent bonds.

To draw a Lewis structure, like that of dmpe \\((CH_3)_2PCH_2CH_2P(CH_3)_2\), follow these steps:

• Identify the central atoms, such as the phosphorus atoms in dmpe.
• Determine how surrounding atoms, such as methyl (CH₃) groups, connect, ensuring each atom's electron requirements are met.
• Ensure each phosphorus atom completes its octet by counting shared and lone pairs of electrons.

Lewis structures are invaluable in predicting molecular geometry, reactivity, and explaining the comparison between different ligands, as seen with dmpe and ethylenediamine. This understanding guides us in foreseeing how these molecules might function when bonded to different metal centers in complex formation.