Question

A You have isolated a solid organometallic compound containing manganese, some number of CO ligands, and one or more \(\mathrm{CH}_{3}\) ligands. To find the molecular formula of the compound, you burn \(0.225 \mathrm{g}\) of the solid in oxygen and isolate \(0.283 \mathrm{g}\) of \(\mathrm{CO}_{2}\) and \(0.0290 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) The molar mass of the compound is \(210 \mathrm{g} / \mathrm{mol}\). Suggest a plausible formula and structure for the molecule. (Make sure it satisfies the EAN rule. The \(\mathrm{CH}_{3}\) group can be thought of as a \(\mathrm{CH}_{3}^{-}\) ion, a two-electron donor ligand.)

Short answer

The suggested formula is \( \text{Mn}(\text{CO})_4(\text{CH}_3)_2 \).

Step-by-step solution

Calculate Moles of CO2 and H2O

The molar mass of CO2 is 44.01 g/mol, and the molar mass of H2O is 18.02 g/mol.Calculate the moles of CO2: \[ \text{Moles of } \mathrm{CO}_2 = \frac{0.283 \, \text{g}}{44.01 \, \text{g/mol}} \approx 0.00643 \, \text{mol} \]Calculate the moles of H2O: \[ \text{Moles of } \mathrm{H}_2\mathrm{O} = \frac{0.0290 \, \text{g}}{18.02 \, \text{g/mol}} \approx 0.00161 \, \text{mol} \]

Calculate Moles of Carbon and Hydrogen

From the moles of CO2, determine the moles of carbon, and from the moles of H2O, determine the moles of hydrogen.- Each mole of CO2 contains 1 mole of C, so moles of C: \[ \text{Moles of C} = 0.00643 \, \text{mol} \]- Each mole of H2O contains 2 moles of H, so moles of H: \[ \text{Moles of H} = 0.00161 \, \text{mol} \times 2 = 0.00322 \, \text{mol} \]

Calculate the Mass of Carbon and Hydrogen

Using the atomic masses (C = 12.01 g/mol, H = 1.01 g/mol), calculate the mass of carbon and hydrogen.- Mass of Carbon: \[ \text{Mass of C} = 0.00643 \, \text{mol} \times 12.01 \, \text{g/mol} = 0.0772 \, \text{g} \]- Mass of Hydrogen: \[ \text{Mass of H} = 0.00322 \, \text{mol} \times 1.01 \, \text{g/mol} = 0.00325 \, \text{g} \]

Calculate Mass of Oxygen in the Compound

Knowing the initial mass of the compound and the mass of carbon and hydrogen, find the mass of oxygen.- Total mass accounted for is mass of C + mass of H: \[ 0.0772 \, \text{g} + 0.00325 \, \text{g} = 0.08045 \, \text{g} \]- Mass of oxygen: \[ 0.225 \, \text{g} - 0.08045 \, \text{g} = 0.14455 \, \text{g} \]

Determine Moles of Oxygen

Using the molar mass of oxygen (O = 16.00 g/mol), calculate the moles of oxygen.- Moles of oxygen: \[ \text{Moles of O} = \frac{0.14455 \, \text{g}}{16.00 \, \text{g/mol}} = 0.00903 \, \text{mol} \]

Suggest Molecular Formula

The total structure should balance the EAN rule (Effective Atomic Number rule), Mn provides 7 electrons, CO contributes 2 each, CH3 contributes 2, and determine based on known masses and moles:Let's propose a formula: \( \mathrm{Mn}(\mathrm{CO})_4(\mathrm{CH}_3)_2 \)- Molar mass calculation: Mn (54.94 g/mol) + 4 CO (176.04 g/mol) + 2 CH3 (30.06 g/mol) = 210 g/mol- EAN: Mn (7) + 4 CO (8) + 2 CH3 (4) = 18 (which satisfies 18-electron rule for transition metals).

Verify Structure Satisfying EAN Rule

The structure with Mn surrounded by 4 CO ligands and 2 CH3 makes the Mn center 18-electron compliant, stabilizing it as per the EAN rule.

Key concepts

EAN rule

The Effective Atomic Number (EAN) rule is a fundamental guideline in organometallic chemistry. It helps predict the stability of metal complexes. According to this rule, the central metal atom in a coordination compound tends to achieve the electron configuration of the nearest noble gas through bonding.
This often means the complex is most stable when the total number of electrons around the central metal equals 18. This electron count is similar to the filled electron shell configuration of noble gases, which is highly stable.
In our exercise, manganese ( Mn ) acts as the central metal atom. When it is bonded with ligands like carbonyl ( CO ) and methyl ( CH_3 ), each ligand donates electrons to the central metal, helping it reach the EAN target of 18 electrons. For manganese, which has 7 valence electrons in this context, we add 8 electrons from 4 carbonyl groups (2 electrons each) and 4 electrons from 2 methyl groups (2 electrons each), totaling 18 electrons.

molecular formula

The process of determining the molecular formula involves analyzing the composition and structure of a compound. For organometallic compounds, this includes accounting for the central metal, ligands, and their interactions.
In the problem, the molecular formula is determined by balancing the observed data from the burning experiment. This includes the precise mass of each element and the molar mass of the compound. Using these details, we propose a plausible formula for the compound.

• Manganese (Mn) contributes its atomic mass and electron count.
• Carbonyl groups ( CO ) and methyl groups ( CH_3 ) provide additional atoms and electrons.

The calculated formula, Mn(CO)_4(CH_3)_2 , uses the total mass, in this case 210 g/mol, matching the experimental data and satisfies the EAN rule. Each element and ligand role is crucial to ensure the formula accounts for all masses and achieves stability.

transition metals

Transition metals are a group of elements characterized by their ability to form various oxidation states and complex compounds. Found in the d-block of the periodic table, they are known for their rich chemistry and applications in areas like catalysis and materials.
Manganese, the central metal in our exercise, is a transition metal. It exemplifies typical characteristics of transition metals:

• The ability to interact with multiple ligands and form stable coordination complexes.
• A variable oxidation state that accommodates electron donation from different ligands.

These properties allow manganese to bond with different ligands like carbonyl ( CO ) and methyl ( CH_3 ) groups. This flexibility is crucial for the formation of stable organometallic compounds that obey the EAN rule, which is a testament to its widely varied chemistry.

organometallic compound analysis

Analyzing organometallic compounds involves understanding both their molecular composition and their structural geometry. This analysis includes determining how metals and organic groups such as carbonyl and methyl align and interact.
For the given exercise, observing the products of combustion is a key method of analysis. When the compound burns, the masses of resulting CO_2 and H_2O provide insights into the carbon and hydrogen content of the compound. In addition, assessing analysis techniques like mass and nuclear magnetic resonance (NMR) spectroscopy can offer more clues on structure and composition.
Analyzing organometallic compounds like Mn(CO)_4(CH_3)_2 demands a deep understanding of coordination chemistry to explain properties developed by metal-ligand interactions. It involves calculation, prediction, and empirical data collection to ensure the formula accurately reflects the structure and behavior of the compound.