Question

A palladium complex formed from a solution containing bromide ion and pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\) (a good electronpair donor), is found on elemental analysis to contain \(37.6 \%\) bromine, \(28.3 \%\) carbon, \(6.60 \%\) nitrogen, and \(2.37 \%\) hydrogen by mass. The compound is slightly soluble in several organic solvents; its solutions in water or alcohol do not conduct electricity. It is found experimentally to have a zero dipole moment. Write the chemical formula, and indicate its probable structure.

Short answer

The chemical formula of the palladium complex is \(PdBr(C_5H_5N)\), and its probable structure has a square-planar geometry with the bromide ligand opposite to the pyridine nitrogen atom. This structure results in a nonpolar compound with a zero dipole moment.

Step-by-step solution

Find the number of moles of each element present in the compound

To find the number of moles of each element in the compound, we can assume a sample of 100g and convert percentages to grams. Then we can use the molar mass of each element to calculate the number of moles. \(Br: \frac{37.6 g}{79.9 g \cdot mol^{-1}} \approx 0.471 mol\) \(C: \frac{28.3 g}{12.01 g \cdot mol^{-1}} \approx 2.36 mol\) \(N: \frac{6.60 g}{14.01 g \cdot mol^{-1}} \approx 0.471 mol\) \(H: \frac{2.37 g}{1.007 g \cdot mol^{-1}} \approx 2.36 mol\) Note that these mole numbers are in a near 1:5 ratio to each other (C:H, and Br:N), suggesting that the palladium complex could have a formula like PdBrCNH.

Determine the empirical formula of the complex

Since the number of N atoms is equal to the number of Br atoms, we can assume the empirical formula of the complex is: \(PdBr(C_5H_5N)\) Now we can move to propose its molecular structure.

Examine the given properties of the compound

The compound is slightly soluble in organic solvents and does not conduct electricity when dissolved in water or alcohol. As a rule of thumb, a solute's solubility depends on how similar it is to the solvent it interacts with. The compound's solubility in organic solvents would indicate that it may have some nonpolar characteristics. Since the compound does not conduct electricity, it is likely a molecular compound with covalent bonds rather than an ionic compound. The compound also has a zero dipole moment, which indicates that the compound should have a symmetric structure.

Propose the molecular structure of the palladium complex

Consider the empirical formula of the complex, \(PdBr(C_5H_5N)\), and the fact that pyridine is an electron-pair donor. The pyridine is likely bound to the palladium as a ligand through the nitrogen atom. The symmetry in the molecule can be achieved by having the bromide ligand located opposite to the nitrogen donor of the pyridine ligand on the palladium. Therefore, we can propose that the molecular structure of this palladium complex is a four-coordinate square-planar geometry with the bromide ligand opposite to the pyridine nitrogen atom. This structure would make the compound nonpolar and justify the zero dipole moment property observed. Ultimately, the chemical formula and probable structure of the palladium complex are \(PdBr(C_5H_5N)\) and a square-planar geometry, respectively.

Key concepts

Coordination Chemistry

Coordination chemistry is a branch of chemistry focused on the structure and function of compounds formed between metals and ligands. A ligand is essentially an ion or molecule that can donate a pair of electrons to a metal, creating a complex. In our case, pyridine (\[\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}\]) acts as a ligand due to the nitrogen atom, which has a lone pair of electrons. This compound specifically forms a coordination complex with palladium.

• Coordination Number: This refers to the number of ligand binding sites around the central metal; here, palladium forms four bonds due to its four-coordinate square-planar arrangement.
• Ligands: Ligands like pyridine contribute to the stabilization of the complex and can influence its overall properties.

Coordination compounds are incredibly important in various fields of science, from catalysis to biological systems.

Empirical Formula Determination

Determining the empirical formula of a compound involves identifying the simplest ratio of the different types of atoms in the molecule. To illustrate, in the exercise, the compound's elemental analysis gives us percentages of bromine, carbon, nitrogen, and hydrogen. By assuming a sample of 100g, we convert these percentages into grams, and then calculate the moles of each element using their atomic masses. Steps include:

• Finding moles of each element: Use ratios and atomic masses to determine relative moles.
• Dividing by the smallest number of moles: This gives the smallest integer ratio of the elements involved.
• Understanding the relationship between elements: Helps inform the structure and properties of the compound.

The empirical formula gives a straightforward representation of the elements present in a compound and their ratios but does not provide structural information.

Molecular Structure Analysis

Understanding a compound's molecular structure involves looking at how the atoms are arranged relative to one another. Here, the palladium complex with pyridine and bromide must be examined carefully to predict its structure.

• Electron Donor Interactions: The nitrogen in pyridine acts as a ligand and binds to palladium via electron-pair donation.
• Symmetry Considerations: Due to its zero dipole moment, the structure is likely symmetric, with pyridine nitrogen and bromide located opposite each other in a square-planar arrangement.

This analysis is critical in understanding not only the basic geometry of a compound but also its reactivity and interaction with other molecules.

Square-Planar Geometry

Square-planar geometry is a common structure for palladium complexes, characterized by four ligands surrounding a central metal atom in the same plane. This geometry is significant for several reasons:

• Stereochemistry: The arrangement of ligands around palladium in a flat, square plane ensures maximum bonding efficiency and stability.
• Non-ionic Nature: A square-planar arrangement tends towards covalency rather than ionic bonding, which fits with the non-conductive nature of the complex in water.
• Symmetrical Structure: The perfect 90-degree angles between ligands in the square-planar geometry lead to a nonpolar compound, indicating symmetry and no net dipole moment, as observed in the exercise.

Understanding square-planar geometry is crucial for comprehending the nonpolar and stable nature of certain coordination compounds.

Nonpolar Compounds

Nonpolar compounds are characterized by a lack of significant dipole moments due to symmetrical structure or equivalent charge distribution. The palladium complex in the exercise exemplifies this, as it showcases important aspects of nonpolarity:

• Zero Dipole Moment: None of the charges in the molecule create a net positive or negative area, validating the nonpolar characterization.
• Solubility Characteristics: Nonpolar compounds typically dissolve in nonpolar solvents due to similar interactions—which matches the compound’s observed solubility in organic solvents.
• Square-Planar Influence: As the geometry leads to uniform charge distribution and no net polarity, this underpins the nonpolar nature of the palladium complex.

Understanding nonpolar compounds is essential, as it affects solubility, chemical reactivity, and even the biological interactions of many molecules.