Question

Bromine and fluorine react at temperatures higher than \(150^{\circ} \mathrm{C}\) to give a compound that is \(45.69 \%\) Br and \(54.31 \% \mathrm{F}\) (a) What is the empirical formula of the compound? (b) Assuming the molecular formula of the compound is the same as its empirical formula, suggest a structure for the molecule. What is the Br atom hybrid. ization in the molecule? (c) The molecule has a small dipole moment. Does this agree with your structural proposal in (b) above? Why or why not? If it does not agree, can you propose an alternative structure?

Short answer

(a) \( \text{BrF}_5 \) (b) Structure: square pyramidal; Hybridization: \( \text{sp}^3\text{d}^2 \) (c) Yes, agrees due to asymmetry causing dipole moment.

Step-by-step solution

Determine Empirical Formula

First, convert the percentages into grams, assuming you have 100 grams of the compound. This means you have 45.69 grams of Br and 54.31 grams of F. Next, convert the grams to moles:- Moles of Br: \( \frac{45.69}{79.9} = 0.572 \) moles- Moles of F: \( \frac{54.31}{19.0} = 2.859 \) molesFind the simplest whole number ratio:- Divide by the smallest number of moles: - Br: \( \frac{0.572}{0.572} = 1 \) - F: \( \frac{2.859}{0.572} = 5 \)Therefore, the empirical formula is \( \text{BrF}_5 \).

Suggest Molecular Structure and Hybridization

Assuming the molecular formula is the same as the empirical formula, the compound is \( \text{BrF}_5 \). In \( \text{BrF}_5 \), bromine is the central atom. The hybridization of Br in \( \text{BrF}_5 \) is \( \text{sp}^3\text{d}^2 \), which allows for the formation of a square pyramidal structure with one lone pair.

Analyze Dipole Moment and Structural Agreement

The structure of \( \text{BrF}_5 \) is square pyramidal, meaning it contains a lone pair of electrons that causes a non-symmetrical molecule. As a result, \( \text{BrF}_5 \) does have a small dipole moment, which is consistent with the structure provided. The asymmetrical shape, caused by the lone pair, does indeed result in a small dipole moment, thus agreeing with the suggested structure.

Key concepts

Bromine and Fluorine Reaction

When bromine and fluorine react at temperatures above 150°C, they form a compound with specific mass percentages of bromine and fluorine. In this reaction, bromine and fluorine atoms combine to form molecules. To determine the empirical formula of the compound formed, we analyze the percentages by converting them into moles. We then find the simplest whole number ratio of bromine to fluorine atoms, which is essential for determining the empirical formula. This approach allows chemists to understand the basic ratios of elements within the compound, thus deducing that the resulting compound from this reaction is BrF₅.

Molecule Hybridization

Molecule hybridization explains how atoms in a molecule, such as in bromine pentafluoride (BrF₅), form bonds with different atoms. In BrF₅, the central bromine atom undergoes hybridization, which is a process where atomic orbitals mix to form new hybrid orbitals. Specifically, bromine in BrF₅ exhibits sp³d² hybridization. This hybridization is key because it allows bromine to form five bonds with fluorine atoms, resulting in a particular geometric arrangement. The structure accommodates a lone pair, leading to a square pyramidal shape. The hybridization determines the spatial arrangement of the bonds and lone pairs, which affects the molecule’s shape and properties.

Dipole Moment Analysis

Dipole moment analysis is vital for understanding the polarity of a molecule. In the context of BrF₅, the molecular shape significantly influences its dipole moment. BrF₅, being square pyramidal due to the lone pair on bromine, is not completely symmetrical. This asymmetry causes the molecule to have a small dipole moment, resulting in a slight separation of charges within the molecule. - The lone pair influences the electron distribution, making one side of the molecule slightly negative compared to the other. - This results in a polar molecule, which can interact with other molecules through dipole-dipole interactions. Thus, the small dipole moment of BrF₅ agrees with the predicted square pyramidal structure, affirming the presence of polar characteristics in the molecule.

Molecular Structure Determination

Determining the molecular structure involves understanding both the geometric shape and bonding of the atoms within a molecule. For BrF₅, the structure can be determined through considerations like hybridization and dipole moment analysis. - Bromine pentafluoride adopts a square pyramidal shape due to sp³d² hybridization. - The presence of a lone pair on bromine leads to this distinctive shape. Considerations of molecular geometry and electronic distribution help clarify why BrF₅, despite being mostly symmetrical with respect to its bonded atoms, isn't fully nonpolar due to its lone pair. This leads to a better comprehension of how bonding and electron arrangement dictate the physical and chemical behaviors of such molecules.